Originally Posted by Unregisteredpag View Post
1) A square countertop has a square tile inlay in the cente, leaving an untiled stripof uniform width around the tile. If the ratio of the tiled area to the untiled area is 25 to 39, which of the following could be the width in inches of the strip?
a) 1.5
b) 3
c) 4.5
a) a only
b) b only
c) a and b only
d) a and c only
e) a, b and c
One of the question from the previous post.
@Sujit:
Here A2 = A square and B2 = B square
Let A be size of smaller square and B be size of larger square. Then
A2 / (B2 - A2) = 25/39
If we take direct relation we will have
A2 = 25 , so A = 5
B2 - A2 = (B -A) (B + A) = 39 = 3 X 13
With above equations we will have B = 8, when A = 5
Width of the strip = (B - A) /2 = 1.5
Multiples of 1.5 will also work. So answer is E
This is regarding questions posted earlier:
1)If x is a positive integer and z is a non-negative integer such that (2,066)^z is a divisor of 3,176,793, what is the value of z^x - x^z?
A)-81
B)-1
C)0
D)1
E)It Cannot Be Determined
2)A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 55% have red flags, what percentage of children have flags of both the colors?
A)5%
B)10%
C)15%
D)20%
E)It can not be determined
---------------------------------------------
1. Answer given for first question on the forum is B (-1). But I think it should E(It Cannot Be Determined)
Here value of z = 1. So z^x - x^z = 1 - x
We do not know value of x and so answer should be E
2. For second question answer given on forum is C (15%). But here there is no information about how many students are holding only red, or only blue or both red and blue. There is no way to calculate percentage of students holding both flags. So I think answer should be E (It cannot be calculated).
If there is another answer please elaborate the solution.
The second question could be which score interval contains the media of the 73 scores.
In that case, the question has simplified by providing the total number of scores in each interval.
The median of 73 scores will be the 37th score.
29th till 55th scores appear in the interval 70-79.
Answer: B
This is regarding questions posted earlier:
1)If x is a positive integer and z is a non-negative integer such that (2,066)^z is a divisor of 3,176,793, what is the value of z^x - x^z?
A) -81
B) -1
C) 0
D) 1
E) It Cannot Be Determined
2)A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 55% have red flags, what percentage of children have flags of both the colors?
A) 5%
B) 10%
C) 15%
D) 20%
E) It can not be determined
---------------------------------------------
1. Answer given for first question on the forum is B (-1). But I think it should E(It Cannot Be Determined)
Here value of z = 1. So z^x - x^z = 1 - x
We do not know value of x and so answer should be E
2. For second question answer given on forum is C (15%). But here there is no information about how many students are holding only red, or only blue or both red and blue. There is no way to calculate percentage of students holding both flags. So I think answer should be E (It cannot be calculated).
If there is another answer please elaborate the solution.
For the 1st one:
You do not have to acutally know the value of 'X' as it is already mentioned that it is positive integer. That is more than enough for answering. The only thing which could have stopped from answering is if 'X' is zero but it is already mentioned that 'X' is a positive integer and 'Z' has to be '0'. So the answer -1 is correct. and why Z is '0' an even interger '2066' to become a divisor of an odd number it is possible only when 'Z' is zero. I hope this helps
This is regarding questions posted earlier:
1)If x is a positive integer and z is a non-negative integer such that (2,066)^z is a divisor of 3,176,793, what is the value of z^x - x^z?
A) -81
B) -1
C) 0
D) 1
E) It Cannot Be Determined
2)A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 55% have red flags, what percentage of children have flags of both the colors?
A) 5%
B) 10%
C) 15%
D) 20%
E) It can not be determined
---------------------------------------------
1. Answer given for first question on the forum is B (-1). But I think it should E(It Cannot Be Determined)
Here value of z = 1. So z^x - x^z = 1 - x
We do not know value of x and so answer should be E
2. For second question answer given on forum is C (15%). But here there is no information about how many students are holding only red, or only blue or both red and blue. There is no way to calculate percentage of students holding both flags. So I think answer should be E (It cannot be calculated).
