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If x is a prime number, what is the value of x?

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If x is a prime number, what is the value of x? [#permalink] New post 12 Apr 2009, 22:25
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GMAT experts, can anyone help me with these problems? I've been trying, but hitting walls... I'm much more of a verbal person than quant. Any help would be greatly appreciated, and I will lavish you in compliments/gratitude via internet. THANK YOU.

DATA SUFFICIENCY QUESTION:
1) If x is a prime number, what is the value of x?
(1) x<15
(2) (x-2) is a multiple of 5
*The answer key says the answer is (E) statements 1 & 2 taken together are not sufficient to answer, but I thought it was (C) statements 1 & 2 together are sufficient to answer, since the only number x could be is 7...?

2) Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at those rate, at which floor will their paths cross?
a. 19
b. 28
c. 30
d. 32
e. 44
*I ruled out answers d and e since I know the floor has to be below the midway point between the 11th floor and 51st floor. But where do I go from there?

3) If both 5^2 and 3^3 are factors of n * 2^5 * 6^2 * 7^3, what is the smallest possible positive value of n?
a. 25
b. 27
c. 45
d. 75
e. 125
*no clue on this one... help?
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Re: Please help? [#permalink] New post 12 Apr 2009, 23:19
meesawoosa wrote:
GMAT experts, can anyone help me with these problems? I've been trying, but hitting walls... I'm much more of a verbal person than quant. Any help would be greatly appreciated, and I will lavish you in compliments/gratitude via internet. THANK YOU.

DATA SUFFICIENCY QUESTION:
1) If x is a prime number, what is the value of x?
(1) x<15
(2) (x-2) is a multiple of 5
*The answer key says the answer is (E) statements 1 & 2 taken together are not sufficient to answer, but I thought it was (C) statements 1 & 2 together are sufficient to answer, since the only number x could be is 7...?
You are partially correct.. Along with 7, another number can be 2, x-2 = 0..which is also multiply of 5.. so we cannot answer combining one and two...

2) Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at those rate, at which floor will their paths cross?
a. 19
b. 28
c. 30
d. 32
e. 44
*I ruled out answers d and e since I know the floor has to be below the midway point between the 11th floor and 51st floor. But where do I go from there?
The rate of S & J varies in the ration of 57:63 => 19:21.
It means, by the time, S has climbed 19 floor, J would have came down by 21.
Incidently, the gap between them is 40 floors...

so..they would meet at 19+11= 30th floor...
or.. 51-21=30 floor...


3) If both 5^2 and 3^3 are factors of n * 2^5 * 6^2 * 7^3, what is the smallest possible positive value of n?
a. 25
b. 27
c. 45
d. 75
e. 125
*no clue on this one... help?



if you factorize.. n*2^5 * 6^2*7^3==> n*2^7*3^2*7^3....

Now, 5^2 is factor of the above number.. so it should be divisible by 5^2....
also, it is divisible by 3^3... so it should be divisible by 3^3...but we have only 3^2..s0..we need one more 3..

so..if we multiply it by 5^2*3.. it will satisfy the equation..
so n should be 75
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Re: Please help? [#permalink] New post 12 Apr 2009, 23:30
meesawoosa wrote:
GMAT experts, can anyone help me with these problems? I've been trying, but hitting walls... I'm much more of a verbal person than quant. Any help would be greatly appreciated, and I will lavish you in compliments/gratitude via internet. THANK YOU.

DATA SUFFICIENCY QUESTION:
1) If x is a prime number, what is the value of x?
(1) x<15
(2) (x-2) is a multiple of 5
*The answer key says the answer is (E) statements 1 & 2 taken together are not sufficient to answer, but I thought it was (C) statements 1 & 2 together are sufficient to answer, since the only number x could be is 7...?

You ignored the prime 2, so x can be 2 and 7, so 1 and 2 combined is not suff

2) Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at those rate, at which floor will their paths cross?
a. 19
b. 28
c. 30
d. 32
e. 44
*I ruled out answers d and e since I know the floor has to be below the midway point between the 11th floor and 51st floor. But where do I go from there?

I found 30, but not sure
3) If both 5^2 and 3^3 are factors of n * 2^5 * 6^2 * 7^3, what is the smallest possible positive value of n?
a. 25
b. 27
c. 45
d. 75
e. 125
*no clue on this one... help?


n * 2^5 * 6^2 * 7^3 = n *2^5*(2^2*3^2)*7^3 =2^7*[color=#FF0000][b]3^2*7^3. so If both 5^2 and 3^3 are factors of n * 2^5 * 6^2 * 7^3, n must be = 5^2*3=75

D[/b][/color]
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Re: Please help? [#permalink] New post 12 Apr 2009, 23:51
sondenso, Igon, THANK YOU BOTH SO MUCH.

i completely forgot that 0 was also a multiple of 5! and Igon, your explanation of the second problem suddenly makes everything clear... i had gotten to the point of comparing 57 and 63 but couldn't figure out where to go from there. and as for that last problem... yeah... i was going nuts. thank you both again.
Re: Please help?   [#permalink] 12 Apr 2009, 23:51
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