If x is divisible by 42. Which of the following numbers is d : GMAT Problem Solving (PS)
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# If x is divisible by 42. Which of the following numbers is d

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If x is divisible by 42. Which of the following numbers is d [#permalink]

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26 Jun 2010, 02:20
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If x is divisible by 42. Which of the following numbers is definitely a factor of x2? (Choose all that apply.)

A. 63
B. 33
C. 36
D. 8
[Reveal] Spoiler: OA

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Manager
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26 Jun 2010, 03:17
Is it x*2 or x^2

If x^2 then my answer is C

6 is a factor of 42 ( x is a multiple of 42) then 6 will repeat in every multiple of 42 (84, 126, .......) so 36 will definately be the factor
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26 Jun 2010, 03:25
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Expert's post
If x is divisible by 42. Which of the following numbers is definitely a factor of x2? (Choose
all that apply.)
a) 63 b) 33 c) 36 d) 8

It will be helpful if group can explain the answer as well.

Given: $$x=42k=2*3*7*k$$ (where $$k$$ is an integer) --> $$x^2=2^2*3^3*7^2*k^2$$.

A. $$63=3^2*7$$ is a factor of $$x^2$$;

B. $$33=3*11$$ may NOT be a factor of $$x^2$$ (we don't know whether 11 is a factor $$x^2$$);

C. $$36=2^2*3^2$$ is a factor of $$x^2$$;

D. $$8=2^3$$ may NOT be a factor of $$x^2$$ ($$2^2=4$$ is a factor of $$x^2$$, but we need one more 2 and we don't know whether unknown multiple, $$k^2$$, contains it or not).

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26 Jun 2010, 08:47
Bunuel wrote:
If x is divisible by 42. Which of the following numbers is definitely a factor of x2? (Choose
all that apply.)
a) 63 b) 33 c) 36 d) 8

It will be helpful if group can explain the answer as well.

Given: $$x=42k=2*3*7*k$$ (where $$k$$ is an integer) --> $$x^2=2^2*3^3*7^2*k^2$$.

A. $$63=3^2*7$$ is a factor of $$x^2$$;

B. $$33=3*11$$ may NOT be a factor of $$x^2$$ (we don't know whether 11 is a factor $$x^2$$);

C. $$36=2^2*3^2$$ is a factor of $$x^2$$;

D. $$8=2^3$$ may NOT be a factor of $$x^2$$ ($$2^2=4$$ is a factor of $$x^2$$, but we need one more 2 and we don't know whether unknown multiple, $$k^2$$, contains it or not).

Thanks for the solution

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Re: Number System- Divisibility   [#permalink] 26 Jun 2010, 08:47
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