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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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New post 26 Jun 2010, 03:20
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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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Re: Number System- Divisibility [#permalink]

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New post 26 Jun 2010, 04:17
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]

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New post 26 Jun 2010, 04:25
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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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Manager
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Joined: 24 Jan 2010
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Kudos [?]: 45 [0], given: 14

Re: Number System- Divisibility [#permalink]

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New post 26 Jun 2010, 09:47
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, 09:47
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If x is divisible by 42. Which of the following numbers is d

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