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11^2 and 3^3 are factors

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by sanju09 » Tue Feb 24, 2009 4:43 am
If both 11^2 and 3^3 are factors of the number a * 4^3 * 6^2 * 13^11, then what is the smallest possible value of a?

A. 121
B. 3267
C. 363
D. 33
E. None of the above
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by bluementor » Tue Feb 24, 2009 4:52 am
a x 4^3 x 6^2 x 13^11
=a x 2^6 x (2^2 x 3^2) x 13^11
=a x 2^8 x 3^2 x 13^11 (Prime factorized)

Since 3^3 is a factor (with 3^2 already accounted apart from a), therefore a must contain at least one multiple of 3.

Since 11^2 is a factor and has not been accounted anywhere else, therefore it must be contained within a.

Therefore, a must be at least 11^2 x 3 = 363.

Choose C.

-BM-
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Re: 11^2 and 3^3 are factors

by sureshbala » Tue Feb 24, 2009 4:54 am
sanju09 wrote:If both 11^2 and 3^3 are factors of the number a * 4^3 * 6^2 * 13^11, then what is the smallest possible value of a?

A. 121
B. 3267
C. 363
D. 33
E. None of the above
Clearly we need to have a minimum of 11^2 and a 3 in the value of a.

Hence minimum value of a = 11^2 x 3 = 363
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by willbeatthegmat » Tue Feb 24, 2009 4:58 am
If both 11^2 and 3^3 are factors of the number a * 4^3 * 6^2 * 13^11, then what is the smallest possible value of a?

A. 121
B. 3267
C. 363
D. 33
E. None of the above

Ans

If 11^2 and 3^3 are factors of the number a * 4^3 * 6^2 * 13^11 , that means a * 4^3 * 6^2 * 13^11 should be divisible by 11^2 and 3^3.
look for common factors in the number & cancel them out. Like both have 3^2 in common.

(a * 4^3 * 3^2 *2^2 * 13^11) /11^2 * 3^3
= (a * 4^3 *2^2 * 13^11) /11^2 * 3^1
A should be equal to 11^2 *3 = 363 to be divible by 11^2 * 3^3.

Ans C
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Re: 11^2 and 3^3 are factors

by sudi760mba » Tue Feb 24, 2009 12:55 pm
sureshbala wrote:
sanju09 wrote:If both 11^2 and 3^3 are factors of the number a * 4^3 * 6^2 * 13^11, then what is the smallest possible value of a?

A. 121
B. 3267
C. 363
D. 33
E. None of the above
Clearly we need to have a minimum of 11^2 and a 3 in the value of a.

Hence minimum value of a = 11^2 x 3 = 363
Suresh,

I can understand the need for 11^2 but why only one 3?

Thanks.

Sudi
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Re: 11^2 and 3^3 are factors

by x2suresh » Tue Feb 24, 2009 1:04 pm
sudi760mba wrote:
sureshbala wrote:
sanju09 wrote:If both 11^2 and 3^3 are factors of the number a * 4^3 * 6^2 * 13^11, then what is the smallest possible value of a?

A. 121
B. 3267
C. 363
D. 33
E. None of the above
Clearly we need to have a minimum of 11^2 and a 3 in the value of a.

Hence minimum value of a = 11^2 x 3 = 363
Suresh,

I can understand the need for 11^2 but why only one 3?

Thanks.

Sudi
a * 4^3 * 6^2 * 13^11

because 6^2 already has two 3's
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