Please try another GMATPrep question in the thumbnail

GMATPrep Question:
Please try the question in the attachment.

imo:
1. D
2. D

Just a query..
In Q1. What if z = 0.
In this case (nk)^z > 0, does not yield any additional data about the sign of k.

If the answer is D as you have mentioned, 0 is considered and integer divisible by 2!!
Is that right??

From1. x/y=(27/^1/3 Suff
From2. x/y=(9/4)^1/2=3/2, -3/2

Hence A

got it. for question 2. I ignored the -ve root.

Pretty good ones.... :)


1.If n and k are integers and (-2)n^5 > 0, is k^37 < 0?

(1). (nk)^z > 0, where z is an integer that is not divisible by two
(2). k < n

A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

n is negative.
From 1. k will also be negative and Z will an odd number, -ve power raise to odd power is also negative. SO suff.
From2. K negative so suff.

Hence D

2. If x and y are integers, what is the ratio of 2x to y?
(1). 8x^3 = 27y^3
(2) 4x^2 = 9y^2

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

From1. x/y=(27/^1/3 Suff
From2. x/y=(9/4)^1/2=3/2, -3/2

Hence A

Just a query..
In Q1. What if z = 0.
In this case (nk)^z > 0, does not yield any additional data about the sign of k.

If the answer is D as you have mentioned, 0 is considered and integer divisible by 2!!
Is that right??

ANSWERS!!

1. D
2. A !!

pretty good ones.... :)


1.if n and k are integers and (-2)n^5 > 0, is k^37 < 0?

(1). (nk)^z > 0, where z is an integer that is not divisible by two
(2). K < n

a)statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B) statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C) both statements together are sufficient, but neither statement alone is sufficient.
D) each statement alone is sufficient.
E) statement (1) and (2) together are not sufficient to answer the question asked, and additional data are needed.

2. If x and y are integers, what is the ratio of 2x to y?
(1). 8x^3 = 27y^3
(2) 4x^2 = 9y^2

a) statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B) statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C) both statements together are sufficient, but neither statement alone is sufficient.
D) each statement alone is sufficient.
E) statement (1) and (2) together are not sufficient to answer the question asked, and additional data are needed.

imo:
1. D
2. D

Pretty good ones.... :)


1.If n and k are integers and (-2)n^5 > 0, is k^37 < 0?

(1). (nk)^z > 0, where z is an integer that is not divisible by two
(2). k < n

A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

2. If x and y are integers, what is the ratio of 2x to y?
(1). 8x^3 = 27y^3
(2) 4x^2 = 9y^2

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

ANSWERS!!

1. D
2. A !!

1) d
2) a

pretty good ones.... :)
1.if n and k are integers and (-2)n^5 > 0, is k^37 < 0?
(1). (nk)^z > 0, where z is an integer that is not divisible by two
(2). K < n

a)statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B) statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C) both statements together are sufficient, but neither statement alone is sufficient.
D) each statement alone is sufficient.
E) statement (1) and (2) together are not sufficient to answer the question asked, and additional data are needed.

2. If x and y are integers, what is the ratio of 2x to y?
(1). 8x^3 = 27y^3
(2) 4x^2 = 9y^2

a) statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B) statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C) both statements together are sufficient, but neither statement alone is sufficient.
D) each statement alone is sufficient.
E) statement (1) and (2) together are not sufficient to answer the question asked, and additional data are needed.

My cents
1. D
2. A

Pretty good ones.... :)


1.If n and k are integers and (-2)n^5 > 0, is k^37 < 0?

(1). (nk)^z > 0, where z is an integer that is not divisible by two
(2). k < n

A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

2. If x and y are integers, what is the ratio of 2x to y?
(1). 8x^3 = 27y^3
(2) 4x^2 = 9y^2

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Q. The integers m and p are such that 2

1 ?

1. the greatest common factor of m and p is 2

2. the least common multiple of m and p is 30

IMO...
Facts:
1. p & m are integers greater than 2.
2. m is not factor of p
3. p = K*m + r (r != 0 and integer K > 0)


Now,
1. If GCF of p and m is 2, it implies that both are even numbers. Since m is not a factor of p, r will at the least be 2. (can be more)

So 1 alone is sufficient.

2. LCM of m and p is 30
We can have (1,30) (2,15) (3,10) and (5,6). Out of these combinations (1,30) is eliminated since both m & p > 2
In all other three cases, the remainder (r) is exactly 1 and hence we can answer the question.

So 2 alone is also sufficient.

But both together cannot be used, since according to 1 both are even integers and according to 2, we get odd-even combination.

So either one on it own is sufficient!!

Pretty good ones.... :)


1.If n and k are integers and (-2)n^5 > 0, is k^37 < 0?

(1). (nk)^z > 0, where z is an integer that is not divisible by two
(2). k < n

A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

2. If x and y are integers, what is the ratio of 2x to y?
(1). 8x^3 = 27y^3
(2) 4x^2 = 9y^2

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Yes it is. Lol. Horrible silly mistake dat was. Oops! Neway Thanks a ton.

If u see that question clearly, it was mentioned that 5apples n 2bananas cost Rs.12. Hence, no .of apples and no. of bananas are 5 n 2 respectively. The price of apple can be Rs. 1.80 and banana can be Rs. 1.50.
5*1.80 + 2*1.50 = 9+3 = 12
I hope my explanation is clear to u

Yes it is. Lol. Horrible silly mistake dat was. Oops! Neway Thanks a ton.

It is not mandatory that x and y are only integers unless it is explicitly mentioned.

I have a doubt in this particular kind of question.

What is the price of 3 apples and 4 bananas?
Statement 1. 5 apples and 2 bananas cost Rs.12
Statement 2. 8 bananas and 6 apples cost Rs. 20.

Solution: Statement 2 alone can answer the question and not statement 1.

My argument is, if you look at statement 1, it can be written in the form of,

5x + 2y = 12 where x,y are positive integers.
So, there is only one possible solution set i.e. x = 2, y = 1

Hence, isn't statement 1 enough to answer the question? So wont the solution be "can be answered by either statements".
Can someone please explain as to why my argument is not valid?

