## Problem of the day 14.7.09

**Given that 1025/1024=1.0009765625, find the sum of the digits of 5 ^{10}?**

** **

**(a) 36 (b) 40 (c) 50 (d) 102 (e) 41**

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For All Your Quant Queries

**Given that 1025/1024=1.0009765625, find the sum of the digits of 5 ^{10}?**

** **

**(a) 36 (b) 40 (c) 50 (d) 102 (e) 41**

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Written by Implex

July 14, 2009 at 1:22 pm

Posted in Algebra, CAT 2009, Mock Cat, Mock Quant, Number Thoery, Online CAT, Problem of the week, Problems

Tagged with Algebra, CAT 2009, IIM, Number Theory, Online CAT

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“the sum of the digits should leave 4 as the remainder on division by 9”

anonymousJuly 14, 2009 at 6:10 pm

Nicely done, this is the method I was looking for!

RahulJuly 14, 2009 at 7:42 pm

guys could you elaborate on the method ?

HariJuly 15, 2009 at 4:57 am

First one is 5^10 gives a remainder 4 on division by 9. only one option gives the same. Hint: Whenever we talk about digit sum, think of modulo 9.

Second 1025/1024-1=1/2^10=0.0009675625

Hence 5^10=10^10/1024=9765625

hence sum of digits is 40.

RahulJuly 15, 2009 at 10:10 am

thanx a lot ..buddies ..for d xplanation

anupJuly 15, 2009 at 4:34 pm

Rahul…it is always required ro see in terms of 9…

PrateekJuly 15, 2009 at 5:47 pm

it helps to think in terms of modulo 9

as divisibility rule of 9 talks about sum of digits

RahulJuly 15, 2009 at 5:50 pm

Hey rahul can u even tell me how to prepare for DI and Verbal part..in terms of CAt

PrateekJuly 15, 2009 at 5:53 pm

for verbal I have another blog, http://verballogic.wordpress.com

FOr DI, practice as many sets as possible.

The best advice is visit http://www.testfunda.com regularly..

I am active there, along with a huge group of CAT aspirants

RahulJuly 15, 2009 at 6:50 pm

Thnx man…

HariJuly 15, 2009 at 6:47 pm

hey…u posted a hint above..

Hint: Whenever we talk about digit sum, think of modulo 9.

pl could u elaborate on that..thnkss:)

SamJuly 17, 2009 at 9:31 am

I have explained in the comment above yours

RahulJuly 23, 2009 at 8:15 am