If there is another answer please elaborate the solution.
1. How is Z = 1, my good friend??
If that is the case, then 3,176,793 / (2066)^1 gives a remainder 0 according to information mentioned in the question!! :shocked:
You would have discovered the first odd number that is divisible by an even number!!
Jokes aside, since, z is non-negative the only value it can take is 0.
(2066)^0 = 1, which will be a divisor for 3,176,793.
With this in mind, z^x - x^z ==> 0^x - x^0 ==> 0 - 1 ==> -1. Hence (B)
2.
Given:
# of Flags is even. Let it be 2n.
Also, since each student takes 2 flags and all the flags are consumed, the number of students will be 2n/2 = n.
Now if you ask everyone with a blue flag to raise their hand and you find that 60% of them raise their hands. i.e. 0.6n children
Then you ask everyone with a red flag to raise their hand and you find that 55% of them raise their hands. i.e. 0.55n children
Adding both you get 0.6n + 0.55n = 1.15n!!
But we know for a fact that there are only n children, so the additional number is only those who have raised their hand twice and hence have been counted twice!! That number is 1.15n - n = 0.15n or 15%. Hence (C)
Btw.. this is one of the most basic principles of Set theory:
n(A U B ) = n(A) + n(B) - n (A ^ B)
Cheers,
Nirav
(1)B
(2)C
OG itself has given beautiful explanation to these :)
This is regarding questions posted earlier:
1)If x is a positive integer and z is a non-negative integer such that (2,066)^z is a divisor of 3,176,793, what is the value of z^x - x^z?
A)-81
B)-1
C)0
D)1
E)It Cannot Be Determined
2)A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 55% have red flags, what percentage of children have flags of both the colors?
A)5%
B)10%
C)15%
D)20%
E)It can not be determined
---------------------------------------------
1. Answer given for first question on the forum is B (-1). But I think it should E(It Cannot Be Determined)
Here value of z = 1. So z^x - x^z = 1 - x
We do not know value of x and so answer should be E
2. For second question answer given on forum is C (15%). But here there is no information about how many students are holding only red, or only blue or both red and blue. There is no way to calculate percentage of students holding both flags. So I think answer should be E (It cannot be calculated).
If there is another answer please elaborate the solution.
This is regarding questions posted earlier:
1)If x is a positive integer and z is a non-negative integer such that (2,066)^z is a divisor of 3,176,793, what is the value of z^x - x^z?
A) -81
B) -1
C) 0
D) 1
E) It Cannot Be Determined
2)A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 55% have red flags, what percentage of children have flags of both the colors?
A) 5%
B) 10%
C) 15%
D) 20%
E) It can not be determined
---------------------------------------------
1. Answer given for first question on the forum is B (-1). But I think it should E(It Cannot Be Determined)
Here value of z = 1. So z^x - x^z = 1 - x
We do not know value of x and so answer should be E
2. For second question answer given on forum is C (15%). But here there is no information about how many students are holding only red, or only blue or both red and blue. There is no way to calculate percentage of students holding both flags. So I think answer should be E (It cannot be calculated).
If there is another answer please elaborate the solution.
1. How is Z = 1, my good friend??
If that is the case, then 3,176,793 / (2066)^1 gives a remainder 0 according to information mentioned in the question!! :shocked:
You would have discovered the first odd number that is divisible by an even number!!
Jokes aside, since, z is non-negative the only value it can take is 0.
(2066)^0 = 1, which will be a divisor for 3,176,793.
With this in mind, z^x - x^z ==> 0^x - x^0 ==> 0 - 1 ==> -1. Hence (B)
2.
Given:
# of Flags is even. Let it be 2n.
Also, since each student takes 2 flags and all the flags are consumed, the number of students will be 2n/2 = n.
Now if you ask everyone with a blue flag to raise their hand and you find that 60% of them raise their hands. i.e. 0.6n children
Then you ask everyone with a red flag to raise their hand and you find that 55% of them raise their hands. i.e. 0.55n children
Adding both you get 0.6n + 0.55n = 1.15n!!
