The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then n=?
Sol: First term a=2, common difference d=2 since even number
therefore sum to first n numbers of Arithmetic progression would be
n/2(2a+(n-1)d)
= n/2(2*2+(n-1)*2)=n(n+1) and this is equal to 79*80
therefore n=79 which is odd...
Guys,
I think the soln should be 79*2+1=159 am i right?

yes...n should be 159

The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then n=?
Sol: First term a=2, common difference d=2 since even number
therefore sum to first n numbers of Arithmetic progression would be
n/2(2a+(n-1)d)
= n/2(2*2+(n-1)*2)=n(n+1) and this is equal to 79*80
therefore n=79 which is odd...
Guys,
I think the soln should be 79*2+1=159 am i right?

If function satisfies for all , which of the following must be true?

1. 
   
2. 
   
3. 
   
4. 
   
5. 
   

A) F(4) = F(2) - wrong
B)F(16) = F(4) (or F(-4); not relevant) = F(-2) (or F(2); not relevant)
Hence F(16) = F(-2)
B is the answer

I wouldn't check the rest.

Please answer with explanation...

Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as a result, 40% solution of acid was obtained, what part of the original solution was replaced?

1. 
   
2. 
   
3. 
   
4. 
   
5. 
   

(0.5 * x + 0.3 (1-x))/1 = 0.4

0.2 *x = 0.1

x = 1\2

If function satisfies for all , which of the following must be true?

1. 
   
2. 
   
3. 
   
4. 
   
5. 
   

1. is the answer ,
   
   

coz f(-2) = f(-2 * -2) = f (4)

then f(4) = f(4*4) = f(6)

so f(16)-f(-2) = 0

correct me if i am wrong !!

If function satisfies for all , which of the following must be true?

1. 
   
2. 
   
3. 
   
4. 
   
5. 
   

I will go with option 2) f(16) - f(2) = 0

Please answer with explanation...

Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as a result, 40% solution of acid was obtained, what part of the original solution was replaced?

1. 
   
2. 
   
3. 
   
4. 
   
5. 
   

I will go with option 3)1/2

Please answer with explanation...

Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as a result, 40% solution of acid was obtained, what part of the original solution was replaced?

1. 
   
2. 
   
3. 
   
4. 
   
5. 
   

option 3 - 1/2. considering that the final solution (40%) is average of 50% and 30% so equal amount will be needed of 50% and 30% solution respectively

Please answer with explanation...

Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as a result, 40% solution of acid was obtained, what part of the original solution was replaced?

1. 
   
2. 
   
3. 
   
4. 
   
5. 
   

If function satisfies for all , which of the following must be true?

1. 
   
2. 
   
3. 
   
4. 
   
5. 
   

thanks...it was quite easy to understand like this.

Please answer with explanation.

A box has 6 red hats and 5 green hats. What is the probability of drawing at least one green hat in two consecutive drawings if the hat is not replaced?

a. 10/11

b. 8/11
c.7/12
d.5/13
e.2/7

IMO: B

Explanation:
probability of drawing at least one green hat = 1 - probability of drawing no green hat

probability of drawing no green hat = probability of drawing only red hats = (6/11)*(5/10) = 3/11

Hence, Ans = 1 - 3/11 = 8/11


Cheers.

Please answer with explanation.

A box has 6 red hats and 5 green hats. What is the probability of drawing at least one green hat in two consecutive drawings if the hat is not replaced?

a. 10/11

b. 8/11
c.7/12
d.5/13
e.2/7

A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9 of the marbles are removed, how many of the marbles left in the jar are red?


(1) Of the marbles removed, the ratio of the number of red ones to the number of blue ones is 2 : 1.
(2) Of the first 6 marbles removed, 4 are red.

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 Statements (1) and (2) TOGETHER are NOT sufficient.

ANS) A...very easy

The answer is "E"

In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r =
A. 6
B. 5
C. 4
D. 3
E. 2.

Ans : B bery bery veezee

In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r =
A. 6
B. 5
C. 4
D. 3
E. 2.

Let , A(-2,1) B(-2,-3) & C (4,-3).

Distance (AB) = 4
Distance (BC) = 6.

Radius must lie in between these distances.So only value satisfying the above condition is 5

I will go with option B

In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r =
A. 6
B. 5
C. 4
D. 3
E. 2.

IMO: B
Pretty easy one though.

Cheers.
Ankit.

In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r =
A. 6
B. 5
C. 4
D. 3
E. 2.

IMO B, r=5

In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r =
A. 6
B. 5
C. 4
D. 3
E. 2.

Solve this

How many diagonals does a 63-sided convex polygon have?