1)x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x 3) an odd number?
a)the sum of any prime factor of x and x is even
b)3x is an even number

The expression will not be odd if any of the three expression is even.
from 1-if x is even number, sum will be even or odd/ x is odd, sum will be-even or odd/x is prime, sum will always be even. So cant say
from2-x is even, so the expression will be-
odd*odd*odd=odd
So B

2)If w, x, y, and z are the digits of the four-digit number N, a positive integer, what is the remainder when N is divided by 9?
a)w + x + y + z = 13
b)N + 5 is divisible by 9

From 1- Remider would be 4
From2- Number would be 9*K-5., reminder would be 5.
So D

3)x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7^x-1 - 5^x?
a)z < 25 and w = 7^x
b)x = 4

x is a +ive I.
when x=1, expression would be w-z>5*-4=-20
when x=2,expression would be w-z>5*-18=-90
so the w-z would be -ive always for all x.
May be Not able to understand the question.


4)If z = x^n - 19, is z divisible by 9?
a)x = 10; n is a positive integer
b)z + 981 is a multiple of 9

From 1, 10^n-19=(9+1)^n-9*2-1=9*(xyz......)-always divisible, Suff.
From2, Z will also be a multiple of 9
So D

5)If b is prime and the symbol # represents one of the following operations: addition, subtraction, multiplication, or division, is the value of b # 2 even or odd?
a) (b # 1) # 2 = 5
b) 4 # b = 3 # (1 # b) and b is even

Thanks.
pH

From 1, B has to be 2 and # is a + symbol, so Suff
From2, B is 2 as B is mentioned even as well as prime, so Suff
So D

Ankit your assumption for Q3 is correct and you get everything right. Sorry for confusing. The OAs:
1)B
2)D
3)A
4)D
5)D

Thanks and feel free to give feedback on the questions. Like them or not?

1)x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x - 3) an odd number?
a)the sum of any prime factor of x and x is even
b)3x is an even number

2)If w, x, y, and z are the digits of the four-digit number N, a positive integer, what is the remainder when N is divided by 9?
a)w + x + y + z = 13
b)N + 5 is divisible by 9

3)x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7^x-1 - 5^x?
a)z < 25 and w = 7^x
b)x = 4

4)If z = x^n - 19, is z divisible by 9?
a)x = 10; n is a positive integer
b)z + 981 is a multiple of 9

5)If b is prime and the symbol # represents one of the following operations: addition, subtraction, multiplication, or division, is the value of b # 2 even or odd?
a) (b # 1) # 2 = 5
b) 4 # b = 3 # (1 # b) and b is even

Thanks.
pH

1)x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x - 3) an odd number?
a)the sum of any prime factor of x and x is even
b)3x is an even number


Soln :
from a) X can be {primes > 2, Odd-composites, Even composites with prime factor only 2}.
Hence for primes > 2 expression is even. For odd composites expression is even. For Even composites with prime factor only 2 expression is odd. Hence insufficient.
From b) 3x = even => x is even. Answer Odd. Trying 4 and 6.
(64+19837)(16+5)(1) = odd*odd*odd=odd.
(216+19837)(36+5)(3)= odd*odd*odd = odd. Hence holds. Sufficient.
Answer choice B


2)If w, x, y, and z are the digits of the four-digit number N, a positive integer, what is the remainder when N is divided by 9?
a)w + x + y + z = 13
b)N + 5 is divisible by 9
Soln:
From a) We get no much info as there can be multiple combinations.
From b) If N+5 divided by 9 = remainder 0. Then N+5-5=N will leave remainder 9-5=4 when divided by 9. Hence sufficient.
Try N=67. N+5=72 is divisible by 9. When N/9 remainder = 4. N=76. N+5=81. 76/9 remainder = 4.
Asnwer B.
Got this wrong. @ankitgarg20 can you explain how you arrived at D? Even after checking the answer I am not convinced. Let me know the problem with the reasoning. A million dollar question is why do we need the digits to find the remainder.




3)x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7^x-1 - 5^x?
a)z < 25 and w = 7^x
b)x = 4
Stem : x = Int. x > 0. Is w-z > 5(7x-1 - 5x).
From a) is w-z = 73-24 > 5(72-53). +ve > -ve. True. 7^4-23> 5(7^3- 5^4). The RHS turns out to be -ve and LHS +ve. Hence this always holds. Sufficient.

From b). No info about w and Z hence insufficient.
Answer choice A






4)If z = x^n - 19, is z divisible by 9?
a)x = 10; n is a positive integer
b)z + 981 is a multiple of 9


From a alone. z = x^n - 19 is always divisible by 9. Check for n=1,2,3. Sufficient.
From b alone. Since 981 = 9*109. Hence z+981 = z+9*109 = 9*K. For K to be an integer. Z should be divisible by 9. Answer Yes. Hence sufficient.
Answer choice D



5)If b is prime and the symbol # represents one of the following operations: addition, subtraction, multiplication, or division, is the value of b # 2 even or odd?
a) (b # 1) # 2 = 5
b) 4 # b = 3 # (1 # b) and b is even
From a) The only prime number b that satisfies this is 2 and # = +. 2+1+2=5. Hence B+2 = even. Sufficient.
From b) Since B is even(from stmt) and prime(stem) b=2. And 4+2=3+1+2=6. Hence # = +. B+2=even. Sufficient.

Answer choice D

3)x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7^x-1 - 5^x?
a)z < 25 and w = 7^x
b)x = 4

Thanks.
pH

noob_doc Says

hey ankit i arrived at similar conclusions for questions 1,2,4 and 5 but i dint get the third one .....would u mind explaining?

The answer to Q 3 depends on what exactly the expression is. I have given two answers depending on what the expression would be.

If PH can post the correct expression and OA, I can explain it clearly. I hope that wont be a problem.

So here is my explanation of A being the right answer.

Given: x is integer. x raised to an Odd number gives us >0. This means x>0.

Stem: Is w-z> 5(7^(x-1)-5^x) ?

1. z<25 and w=7^x

Substituting the value of w in question stem, we get.

Is 7^x - z > 5.7^(x-1) - 5^(x+1) ?

Solving,

Is 2.7^(x-1) + 5^(x+1) > z ?

Now, we are given that x>0, thus min possible value of x =1

Substitute x=1

Is 27> z ?

We are given that z<25 and thus the answer is yes. SUFFICIENT.



2. x=4

Even if we substitute this value in the question stem, we have no clue about w and z. Thus Insufficient.


Hence the answer A.

Ankit your assumption for Q3 is correct and you get everything right. Sorry for confusing. The OAs:
1)B
2)D
3)A
4)D
5)D

Thanks and feel free to give feedback on the questions. Like them or not?