But we know for a fact that there are only n children, so the additional number is only those who have raised their hand twice and hence have been counted twice!! That number is 1.15n - n = 0.15n or 15%. Hence (C)
Btw.. this is one of the most basic principles of Set theory:
n(A U B ) = n(A) + n(B) - n (A ^ B)
Cheers,
Nirav
I recall these questions from the platinum GMAT test.
I got the 1st one wrong too. jawaharnr has already explained it.
For the 2nd question; With all due respect, I honestly did not read my buddy, jawaharnr's solution. No offense dude..you are a champ with a 780... Just saw its long. Here is my take:
Given "all the flags are used up in the process" = 100% used up.
Now if %Blue + % red > 100% ; The kids who have both would obviously be total - 100 => 115 - 100 = 15% Ans. Like Nirav said this is one of the most basic principles of Set theory: n(A U B ) = n(A) + n(B) - n (A ^ B)
Originally Posted by vpitc View Post
1) Anthony and Michael sit on the six-member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?
20%
30%
40%
50%
60%
@ hemanth:
Why did you had number of groups as 6c3/2 and not as 6c3 in your solution? Why is it divided by 2?
Hey Nirav, Thanks for the explanations. Silly mistake in 1st question. 2nd one I just goofed up.
* Total number of team possibilities = 6C3 = 20.
* Since 2 teams are to be formed, total possibilities becomes half of 20 = 10
* For Michael and Anthony to be in the same team, they shall be considered as single group. So, the requirement becomes "2C2 X 4C1" = 4.
Percentage solution is (4/10) = 40% :)
Originally Posted by vpitc View Post
1) Anthony and Michael sit on the six-member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?
20%
30%
40%
50%
60%
@ hemanth:
Why did you had number of groups as 6c3/2 and not as 6c3 in your solution? Why is it divided by 2?
* Total number of team possibilities = 6C3 = 20.
* Since 2 teams are to be formed, total possibilities becomes half of 20 = 10
* For Michael and Anthony to be in the same team, they shall be considered as single group. So, the requirement becomes "2C2 X 4C1" = 4.
Percentage solution is (4/10) = 40% :)
Hi Ravi,
In the overall 20 combinations possible, there are only 4 combinations which can have both michael and anthony. Now if you divide the number of combinations by 2 (i.e. 20/2), then you will have two sets of 10 combinations - lets call this set A and set B. Now out of the 4 combinations which have both anthony and michael, some combination may be in set A and some in set B. In that case answer will not be 40%. Am I missing something?
Regards,
Sujit
Two problems related to Factorials and Permutation...
(1) If 6^m divides 25! then what is the largest value of m?
(A) 5
(B) 8
(C) 10
(D) 22
(E) 26
(2) If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?
(A) 250
(B) 276
(C) 300
(D) 600
(E) 2300
Two problems related to Factorials and Permutation...
(1) If 6^m divides 25! then what is the largest value of m?
(A) 5
(B) 8
(C) 10
(D) 22
(E) 26
(2) If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?
(A) 250
(B) 276
(C) 300
(D) 600
(E) 2300
1. Question is what is the max power of 6(Prime factors 2,3) that divides 25! For such question we typically take the Greater number i.e. 3 and use the division method. Ignore the remainders
25/3 = 8
8/3 = 2
hence max power is 8+2=10. Option C.
2. Question gives us the info that any two lines can intersect no two of them are parallel and no three are concurrent(No common point of intersection). Number of intersection points = Number of sets of 2 lines each.
=> 25!/2!23! = 25*12 = 300 Option C.
1. Question is what is the max power of 6(Prime factors 2,3) that divides 25! For such question we typically take the Greater number i.e. 3 and use the division method. Ignore the remainders
25/3 = 8
8/3 = 2
hence max power is 8+2=10. Option C.
