A couple of tricky GMAT math questions

[chalven]

Hi all:

Here are a couple of questions, which I found tricky and could not get to the correct answer. I look forward to inputs from you guys:

1. If n and y are positive integers and 450y = n^3, which of the following must be an integer:

a. y/(3x5x(2^2)) b. y/((3^2)x5x2) c. y/(3x2x(5^2))

2. If x^4 + y^4 = 100, then the greatest possible value of x is between

A. 0 and 3 B. 3 and 6 C. 6 and 9 D. 9 and 12 E. 12 and 15

I shall post the answers soon. Thanks for everyone's time and I look forward to your response.

Cheers,

chalven.

[bose]

i-A, y should be a multiple of 3*5*2*2, but it could be 3*5*2*2, so only A must be an integer
2-B greatest value for x is when y=0 so x=4rt(100)=sqrt(10)

[SaGo]

1) is A
450=3^2*5^2*2
Hence Y need to be multiple of 3*5*2^2 to make an integer cubed.
2) is B
Nothin is said about x, y being non zero or integers. So the y can be 0 for x to be maxiumum
therefore 100^.25=3.xx

[RamN]

Originally Posted by SaGo

1) is A
450=3^2*5^2*2
Hence Y need to be multiple of 3*5*2^2 to make an integer cubed.
2) is B
Nothin is said about x, y being non zero or integers. So the y can be 0 for x to be maxiumum
therefore 100^.25=3.xx

perfect...

1) A
2) B

[nerrad_oh]

I;m still not very clear about question #1.
Can someone further explain it more

[nerrad_oh]

Originally Posted by nerrad_oh

I;m still not very clear about question #1.
Can someone further explain it more

Never mind.. I've figure it out already ..
My weakness in quan is always on properties of numbers. It's worse with DS.

Examples are those questions like "xyz is a three digit number, is xyz>550"

Any good advice to improve on this ?

[ssky]

Same here I am struggling with number properties. Remember in GMAT most of these things come as part of DS..so I consider myself in deep trouble. I hardly get such questons correct. Any clues guys how we can correct that?

[nerrad_oh]

Right now, just keep practising and read the OG explaination. I'm ok with those questions that have proper systemetic methods to derive the answer, with proper equations etc. But I'm having problem with those which require trial and error. Test with number 2, 3, 5, 7... Sometimes will miss out certain answers or possibilities

[Gags]

i am afraid to say but i am still unable to understand the answer..
how is 450=3^2*5^2*2 and the value of y related ...
can someone explain from the concept level

[chimerical]

Gags - Each prime factor of a cubed integer must also be cubed. So if a, b, and c are the prime factors of n, a^3, b^3, and c^3 must be factors of n^3.

We see that n^3 is equal to 450*y. Doing the prime factorization of 450 gives us 2*3*3*5*5. So we have 2, 3^2, and 5^2. Because 450*y is equal to a cube, y needs to complete the cube by filling in the missing factors. So y must include 2^2, 3, and 5.

Now look at the answer choices. A has exactly those factors in the denominator, which means that they must completely cancel out and leave only the numerator, i.e. an integer. B has an extra 3 in the denominator, and C has an extra 5 in the denominator. We cannot be sure that these will cancel out, so we cannot be sure that B or C will be an integer.

I hope that helped.