The questions were fine. At least they were not weirdly absurd/difficult. Will edit this post in a while to post the explanation for Q3 as requested by a fellow puy.

My answers would be:

1. B
2. D
3. E
4. D
5. D

The explanations are too long to post for wrong answers. Please post the OAs and I will post the explanations to my correct attempts.

For Q3, I have taken the expression as 7^x - 1 - 5^x

If it is 7^(x-1)- 5^x, the answer should be A.

Ankit your assumption for Q3 is correct and you get everything right. Sorry for confusing. The OAs:
1)B
2)D
3)A
4)D
5)D

Thanks and feel free to give feedback on the questions. Like them or not?

1) If the base of triangle PQR is 5, what is the perimeter of the triangle?

(1) The area of triangle PQR is 12.5
(2) The length of a side of triangle PQR is

2) If m and q are divisors of c, is mq a divisor of c that is not c or 1?


(1) mq < c
(2) m and q have no common divisors.

3) Group A, which is a set of numbers, has an average (arithmetic mean) of 8 while group B, a different set of numbers, has an average of 10. In which group is the sum of the numbers greater?

(1) The average of all numbers in both groups combined is .
(2) The sum of all numbers in both groups is 52

4) If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 56.
(2) y = 168

5) If c and k are distinct positive integers, is c divisible by k?

(1) 2k > c
(2) k2 + k = c

The OA s are
1) E 2) C 3) A 4) C 5) D

3)x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7^x-1 - 5^x?
a)z < 25 and w = 7^x
b)x = 4

Thanks.
pH

My answers would be:

3. E

For Q3, I have taken the expression as 7^x - 1 - 5^x

If it is 7^(x-1)- 5^x, the answer should be A.

noob_doc Says

hey ankit i arrived at similar conclusions for questions 1,2,4 and 5 but i dint get the third one .....would u mind explaining?

The answer to Q 3 depends on what exactly the expression is. I have given two answers depending on what the expression would be.

If PH can post the correct expression and OA, I can explain it clearly. I hope that wont be a problem.

hey ankit i arrived at similar conclusions for questions 1,2,4 and 5 but i dint get the third one .....would u mind explaining?

My answers would be:

1. B
2. D
3. E
4. D
5. D

The explanations are too long to post for wrong answers. Please post the OAs and I will post the explanations to my correct attempts.

For Q3, I have taken the expression as 7^x - 1 - 5^x

If it is 7^(x-1)- 5^x, the answer should be A.

1)x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x - 3) an odd number?
a)the sum of any prime factor of x and x is even
b)3x is an even number

2)If w, x, y, and z are the digits of the four-digit number N, a positive integer, what is the remainder when N is divided by 9?
a)w + x + y + z = 13
b)N + 5 is divisible by 9

3)x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7^x-1 - 5^x?
a)z < 25 and w = 7^x
b)x = 4

4)If z = x^n - 19, is z divisible by 9?
a)x = 10; n is a positive integer
b)z + 981 is a multiple of 9

5)If b is prime and the symbol # represents one of the following operations: addition, subtraction, multiplication, or division, is the value of b # 2 even or odd?
a) (b # 1) # 2 = 5
b) 4 # b = 3 # (1 # b) and b is even

Thanks.
pH

1)x is a positive integer greater than two; is (x^3 + 19837)(x^2 + 5)(x 3) an odd number?
a)the sum of any prime factor of x and x is even
b)3x is an even number

2)If w, x, y, and z are the digits of the four-digit number N, a positive integer, what is the remainder when N is divided by 9?
a)w + x + y + z = 13
b)N + 5 is divisible by 9

3)x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7^x-1 - 5^x?
a)z < 25 and w = 7^x
b)x = 4

4)If z = x^n - 19, is z divisible by 9?
a)x = 10; n is a positive integer
b)z + 981 is a multiple of 9

5)If b is prime and the symbol # represents one of the following operations: addition, subtraction, multiplication, or division, is the value of b # 2 even or odd?
a) (b # 1) # 2 = 5
b) 4 # b = 3 # (1 # b) and b is even

Thanks.
pH

Akshay, you are making us sound as though we are the teachers of this thread. :). There are many GMAT related threads, one for each type of section in GMAT. You should be able to locate them easily.

Look forward for some really cruel GMAT level posts from you.

- ph

@above 2 post's
GW and PH , I have just started my GMAT preps, I'll be a regular to this thread today onwards are there any more forums for GMAT?

Thanks a lot.
Akshay

These are real quality questions and would be a fight to do within 2 mins each. VPITC, where are you getting these from?

Gail, lets keep discussing. I learn a lot from you all.

Thank you.
Hemanth

I have been hearing from everyone now-a-days that the QA section is getting tougher by the day. Obviously because of us "IT" fellas. I think quality questions are exactly what we need here. Although I am sure that the GMAT will not go out of its league to come-up with Algebra intensive stuff but they will definitely throw tricky questions in which we will usually miss a case or two as I did in these questions.
More....more....more....

These are real quality questions and would be a fight to do within 2 mins each. VPITC, where are you getting these from?

Gail, lets keep discussing. I learn a lot from you all.

Thank you.
Hemanth

Replies in ladies color MAGENTA.
I like the discussion Gail. Feel free to disagree

thank you,
Hemanth

Originally Posted by Gail.Wynand
Originally Posted by Gail.Wynand
1) If the base of triangle PQR is 5, what is the perimeter of the triangle?

(1) The area of triangle PQR is 12.5
(2) The length of a side of triangle PQR is

Lets say base = c = 5. We need the other 2 sides for perimeter.
from (1). area= 12.5 = sqrt(s(s-a)(s-b)(s-c)) where s = (a+b+5)/2..so one eqn 2 variables. not sufficient.
from (2). b=. and c=5 ; again do we Know a? No. Not sufficient.
combining: 12.5 = 12.5 = sqrt(s(s-a)(s-)(s-5)) and s= (a+5+)/2...so one variable, one eqn. Hence sufficient.

So choice C.

I agree.
With 1, we can get the height to be 5 but that doesn't tell us how the other sides are set up. Insufficient.
With 2, We know the other side but don't about the 3rd Side. Insufficinet.
1+2 - It is a right triangle with sides 5,5,5*2^0.5. Sufficient.

-----------------------------------------------------------------

2) If m and q are divisors of c, is mq a divisor of c that is not c or 1?

(1) mq < c
(2) m and q have no common divisors.