A. 3780
B. 1890
C. 3843
D. 3906
E. 1953

Ans should indeed be B.
An extension of nC2 - n formula is that from any vertex of the poygon there are n-3 other vertices to form a diagonal .
Hence, total no of diagonals is n(n-3) / 2 which is same as nC2 - n ...

Ans B

Solve this

How many diagonals does a 63-sided convex polygon have?

A. 3780
B. 1890
C. 3843
D. 3906
E. 1953

i guess option (B) will be the answer. the number of diagonals of any convex polygon(e.g.- square, pentagon...) can be found by using the formula nC2 - n, where n = no. of sides of the polygon.

Solve this

How many diagonals does a 63-sided convex polygon have?

A. 3780
B. 1890
C. 3843
D. 3906
E. 1953

guys,
cud anybody help me out with this along with the funda:

According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?

A. 15%
B. 20%
C. 25%
D. 0%
E. 35%

IMO: C
I solve these type of Qs using a graphical representation.

Step 1: Draw an axis. Consider vertical length as 100%.

Step 2: Take the highest percentage, and draw a vertical line from bottom to top. This line will cover 80% (from our Q).

Step 3: Take the next highest percentage value. This time draw a vertical line from top to bottom.
Look at the figure closely. If only two percentages are given, answer will be the common area where both the two lines are in common.
But since we have a third percentage, break the third line into parts such that it does not form a common area for all the three lines.
If you look at the figure that I have attached here, this will make more sense.

Step 4: Answer to this question will be the area that is covered by all the three lines.

NOTE: This strategy is for deriving the minimum percentage for all the given percentages. Also, using this representation, it becomes relatively easier to crack for around 4-5 given percentages also.

Hope this helps.

Cheers.
Ankit.

guys,
cud anybody help me out with this along with the funda:

According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?

A. 15%
B. 20%
C. 25%
D. 0%
E. 35%

Are there any ppl who don't take any of the fruits?Then in that case option D can also be an ans

cud u explain ur approach? i worked it out & the answer for me was 20%! amn ot sure, though!!


cheers

Given 70% like apple and 75% like banana (considering the least%) then the minimum % which likes both is 70% + 75% -100% =45%.
Now adding 80% who like cherries we get 80% + 45% -100% =25%


not sure if the explanation convinces

asterixmatrix Says

is the answer C??

cud u explain ur approach? i worked it out & the answer for me was 20%! amn ot sure, though!!


cheers

guys,
cud anybody help me out with this along with the funda:

According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
A. 15%
B. 20%
C. 25%
D. 0%
E. 35%

is the answer C??

guys,
cud anybody help me out with this along with the funda:

According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?

A. 15%
B. 20%
C. 25%
D. 0%
E. 35%

guys,
need some serious inputs urgently!! i have exactly one month to go for G-Day & I need some quality quant material to practise from. am done with OG-12...cud anybody suggest something more challenging given the fact that the quant in gmat has become tougher. looking forward to hearing from you!!


thanx

aliz_khanz Says

@lakshya_iim_ahd ...... first , screw the question .....i love ur signature !!

Well, thank you very much

aliz_khanz Says

@every1 ......now about the question.... how did u know that one has to place the value in the equation provided.? is it some rule that if u want to get a max. of one variable you somehow make the other variable end up in 0 ??? please throw some light on this guys !!

The answer to this is: If you see the equation, you notice two variables (P and S). The question says what is S when P is maximum and in the options, the values of S are given.

Now, you can either hack your brains to try find out the value of P and derive the correct value for S or else you solve backwards.
You just put in the values of S (from the options given) and see for which value of S, your P is maximum.

That my friend, is your answer

P = -(one part) + (other part)

Now, this will maximize only when -ve part is zero.

@lakshya_iim_ahd ...... first , screw the question .....i love ur signature !!

@every1 ......now about the question.... how did u know that one has to place the value in the equation provided.? is it some rule that if u want to get a max. of one variable you somehow make the other variable end up in 0 ??? please throw some light on this guys !!

@lakshya_iim_ahd ...... first , screw the question .....i love ur signature !!

@every1 ......now about the question.... how did u know that one has to place the value in the equation provided.? is it some rule that if u want to get a max. of one variable you somehow make the other variable end up in 0 ??? please throw some light on this guys !!

The number of passengers on a certain bus at any given time is given by the equation P = 2(S 4)2 + 32, where P is the number of passengers and S is the number of stops the bus has made since beginning its route. If the bus begins its route with no passengers, what is the value of S when the bus has its greatest number of passengers?

9

6

4

2

1

no idea where to begin with ?

A simple question where the answer can be found out by substituiting the value of S from the options given. The option that gives you the maximum value of P is the answer

Regards,
Anubhav

The number of passengers on a certain bus at any given time is given by the equation P = 2(S 4)2 + 32, where P is the number of passengers and S is the number of stops the bus has made since beginning its route. If the bus begins its route with no passengers, what is the value of S when the bus has its greatest number of passengers?