2. Question gives us the info that any two lines can intersect no two of them are parallel and no three are concurrent(No common point of intersection). Number of intersection points = Number of sets of 2 lines each.
=> 25!/2!23! = 25*12 = 300 Option C.
Thanks Gail!
Could please elaborate "the division method" that you mentioned above? Some explanation will help in understanding the concept.
1. Question is what is the max power of 6(Prime factors 2,3) that divides 25! For such question we typically take the Greater number i.e. 3 and use the division method. Ignore the remainders
25/3 = 8
8/3 = 2
hence max power is 8+2=10. Option C.
2. Question gives us the info that any two lines can intersect no two of them are parallel and no three are concurrent(No common point of intersection). Number of intersection points = Number of sets of 2 lines each.
=> 25!/2!23! = 25*12 = 300 Option C.
Thanks Gail!
Could please elaborate "the division method" that you mentioned above? Some explanation will help in understanding the concept.
The division method is performing the following steps:
Lets say we have to find the highest power of x that divides K!
The prime factors of X e.g. are 2,3,5,7. And K is say 100.
1. Pick the greatest prime factor i.e. 7
2. Divide the Number 100 by 7 .
3. redivide the quotient by 7(ignore the remainder). keep doing this till you obtain a number smaller than 7.
4. Add all the quotients. That's the answer.
Demonstration:
100/7 = Quotient = 14 Remainder=2(Ignore)
14/7 = Quotient = 2 Remainder=0(Ignore)
Since 2Hence the highest power of 7 that divides 100! is 14+2=16 Ans.
A certain businessman wears only three different colors of shirt white, blue and grey. The probability that he will wear a blue or grey shirt is 2/3. During a four-day work week, what is the probability that the businessman will wear a white shirt at least once?
(A)16/81
(B)2/3
(C)8/27
(D)65/81
(E)19/27
A right triangle ABC has to be constructed in the xy-plane so that the right angle is at A and AB is parallel to x-axis. The coordinates of A, B and C are to satisfy the inequalities -3 x 5 and 2 y 11 and x & y are integers. The number of different triangles that can be constructed with these properties are?
(A)90
(B)900
(C)6480
(D)8100
(E)10000
Official Answers to (D) 65/21 and to (C) 6480
A certain businessman wears only three different colors of shirt white, blue and grey. The probability that he will wear a blue or grey shirt is 2/3. During a four-day work week, what is the probability that the businessman will wear a white shirt at least once?
(A)16/81
(B)2/3
(C)8/27
(D)65/81
(E)19/27
Probability of not wearing a white shirt for al 4 days = Probability of wearing Blue or Grey shirt on all 4 days
Probability of wearing Blue or Grey shirt on all 4 days = (2/3)^ 4 = 16/81
Probability of wearing white shirt atleast 1 day = 1 - Probability of not wearing a white shirt for all 4 days
= 1 - 16/81
= 65/81
Option D
-Deepak.
A right triangle ABC has to be constructed in the xy-plane so that the right angle is at A and AB is parallel to x-axis. The coordinates of A, B and C are to satisfy the inequalities -3 x 5 and 2 y 11 and x & y are integers. The number of different triangles that can be constructed with these properties are?
(A) 90
(B) 900
(C) 6480
(D) 8100
(E) 10000
0
Since points A,B,C are arranged in a manner:
C is exactly vertically aligned with A i.e. CAB is a rt angle. CA is parallel to the Y axis.
and AB is parallel to the X axis.
Implications in terms of the choice of co-ordinates:
A = (a,b)
B = (c,b)
C = (a,d)
Only in the above arrangement will it form the rt triangle with the given conditions.
Number of values that 'a' can take = 9
Number of values that 'b' can take = 10
Number of values that 'c' can take = Num(a)-1 = 8
Number of values that 'd' can take = Num(b)-1 = 9
Hence the total combinations are : 9*10*8*9=6480
Q. What is the probability that at least one of two people was born on a Monday...
guys please help..
guys please help..
Q. What is the probability that at least one of two people was born on a Monday...
guys please help..
There has to be some more information.