Soln:
Lets use plug-in numbers:
mq is a divisor of c that is not c or 1....
C = 28, m = 2, q=7 or m=4, q=7 or m=4, q=2 and so on...
from (1): since mqYes you are correct. It was highly dumb on my part not to simplify the equation. And the 2nd one also seems correct.
------------------------------------------------------------------

4) If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 56.
(2) y = 168

from Stem: prime factors of 840 = 2,2,2,5,3,7.
from (1) : Tells us that max 56 is common in both. prime factors of 56 = 2,2,2,7. hence x= 56*A and Y=56*B where A, B are co-prime. Insufficient.
from (2) : prime factors (y) = 2,2,2,3,7. So X can be anything 3 or less 2s, 1 or less 3s, 1 or less 7s and a 5. hence possible options are 5, 10, 15, 35...So Insufficient.
Combining (1) and (2) : y = 168 and x=56*5 or 56*3*5 hence insufficient.

Answer choice E

I disagree. The answer should be C.
Cond1: Given GCF=56. 840 = 7*8*5*3. Also each of x,y<=840. for the LCM to be 840 x,y should not have any common multiple before 840. Also the given condition is that no common factor after 56. So the possible values of (x,y) are 56*3 and 56*5. We cannot exactly tell what x is is it 56*5 or 56*3?. Insufficient. Good question. So there can actually be two sets of X and Y whose GCD can be 56. they are (56*3,56*5) or (56*1, 56*15). Agree? Else the GCD will not be 56 given that the LCM is 840.
Cond2: y=168 (or 56*3). now x can be 56*5 (280) or 56*15 (840) or ..any other value where LCM=840. Insufficient.
But then combine both of them. Cond2 tells us that Y is 56*3. and if the GCD has to be 56 then X cannot be 56*15 (else the GCD would have been 56*3 not 56). So X has to be 56*5. So now given that one of the numbers is 56*3 the other number,i.e. X has to be 56*5 otherwise the GCD will not be 56.
There is this other vague formula for positive integers which is GCD(x,y)*LCM(x,y) = X*Y. Using that too we can solve for X which comes to be 56*5. But you can do it without remembering that formula.

- You got this one too. I must have been drinking

------------------------------------------------------------------
5) If c and k are distinct positive integers, is c divisible by k?

(1) 2k > c
(2) k2 + k = c

from (1) : Since both are +ve. c/k<2. so the only choice is c/k lies b/w 0 and 2...can be anything that is a non integer or 1. Insufficient.
from (2) : k(k+1)= c hence c/k = k+1 = Integer. Hence c is divisible by K. Sufficient.

Answer choice B

I disagree again. Answer is D.

From 1 you can be certain that it is not divisible since C and K are distinct. Hence it is actually sufficient. That exception is taken care of in the question which reads "DISTINCT POSITIVE INTEGERS" implying that C/K is not 1. Agree?

- Ohh boy!!! I am so careless. You got it buddy.

Of course, Condition 2 is also sufficient.
------------------------------------------------------------------

I'll try to be more careful in the future.

My comments inline in Eco - Green...

Originally Posted by Gail.Wynand
1) If the base of triangle PQR is 5, what is the perimeter of the triangle?

(1) The area of triangle PQR is 12.5
(2) The length of a side of triangle PQR is

Lets say base = c = 5. We need the other 2 sides for perimeter.
from (1). area= 12.5 = sqrt(s(s-a)(s-b)(s-c)) where s = (a+b+5)/2..so one eqn 2 variables. not sufficient.
from (2). b=. and c=5 ; again do we Know a? No. Not sufficient.
combining: 12.5 = 12.5 = sqrt(s(s-a)(s-)(s-5)) and s= (a+5+)/2...so one variable, one eqn. Hence sufficient.

So choice C.

I agree.
With 1, we can get the height to be 5 but that doesn't tell us how the other sides are set up. Insufficient.
With 2, We know the other side but don't about the 3rd Side. Insufficinet.
1+2 - It is a right triangle with sides 5,5,5*2^0.5. Sufficient.

-----------------------------------------------------------------

2) If m and q are divisors of c, is mq a divisor of c that is not c or 1?

(1) mq < c
(2) m and q have no common divisors.

Soln:
Lets use plug-in numbers:
mq is a divisor of c that is not c or 1....
C = 28, m = 2, q=7 or m=4, q=7 or m=4, q=2 and so on...
from (1): since mqYes you are correct. It was highly dumb on my part not to simplify the equation. And the 2nd one also seems correct.
------------------------------------------------------------------

4) If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 56.
(2) y = 168

from Stem: prime factors of 840 = 2,2,2,5,3,7.
from (1) : Tells us that max 56 is common in both. prime factors of 56 = 2,2,2,7. hence x= 56*A and Y=56*B where A, B are co-prime. Insufficient.
from (2) : prime factors (y) = 2,2,2,3,7. So X can be anything 3 or less 2s, 1 or less 3s, 1 or less 7s and a 5. hence possible options are 5, 10, 15, 35...So Insufficient.
Combining (1) and (2) : y = 168 and x=56*5 or 56*3*5 hence insufficient.

Answer choice E

I disagree. The answer should be C.
Cond1: Given GCF=56. 840 = 7*8*5*3. Also each of x,y<=840. for the LCM to be 840 x,y should not have any common multiple before 840. Also the given condition is that no common factor after 56. So the possible values of (x,y) are 56*3 and 56*5. We cannot exactly tell what x is is it 56*5 or 56*3?. Insufficient. Good question. So there can actually be two sets of X and Y whose GCD can be 56. they are (56*3,56*5) or (56*1, 56*15). Agree? Else the GCD will not be 56 given that the LCM is 840.
Cond2: y=168 (or 56*3). now x can be 56*5 (280) or 56*15 (840) or ..any other value where LCM=840. Insufficient.
But then combine both of them. Cond2 tells us that Y is 56*3. and if the GCD has to be 56 then X cannot be 56*15 (else the GCD would have been 56*3 not 56). So X has to be 56*5. So now given that one of the numbers is 56*3 the other number,i.e. X has to be 56*5 otherwise the GCD will not be 56.
There is this other vague formula for positive integers which is GCD(x,y)*LCM(x,y) = X*Y. Using that too we can solve for X which comes to be 56*5. But you can do it without remembering that formula.

------------------------------------------------------------------
5) If c and k are distinct positive integers, is c divisible by k?

