sum of all the digits

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wishkaro: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Wed Feb 18, 2009 3:13 am; Thanked: 3 times

by wishkaro » Tue May 05, 2009 9:14 am

What is the sum of all the digits in the number 9^27-27?
A. 81 B. 24 C. 28 D. 92 E. 100

OA [spoiler] A
9(9^26 – 3)
Sum of digits is always a multiple of 9. So A.[/spoiler]

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Source: Beat The GMAT — Problem Solving | Tue May 05, 2009 9:14 am

Vemuri: Legendary Member; Posts: 682; Joined: Fri Jan 16, 2009 2:40 amFollowed by: 1 member; Thanked: 32 times

Re: sum of all the digits

by Vemuri » Tue May 05, 2009 9:28 am

wishkaro wrote:What is the sum of all the digits in the number 9^27-27?
A. 81 B. 24 C. 28 D. 92 E. 100

OA [spoiler] A
9(9^26 – 3)
Sum of digits is always a multiple of 9. So A.[/spoiler]

Good question. Thanks for posting.

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avenus: Master | Next Rank: 500 Posts; Posts: 238; Joined: Tue Feb 10, 2009 8:44 am; Thanked: 9 times

by avenus » Tue May 05, 2009 3:49 pm

agree with the reasoning, but there's something wrong with this question:

9^27 - 27= 58 149737 003040 059690 390142

Sum of digits is 99, not 81

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Pranay: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Tue May 05, 2009 1:58 am; Thanked: 1 times

by Pranay » Wed May 06, 2009 1:52 am

9^27 results in a number which is a multiple of 9 and whose recursive sum of digits should be equal to 9.

27 is again a multiple of 9.

From my observation,

Any number which is a multiple of 9, has recursive sum of digits summed up to 9.

and

When a multiple of 9 is subtracted from another multiple of 9, the result is always a multiple of 9.

Since, the result is again a multiple of 9, from observation 1, only option A satisifies and matches my observation.

Thus, I conclude the answer to be A.
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Hope, it helps.

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satish.nagdev: Master | Next Rank: 500 Posts; Posts: 130; Joined: Sat Dec 29, 2007 5:35 am; Location: SGP; Thanked: 5 times

by satish.nagdev » Wed May 06, 2009 2:14 am

avenus wrote:agree with the reasoning, but there's something wrong with this question:

9^27 - 27= 58 149737 003040 059690 390142

Sum of digits is 99, not 81

99 isn't given in answer choices !!!

Wounded by GMAT but not dead

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