11^2 and 3^3 are factors

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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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Source: Beat The GMAT — Problem Solving | Tue Feb 24, 2009 4:43 am

bluementor: Master | Next Rank: 500 Posts; Posts: 418; Joined: Wed Jun 11, 2008 5:29 am; Thanked: 65 times

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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sureshbala: Master | Next Rank: 500 Posts; Posts: 319; Joined: Wed Feb 04, 2009 10:32 amFollowed by: 9 members; Location: Delhi; Thanked: 84 times

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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willbeatthegmat: Senior | Next Rank: 100 Posts; Posts: 71; Joined: Sat Sep 20, 2008 5:48 am; Thanked: 5 times

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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sudi760mba: Senior | Next Rank: 100 Posts; Posts: 85; Joined: Wed Aug 13, 2008 2:21 am; Thanked: 1 times

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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x2suresh: Master | Next Rank: 500 Posts; Posts: 258; Joined: Thu Aug 07, 2008 5:32 am; Thanked: 16 times

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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