(1) 2k > c
(2) k2 + k = c

from (1) : Since both are +ve. c/k<2. so the only choice is c/k lies b/w 0 and 2...can be anything that is a non integer or 1. Insufficient.
from (2) : k(k+1)= c hence c/k = k+1 = Integer. Hence c is divisible by K. Sufficient.

Answer choice B

I disagree again. Answer is D.

From 1 you can be certain that it is not divisible since C and K are distinct. Hence it is actually sufficient. That exception is taken care of in the question which reads "DISTINCT POSITIVE INTEGERS" implying that C/K is not 1. Agree?

Of course, Condition 2 is also sufficient.
------------------------------------------------------------------

My comments inline in blue...

Replies in ladies color MAGENTA.
I like the discussion Gail. Feel free to disagree

thank you,
Hemanth

Gail, I differ from your answers on a few of these. Let me know if I got anything wrong.

Thank you,
Hemanth

Originally Posted by Gail.Wynand
1) If the base of triangle PQR is 5, what is the perimeter of the triangle?

(1) The area of triangle PQR is 12.5
(2) The length of a side of triangle PQR is

Lets say base = c = 5. We need the other 2 sides for perimeter.
from (1). area= 12.5 = sqrt(s(s-a)(s-b)(s-c)) where s = (a+b+5)/2..so one eqn 2 variables. not sufficient.
from (2). b=. and c=5 ; again do we Know a? No. Not sufficient.
combining: 12.5 = 12.5 = sqrt(s(s-a)(s-)(s-5)) and s= (a+5+)/2...so one variable, one eqn. Hence sufficient.

So choice C.

I agree.
With 1, we can get the height to be 5 but that doesn't tell us how the other sides are set up. Insufficient.
With 2, We know the other side but don't about the 3rd Side. Insufficinet.
1+2 - It is a right triangle with sides 5,5,5*2^0.5. Sufficient.

-----------------------------------------------------------------

2) If m and q are divisors of c, is mq a divisor of c that is not c or 1?

(1) mq < c
(2) m and q have no common divisors.

Soln:
Lets use plug-in numbers:
mq is a divisor of c that is not c or 1....
C = 28, m = 2, q=7 or m=4, q=7 or m=4, q=2 and so on...
from (1): since mqYes you are correct. It was highly dumb on my part not to simplify the equation. And the 2nd one also seems correct.
------------------------------------------------------------------

4) If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 56.
(2) y = 168

from Stem: prime factors of 840 = 2,2,2,5,3,7.
from (1) : Tells us that max 56 is common in both. prime factors of 56 = 2,2,2,7. hence x= 56*A and Y=56*B where A, B are co-prime. Insufficient.
from (2) : prime factors (y) = 2,2,2,3,7. So X can be anything 3 or less 2s, 1 or less 3s, 1 or less 7s and a 5. hence possible options are 5, 10, 15, 35...So Insufficient.
Combining (1) and (2) : y = 168 and x=56*5 or 56*3*5 hence insufficient.

Answer choice E

I disagree. The answer should be C.
Cond1: Given GCF=56. 840 = 7*8*5*3. Also each of x,y<=840. for the LCM to be 840 x,y should not have any common multiple before 840. Also the given condition is that no common factor after 56. So the possible values of (x,y) are 56*3 and 56*5. We cannot exactly tell what x is is it 56*5 or 56*3?. Insufficient.
Cond2: y=168 (or 56*3). now x can be 56*5 (280) or 56*15 (840) or ..any other value where LCM=840. Insufficient.
But then combine both of them. Cond2 tells us that Y is 56*3. and if the GCD has to be 56 then X cannot be 56*15 (else the GCD would have been 56*3 not 56). So X has to be 56*5.

------------------------------------------------------------------
5) If c and k are distinct positive integers, is c divisible by k?

(1) 2k > c
(2) k2 + k = c

from (1) : Since both are +ve. c/k<2. so the only choice is c/k lies b/w 0 and 2...can be anything that is a non integer or 1. Insufficient.
from (2) : k(k+1)= c hence c/k = k+1 = Integer. Hence c is divisible by K. Sufficient.

Answer choice B

I disagree again. Answer is D.

From 1 you can be certain that it is not divisible since C and K are distinct. Hence it is actually sufficient.

Of course, Condition 2 is also sufficient.
------------------------------------------------------------------

My comments inline in blue...

1) If the base of triangle PQR is 5, what is the perimeter of the triangle?

(1) The area of triangle PQR is 12.5
(2) The length of a side of triangle PQR is

Lets say base = c = 5. We need the other 2 sides for perimeter.
from (1). area= 12.5 = sqrt(s(s-a)(s-b)(s-c)) where s = (a+b+5)/2..so one eqn 2 variables. not sufficient.
from (2). b=. and c=5 ; again do we Know a? No. Not sufficient.
combining: 12.5 = 12.5 = sqrt(s(s-a)(s-)(s-5)) and s= (a+5+)/2...so one variable, one eqn. Hence sufficient.

So choice C.
I agree.
With 1, we can get the height to be 5 but that doesn't tell us how the other sides are set up. Insufficient.
With 2, We know the other side but don't about the 3rd Side. Insufficinet.
1+2 - It is a right triangle with sides 5,5,5*2^0.5. Sufficient.

-----------------------------------------------------------------

2) If m and q are divisors of c, is mq a divisor of c that is not c or 1?

(1) mq < c
(2) m and q have no common divisors.

Soln:
Lets use plug-in numbers:
mq is a divisor of c that is not c or 1....
C = 28, m = 2, q=7 or m=4, q=7 or m=4, q=2 and so on...
from (1): since mqm and q have no common divisors; we can choose m = 2, q=7 or m=4, q=7. does mq divide c in both cases? Yes. hence sufficient.

hence Answer is choice B.
Agree. Well done. I didn't get this one right actually.
------------------------------------------------------------------

3) Group A, which is a set of numbers, has an average (arithmetic mean) of 8 while group B, a different set of numbers, has an average of 10. In which group is the sum of the numbers greater?

(1) The average of all numbers in both groups combined is .
(2) The sum of all numbers in both groups is 52

Soln:
Lets say grp A has x numbers and grp B has y numbers.
Sum of numbers in grp A = 8x
Sum of numbers in grp B = 10y.
We have to find which is greater 8x or 10y?
from (1): (8x+10y)/(x+y) = 8.66..can not find 8x and 10y or any reln b/w them. Not sufficient.
from (2): 8x+10y=52 ...again....can not find 8x and 10y or any reln b/w them. Not sufficient.
combining (1) and (2):52/(x+y) = 8.66...again can not find 8x and 10y or any reln b/w them. Not sufficient.

