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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Wed Sep 28, 2011 4:17 am

WHat is the sum of the digits of (10^25) - 361?

A) 207
B) 216
C) 225
D) 234
E) 241

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Source: Beat The GMAT — Problem Solving | Wed Sep 28, 2011 4:17 am

gmatclubmember: Master | Next Rank: 500 Posts; Posts: 158; Joined: Sat Sep 03, 2011 10:31 amFollowed by: 2 members; Thanked: 29 times

by gmatclubmember » Wed Sep 28, 2011 4:35 am

shankar.ashwin wrote:WHat is the sum of the digits of (10^25) - 361?

A) 207
B) 216
C) 225
D) 234
E) 241

A. 207
There will be 21, 9's followed by 639 (639+361=1000). so sum will be 21*9+6+3+9=189+18=207.

a lil' Thank note goes a long way

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Sep 28, 2011 4:45 am

shankar.ashwin wrote:WHat is the sum of the digits of (10^25) - 361?

A) 207
B) 216
C) 225
D) 234
E) 241

Start with an easier example:
10^4 - 361 = 10,000-361 = 9639.

Notice that 10^4 is a 5-digit integer -- the smallest possible.
When we subtract 361, the result is a 4-digit integer whose 3 rightmost digits are 6, 3, and 9. The remaining digit is 9.
10^25 is a 26-digit integer -- the smallest possible.
Thus, when we subtract 361, the result will be a 25-digit integer whose 3 rightmost digits are 6, 3, and 9. The remaining 22 digits will each be 9.
Sum = (22*9) + (6+3+9) = 216.

The correct answer is B.

Last edited by GMATGuruNY on Wed Sep 28, 2011 6:56 am, edited 2 times in total.

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gmatclubmember: Master | Next Rank: 500 Posts; Posts: 158; Joined: Sat Sep 03, 2011 10:31 amFollowed by: 2 members; Thanked: 29 times

by gmatclubmember » Wed Sep 28, 2011 4:56 am

gmatclubmember wrote:
shankar.ashwin wrote:WHat is the sum of the digits of (10^25) - 361?

A) 207
B) 216
C) 225
D) 234
E) 241
A. 207
There will be 21, 9's followed by 639 (639+361=1000). so sum will be 21*9+6+3+9=189+18=207.

I missed one 9, instead of 21 there will be 22.

and hence the answer would be 216

a lil' Thank note goes a long way

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user123321: Master | Next Rank: 500 Posts; Posts: 385; Joined: Fri Sep 23, 2011 9:02 pmFollowed by: 6 members; Thanked: 62 times

by user123321 » Wed Sep 28, 2011 5:52 am

gmatclubmember wrote:
shankar.ashwin wrote:WHat is the sum of the digits of (10^25) - 361?

A) 207
B) 216
C) 225
D) 234
E) 241
A. 207
There will be 21, 9's followed by 639 (639+361=1000). so sum will be 21*9+6+3+9=189+18=207.

I think there should be 22 9's. then answer should be 216. OA please

user123321

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