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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] New post 26 Jun 2010, 02:20
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A
B
C
D
E

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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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Re: Number System- Divisibility [#permalink] New post 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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Re: Number System- Divisibility [#permalink] New post 26 Jun 2010, 03:25
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RenukaD 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).

Answer: A and C.
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Re: Number System- Divisibility [#permalink] New post 26 Jun 2010, 08:47
Bunuel wrote:
RenukaD 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).

Answer: A and C.

Thanks for the solution :)

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