9

6

4

2

1

no idea where to begin with ?

I will go with option C)4


P = -2(S-4)^2 + 32

S =0 P = 0
S =1 P = 14
S = 2 P = 24
S = 4 P = 32
S = 6 P = 24
S= 9 P = -ve

i m sorry i forgot to place the squaring sign. ur answer is right !!! the question includes -2(s-4)^2............thanks !

The number of passengers on a certain bus at any given time is given by the equation P = -2(S - 4)2 + 32, where P is the number of passengers and S is the number of stops the bus has made since beginning its route. If the bus begins its route with no passengers, what is the value of S when the bus has its greatest number of passengers?

9

6

4

2

1

no idea where to begin with ?

is it -2(S-4)^2?? or -2(S-4) *2??

For the original equation answer will be 1 but if its -2(S-4)^2 then considering this, answer should be 4
Solution: -2(S-4)^2 becomes -2(4-4)^2 =0 and so P equals 32.

If we take any +ve number (S cannot be -ve) other than 4 then P will be less than 32. Lets consider S as 1 then P becomes -2(1-4)^2 +32 = -18+32 = 14.

Solution entirely based on assumption that -2(S-4)2 is actually -2(S-4)^2


Regards

The number of passengers on a certain bus at any given time is given by the equation P = 2(S 4)2 + 32, where P is the number of passengers and S is the number of stops the bus has made since beginning its route. If the bus begins its route with no passengers, what is the value of S when the bus has its greatest number of passengers?

9

6

4

2

1

no idea where to begin with ?

IMO: E
For P to be maximum, S-4 will have to be minimum, which will happen at S=1 (because S can not be 0, since the bus started empty. And also, S being the number of stops, it can not be negative.)


Cheers.
Ankit.

The number of passengers on a certain bus at any given time is given by the equation P = -2(S - 4)2 + 32, where P is the number of passengers and S is the number of stops the bus has made since beginning its route. If the bus begins its route with no passengers, what is the value of S when the bus has its greatest number of passengers?

9

6

4

2

1

no idea where to begin with ?

71 is present in the options

Which of the following numbers is greater than three fourths of the numbers but less than one-fourth of the number in the number list above ?
56
68
69
71
73

thanks!!got it:)

elan1922 Says

Is'nt 7C2*7C2*7C2 =(7C2)^3 !! ...Have I lost it here ?? Pls let me know

Oops! You are right...

And on closer examination, A and D options are the same in the above ques.

I am at wit's end here.

Folks, help...

Is'nt 7C2*7C2*7C2 =(7C2)^3 !! ...Have I lost it here ?? Pls let me know

yserious Says

The option 71 is not there in the original number?can we consider it??

The question doesn't ask you to find a number from the existing series...

Somebody pls pls explain this..... I thought the ans is 7C2*7C2*7C2

A test maker is to design a probability test from a list of 21 questions. The 21 questions are classified into three categories: hard, intermediate and easy. If there are 7 questions in each category and the test maker is to select two questions from each category, how many different combinations of questions can the test maker put on the test?
A) 3*(7!/(5!2!)) B) 3*(7!/(5!)) C) 3*(7!/(2!)) D) 3*21 E) 72

@elan1922
You are right. The answer accordingly is A.

nCr = n!/
Thus, 7C2 = 7!/(5!2!)

yserious Says

The option 71 is not there in the original number?can we consider it??

71 is present in the options

Which of the following numbers is greater than three fourths of the numbers but less than one-fourth of the number in the number list above ?

56
68
69
71
73

function f is defined for all the positive integers n by the following rule:-
f(n) is the no. of positive integers each of which is less than n and has no positive factor is common with n other than 1. If p is any prime number then f(p) =

p-1

p-2

p+1/2

p-1/2

2

Take for example a prime number say 5 then the number of positive integers each of which is less than 5 and has no positive factor is common with n other than 1 is 4 the numbers r 1 2 3 4 ...!!

The question talks about p being a prime number. Given that, we wont have ANY number less than 'p' that has a common factor with 'p', except 1. So, any positive number less than p and greater than 0 (this will include 1 as well) would satisfy the condition (1, 2, 3, 4, 5,..., p-1). And the count of all such numbers will be the answer to this question, i.e. p-1.

IMO: A


Cheers.
Ankit.

Lets first arrange them in ascending order

we get : 13,22,31,38,47,69,73,82.

We have to find a number which is greater than 6 of the nos and less than of nos in the above list.So the no must lie between 69 and 73.From the options only 71 satisfies the above condition.

I wud go with option D)71

The option 71 is not there in the original number?can we consider it??