Answer choice E
I disagree. D is the right answer. You can solve by either of these.
Cond1: Sufficient. As solving the equation we get X/Y=2/1. We know that there are twice the number of elements in A as in B. Lets say if Y=1, then sum of B = 10 and sum A = 16. So for any value of Y, sum of elements in A is always going to be greater than in B.
Cond2: The sum is 8X+10Y = 52 where X and Y are positive integers. The only condition where this will hold true is for X=4 and Y=2. In which case You know that the of each set and hence sufficiency.
------------------------------------------------------------------

4) If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 56.
(2) y = 168

from Stem: prime factors of 840 = 2,2,2,5,3,7.
from (1) : Tells us that max 56 is common in both. prime factors of 56 = 2,2,2,7. hence x= 56*A and Y=56*B where A, B are co-prime. Insufficient.
from (2) : prime factors (y) = 2,2,2,3,7. So X can be anything 3 or less 2s, 1 or less 3s, 1 or less 7s and a 5. hence possible options are 5, 10, 15, 35...So Insufficient.
Combining (1) and (2) : y = 168 and x=56*5 or 56*3*5 hence insufficient.

Answer choice E
I disagree. The answer should be C.
Cond1: Given GCF=56. 840 = 7*8*5*3. Also each of x,y<=840. for the LCM to be 840 x,y should not have any common multiple before 840. Also the given condition is that no common factor after 56. So the possible values of (x,y) are 56*3 and 56*5. We cannot exactly tell what x is is it 56*5 or 56*3?. Insufficient.
Cond2: y=168 (or 56*3). now x can be 56*5 (280) or 56*15 (840) or ..any other value where LCM=840. Insufficient.
But then combine both of them. Cond2 tells us that Y is 56*3. and if the GCD has to be 56 then X cannot be 56*15 (else the GCD would have been 56*3 not 56). So X has to be 56*5.

------------------------------------------------------------------
5) If c and k are distinct positive integers, is c divisible by k?

(1) 2k > c
(2) k2 + k = c

from (1) : Since both are +ve. c/k<2. so the only choice is c/k lies b/w 0 and 2...can be anything that is a non integer or 1. Insufficient.
from (2) : k(k+1)= c hence c/k = k+1 = Integer. Hence c is divisible by K. Sufficient.

Answer choice B
I disagree again. Answer is D.

From 1 you can be certain that it is not divisible since C and K are distinct. Hence it is actually sufficient.

Of course, Condition 2 is also sufficient.
------------------------------------------------------------------

Gail, I differ from your answers on a few of these. Let me know if I got anything wrong.

Thank you,
Hemanth

vpitc Says

...

1) If the base of triangle PQR is 5, what is the perimeter of the triangle?

(1) The area of triangle PQR is 12.5
(2) The length of a side of triangle PQR is

Lets say base = c = 5. We need the other 2 sides for perimeter.
from (1). area= 12.5 = sqrt(s(s-a)(s-b)(s-c)) where s = (a+b+5)/2..so one eqn 2 variables. not sufficient.
from (2). b=. and c=5 ; again do we Know a? No. Not sufficient.
combining: 12.5 = 12.5 = sqrt(s(s-a)(s-)(s-5)) and s= (a+5+)/2...so one variable, one eqn. Hence sufficient.

So choice C.
-----------------------------------------------------------------

2) If m and q are divisors of c, is mq a divisor of c that is not c or 1?


(1) mq < c
(2) m and q have no common divisors.

Soln:
Lets use plug-in numbers:
mq is a divisor of c that is not c or 1....
C = 28, m = 2, q=7 or m=4, q=7 or m=4, q=2 and so on...
from (1): since mqm and q have no common divisors; we can choose m = 2, q=7 or m=4, q=7. does mq divide c in both cases? Yes. hence sufficient.

hence Answer is choice B.
------------------------------------------------------------------

3) Group A, which is a set of numbers, has an average (arithmetic mean) of 8 while group B, a different set of numbers, has an average of 10. In which group is the sum of the numbers greater?

(1) The average of all numbers in both groups combined is .
(2) The sum of all numbers in both groups is 52

Soln:
Lets say grp A has x numbers and grp B has y numbers.
Sum of numbers in grp A = 8x
Sum of numbers in grp B = 10y.
We have to find which is greater 8x or 10y?
from (1): (8x+10y)/(x+y) = 8.66..can not find 8x and 10y or any reln b/w them. Not sufficient.
from (2): 8x+10y=52 ...again....can not find 8x and 10y or any reln b/w them. Not sufficient.
combining (1) and (2):52/(x+y) = 8.66...again can not find 8x and 10y or any reln b/w them. Not sufficient.

Answer choice E

------------------------------------------------------------------

4) If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 56.
(2) y = 168

from Stem: prime factors of 840 = 2,2,2,5,3,7.
from (1) : Tells us that max 56 is common in both. prime factors of 56 = 2,2,2,7. hence x= 56*A and Y=56*B where A, B are co-prime. Insufficient.
from (2) : prime factors (y) = 2,2,2,3,7. So X can be anything 3 or less 2s, 1 or less 3s, 1 or less 7s and a 5. hence possible options are 5, 10, 15, 35...So Insufficient.
Combining (1) and (2) : y = 168 and x=56*5 or 56*3*5 hence insufficient.

Answer choice E

------------------------------------------------------------------
5) If c and k are distinct positive integers, is c divisible by k?

(1) 2k > c
(2) k2 + k = c

from (1) : Since both are +ve. c/k<2. so the only choice is c/k lies b/w 0 and 2...can be anything that is a non integer or 1. Insufficient.
from (2) : k(k+1)= c hence c/k = k+1 = Integer. Hence c is divisible by K. Sufficient.

Answer choice B
------------------------------------------------------------------

1) If the base of triangle PQR is 5, what is the perimeter of the triangle?

(1) The area of triangle PQR is 12.5
(2) The length of a side of triangle PQR is

2) If m and q are divisors of c, is mq a divisor of c that is not c or 1?


(1) mq < c
(2) m and q have no common divisors.

3) Group A, which is a set of numbers, has an average (arithmetic mean) of 8 while group B, a different set of numbers, has an average of 10. In which group is the sum of the numbers greater?

(1) The average of all numbers in both groups combined is .
(2) The sum of all numbers in both groups is 52

4) If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 56.
(2) y = 168

5) If c and k are distinct positive integers, is c divisible by k?