Somebody pls pls explain this..... I thought the ans is 7C2*7C2*7C2

A test maker is to design a probability test from a list of 21 questions. The 21 questions are classified into three categories: hard, intermediate and easy. If there are 7 questions in each category and the test maker is to select two questions from each category, how many different combinations of questions can the test maker put on the test?
A) 3*(7!/(5!2!)) B) 3*(7!/(5!)) C) 3*(7!/(2!)) D) 3*21 E) 72

sdt83 Says

will u plz clarify ur logic??? im not getting it..

One more way to solve...

here after simplifying the exp we get

1 + y/x+y = k/10

now 10,30 are out because x, y are +ve numbers. 10,30 give 0 and -ve numbers resp.
take 12

1+ y/x+y = 12/10 => y/x+y = 2/10 => x/y=4 this is not true becos x/y must be a fraction so any value that is a fraction is the correct ans .

In this case 18.

function f is defined for all the positive integers n by the following rule:-
f(n) is the no. of positive integers each of which is less than n and has no positive factor is common with n other than 1. If p is any prime number then f(p) =

p-1

p-2

p+1/2

p-1/2

2

Take for example a prime number say 5 then the number of positive integers each of which is less than 5 and has no positive factor is common with n other than 1 is 4 the numbers r 1 2 3 4 ...!!

@nee! Says

Answer in Red if 1 is nt included, if 1 is include then answer in green

can u please explain ..... answer is A

If x, y, and k are positive numbers such that (x/x+y)(10) + (y/x+y)(20) = k and if x < y, which of the following could be the value of k?
A. 10
B. 12
C. 15
D. 18
E. 30
------------------------------------------------------------------------------------------------------------
need expln..

On simplification the expr turns

10( 1 + y/x+y) = k

So K can't be 30 or 10 .

Now turning out the values in options we get see 18 is possible when y=4 , x = 1

I wud go with option D

out of head

function f is defined for all the positive integers n by the following rule:-
f(n) is the no. of positive integers each of which is less than n and has no positive factor is common with n other than 1. If p is any prime number then f(p) =

p-1
p-2

p+1/2

p-1/2

2

Answer in Red if 1 is nt included, if 1 is include then answer in green

out of head

function f is defined for all the positive integers n by the following rule:-
f(n) is the no. of positive integers each of which is less than n and has no positive factor is common with n other than 1. If p is any prime number then f(p) =

p-1

p-2

p+1/2

p-1/2

2

Simplifying this expression, we come to:
(x+2y)/(x+y)=k/10
Substituting each answer option one by one.
Answer : D

Any faster approach...


Cheers.
Ankit.

will u plz clarify ur logic??? im not getting it..

Thanx deepak and tiknA_atpuG ..... it really worked ! ur answers are right ! thanks again !

If x, y, and k are positive numbers such that (x/x+y)(10) + (y/x+y)(20) = k and if x < y, which of the following could be the value of k?
A. 10
B. 12
C. 15
D. 18
E. 30
------------------------------------------------------------------------------------------------------------
need expln..

Simplifying this expression, we come to:
(x+2y)/(x+y)=k/10
Substituting each answer option one by one.
Answer : D

Any faster approach...


Cheers.
Ankit.

varma3008 Says

OA 1)D 2)D 3)D u got all 3 right can u explain the first one

If (p^2)q is a multiple of 5, it means either p or q have to be multiple of 5.
Now in option D, we are squaring both, p as well as q. Which means, the result of the product of their squares has to be a multiple of 5.
To understand this with help of an example, consider this.
p = 10 --> multiple of 5
q = 3
(p^2)q = 100*3 = 300 --> This is a multiple of 25.
Now consider this.
p = 3
q = 10 --> multiple of 5
(p^2)q = 9*10 = 90 --> This is not a multiple of 25.

Now, in both these examples, square p and q, and then see the result. In both cases, you will find the (p^2)*(q^2) as a multiple of 25.

Hope this helps.

Cheers.
Ankit.

1) IMO: D
My assumption about the Q is: n = (p^2)q and option D is (p^2)(q^2)

2) IMO: D --> not confident
5C3 * 7C1 = 70

3) IMO: D
This is good one.
Thought Process - If any city has to have the least population, then all other cities should accommodate the extra population with equal distribution.
If we go with D ie. 11000, that means this city is having 1000 less than the ideally equal distribution (ie. 132000/11 = 12000). So, this 1000 has to be distributed equally among rest 10 cities, moving their population to 12100. Difference between 11000 and 12100 is exactly 10%, hence D.

OA Please...

Cheers.
Ankit.

OA 1)D 2)D 3)D u got all 3 right can u explain the first one

Can u please correct the q :(yxx+)(10) + (yxy+)(20)