(1) 2k > c
(2) k2 + k = c

1) E
equivalently - Is x-1/16>5/8 i.e or x>0.625+0.0625=0.6875.
Cond1: x<3/4 = 0.75. Not sufficient.
Cond2: x>2/3=0.667. InSufficient
Both these put together is also inconclusive. As X can be 0.67 or 0.69.

2) B
Cond1: n(n-1)(n+1) is a multiple of 3. Means one of n,n-1 or n+1 is a multiple of 3. This may or may not indicate if (n-1) is a mulitple.
Cond2: n(n+1)(n+1) is a multiple of 3. So either n or (n+1) is a multiple. In this case we can be sure that if n is a multiple, n-1 cannot. or if n+1 is a multiple even then n-1 is not a multiple. So conclusively n-1 is not a multiple.

3) C.
We need both the conditions as with Cond1, the point E can be further away on line CDE in which case it is not a rhombus.
Cond2 tells us that AE|BD but without BCD being 60, the sides of ABDE will not be equal.

|asbhat Says

agreed with both you can find

Asbhat,
I don't see what you are trying to say with question 1. I am not trying to find the value of X, I am using the inequalities. Care to explain your point?

Thank you,
Hemanth

1) E
equivalently - Is x-1/16>5/8 i.e or x>0.625+0.0625=0.6875.
Cond1: x<3/4 = 0.75. Not sufficient.
Cond2: x>2/3=0.667. InSufficient
Both these put together is also inconclusive. As X can be 0.67 or 0.69.


I guess we can conclude if it is greater or less than by either statement, we need not find the exact valuee

2) B
Cond1: n(n-1)(n+1) is a multiple of 3. Means one of n,n-1 or n+1 is a multiple of 3. This may or may not indicate if (n-1) is a mulitple.
Cond2: n(n+1)(n+1) is a multiple of 3. So either n or (n+1) is a multiple. In this case we can be sure that if n is a multiple, n-1 cannot. or if n+1 is a multiple even then n-1 is not a multiple. So conclusively n-1 is not a multiple.

3) C.
We need both the conditions as with Cond1, the point E can be further away on line CDE in which case it is not a rhombus.
Cond2 tells us that AEBD but without BCD being 60, the sides of ABDE will not be equal.

agreed with both you can find

I made the same mistake, I guess its safe to assume that 0 is a multiple of 5.
I am doubtful if anyone can tell us what GMAC thinks.

Yes, 0 is a multiple of 5
Source:
Number properties - is 0 a multiple of every integer? • Manhattan GMAT Forums

Guys,

In some explanation to a question, Kaplan people considered 0 a multiple of 5.
Is it correct??

I made the same mistake, I guess its safe to assume that 0 is a multiple of 5.
I am doubtful if anyone can tell us what GMAC thinks.

Guys,

In some explanation to a question, Kaplan people considered 0 a multiple of 5.
Is it correct??

1) Is x 1/16 greater than 5/8?

(1) Four times the value of x is less than three.

(2) One third of two is less than the value of x.

2) Is positive integer n 1 a multiple of 3?
(1) n3 n is a multiple of 3
(2) n3 + 2n2+ n is a multiple of 3

3) Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?
(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD

1) E
equivalently - Is x-1/16>5/8 i.e or x>0.625+0.0625=0.6875.
Cond1: x<3/4 = 0.75. Not sufficient.
Cond2: x>2/3=0.667. InSufficient
Both these put together is also inconclusive. As X can be 0.67 or 0.69.

2) B
Cond1: n(n-1)(n+1) is a multiple of 3. Means one of n,n-1 or n+1 is a multiple of 3. This may or may not indicate if (n-1) is a mulitple.
Cond2: n(n+1)(n+1) is a multiple of 3. So either n or (n+1) is a multiple. In this case we can be sure that if n is a multiple, n-1 cannot. or if n+1 is a multiple even then n-1 is not a multiple. So conclusively n-1 is not a multiple.

3) C.
We need both the conditions as with Cond1, the point E can be further away on line CDE in which case it is not a rhombus.
Cond2 tells us that AEBD but without BCD being 60, the sides of ABDE will not be equal.

Also for the 1st question are we taking into consideration that its not the actual width , because what I would believe is that when we need to take the TSD questions we will not consider the width of the tyre including tube etc so for the first question
1. Using the second choice we calculate circumfrnce, then using the first choice we calculate the speed using 9 miles ....

Sorry for the late post,
The OAs are 1) E 2) B 3) C 4) A 5) D

Can you explain the first question. Anyways i don't think OA for 4th one can be A. Cos all variables can take 0 and 0 > 0 will not satisfy in that case.

Sorry for the late post,
The OAs are 1) E 2) B 3) C 4) A 5) D

I don't agree with the OA for Q.4) A

4) Is ax > y?

(1) a = y = x
(2) a < 1

Statement 1:
==========
Lets take y =-1 ===> a = 1 ===> X can be +/- 1.
If x = +1 then we have 1 > -1 which is true
If x = -1 then we have -1 > -1 which is false.

So,statement 1 is insuff to ans the q.
Pls correct me if there is a flaw in my approach.

-Deepak.

1) Is x 1/16 greater than 5/8?

(1) Four times the value of x is less than three.

(2) One third of two is less than the value of x.

2) Is positive integer n 1 a multiple of 3?
(1) n3 n is a multiple of 3
(2) n3 + 2n2+ n is a multiple of 3

3) Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?
(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD

My take :
=======
1. E
2. B
3. B


-Deepak.

1) If John traveled 9 miles on his unicycle, what was his speed in miles per hour?
(1) The unicycle has spokes that stretch the 23 inches from the center of the wheel to inner edge of the wheel.
(2) John pedals his unicycle at 19 revolutions per minute.
2) If w and k are distinct positive integers, do they have any common divisors other than 1 ?
(1) k w = 3w
(2) k and w are even.
3) If x and y are integers, is xy divisible by x2?
(1) x divides into y2 with no remainder.
(2) x is a prime.
4) Is ax > y?
(1) a = y = x
(2) a < 1
5) Let (k + m) be a prime number where m and k are positive. How many divisors does k2 + mk have?
(1) k has 4 divisors.
(2) k = 6

Sorry for the late post,
The OAs are 1) E 2) B 3) C 4) A 5) D

1) Is x 1/16 greater than 5/8?

(1) Four times the value of x is less than three.

(2) One third of two is less than the value of x.

2) Is positive integer n 1 a multiple of 3?
(1) n3 n is a multiple of 3
(2) n3 + 2n2+ n is a multiple of 3

3) Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?
(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD

1) If John traveled 9 miles on his unicycle, what was his speed in miles per hour?
(1) The unicycle has spokes that stretch the 23 inches from the center of the wheel to inner edge of the wheel.
(2) John pedals his unicycle at 19 revolutions per minute.
2) If w and k are distinct positive integers, do they have any common divisors other than 1 ?
(1) k w = 3w
(2) k and w are even.
3) If x and y are integers, is xy divisible by x2?
(1) x divides into y2 with no remainder.
(2) x is a prime.
4) Is ax > y?
(1) a = y = x
(2) a < 1
5) Let (k + m) be a prime number where m and k are positive. How many divisors does k2 + mk have?
(1) k has 4 divisors.
(2) k = 6

My take on the above set:

1. C
2. D
3. C
4. C
5. D

Pls post the OA.I will post the explanations.

-Deepak.

Disagreement on 2 answers. Please let me know what i missed.

4) C - From condition 1: we gather that 'a' is positive and 'y' is negative (but both have the same value). Lets take the case where a=2, y=-2, x=+-2 (we dont know about x). now if X is positive, ax>y. but if x is negative axa<1 then, take a=0.5, y=-0.5, x=+-0.5 when this is the case. we know that ax>y is always true. Since we know form condition 1 that a is always positive we need not consider the negative cases.
5)D - either condition works here. K+M is prime. So K(K+M) will have all the divisors of K and K+M and K(K+M). So if we know K has 4 factors then we know the number of factors of K(K+M). Take K=15 (1,3,5,15) are the divisors. take M=2. So 15*17 has known number of divisors. Likewise if K=6 we know the divisors of K(K+M).

Thank you,
Hemanth

4. What if a , x and y are all equal to zeroes.
5. Agreed.

Good point Austin! I did miss that case.
It didn't occur to me to check for 0 where -y was shown in the condition.
Nice!

4. What if a , x and y are all equal to zeroes.
5. Agreed.

1) If John traveled 9 miles on his unicycle, what was his speed in miles per hour?
(1) The unicycle has spokes that stretch the 23 inches from the center of the wheel to inner edge of the wheel.
(2) John pedals his unicycle at 19 revolutions per minute.
2) If w and k are distinct positive integers, do they have any common divisors other than 1 ?
(1) k w = 3w
(2) k and w are even.
3) If x and y are integers, is xy divisible by x2?
(1) x divides into y2 with no remainder.
(2) x is a prime.
4) Is ax > y?
(1) a = y = x
(2) a < 1
5) Let (k + m) be a prime number where m and k are positive. How many divisors does k2 + mk have?
(1) k has 4 divisors.
(2) k = 6

1.C. Radius is given and revolutions per minute is given.
2.B. if both are even then they do have 2 as common divisor. 1 is not sufficient cos w =1 and k= 4 is an exception case.
3. C.
4.E
5. A

Disagreement on 2 answers. Please let me know what i missed.

4) C - From condition 1: we gather that 'a' is positive and 'y' is negative (but both have the same value). Lets take the case where a=2, y=-2, x=+-2 (we dont know about x). now if X is positive, ax>y. but if x is negative axa<1 then, take a=0.5, y=-0.5, x=+-0.5 when this is the case. we know that ax>y is always true. Since we know form condition 1 that a is always positive we need not consider the negative cases.
5)D - either condition works here. K+M is prime. So K(K+M) will have all the divisors of K and K+M and K(K+M). So if we know K has 4 factors then we know the number of factors of K(K+M). Take K=15 (1,3,5,15) are the divisors. take M=2. So 15*17 has known number of divisors. Likewise if K=6 we know the divisors of K(K+M).

Thank you,
Hemanth

1.C. Radius is given and revolutions per minute is given.
2.B. if both are even then they do have 2 as common divisor. 1 is not sufficient cos w =1 and k= 4 is an exception case.
3. C.
4.E
5. A

How many odd numbers are there between m and n?
(1) m n = 9
(2) 15m 15n = 135

Both Statements are not sufficient.
E.
"m and n are integers" is not mentioned.
So, it can be 4,5,6...depending upon the values...
Can you please post the OA...

1) If John traveled 9 miles on his unicycle, what was his speed in miles per hour?
(1) The unicycle has spokes that stretch the 23 inches from the center of the wheel to inner edge of the wheel.
(2) John pedals his unicycle at 19 revolutions per minute.
2) If w and k are distinct positive integers, do they have any common divisors other than 1 ?
(1) k w = 3w
(2) k and w are even.
3) If x and y are integers, is xy divisible by x2?
(1) x divides into y2 with no remainder.
(2) x is a prime.
4) Is ax > y?
(1) a = y = x
(2) a < 1
5) Let (k + m) be a prime number where m and k are positive. How many divisors does k2 + mk have?
(1) k has 4 divisors.
(2) k = 6

Statement 1:
m-n = 9

m = 10 n = 1. So we will have 3 odd nos 3,5,7
m = 9 , n =0 .So we will have 4 odd nos 1,3,5,7.

So insuff.

Statement 2 : This is same as statement 1.So insuff.

combining also we cannot get the solution..

So I will pick option E

-Deepak.

Good approach.

How many odd numbers are there between m and n?
(1) m n = 9
(2) 15m 15n = 135

Statement 1:
m-n = 9

m = 10 n = 1. So we will have 3 odd nos 3,5,7
m = 9 , n =0 .So we will have 4 odd nos 1,3,5,7.

So insuff.

Statement 2 : This is same as statement 1.So insuff.

combining also we cannot get the solution..

So I will pick option E

-Deepak.

How many odd numbers are there between m and n?
(1) m n = 9
(2) 15m 15n = 135

My pick would be D.

How many odd numbers are there between m and n?
(1) m n = 9
(2) 15m 15n = 135

GMAT Prep Question:
In the xy-Plane does the equation y=3x+2 contaion (r,s):

A)(3r+2-s)(4r+9-s)=0
B)(4r-6-s)(3r+2-s)=0

OA C

Statement 1:
==========
Either 3r+2 = s or 4r+9 =s .Hence not sufficient

Statment 2:
=========
Either 3r+2 = s or 4r-6 = s.Hence not sufficient.

Combining both we get 3r+2 =s which definitely lies on the line.

Hence I will go with option C.

-Deepak.