GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 27 Jun 2019, 02:05

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A positive integer is divisible by 9 if and only if the sum of its

Author Message
TAGS:

### Hide Tags

Director
Joined: 19 Oct 2013
Posts: 525
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: A positive integer is divisible by 9 if and only if the sum of its  [#permalink]

### Show Tags

26 Oct 2018, 17:47
A positive integer is divisible by 9 if and only if the sum of its digits is divisible by 9. If n is a positive integer, for which of the following values of k is $$25*10^n + k*10^{2n}$$ divisible by 9?

(A) 9
(B) 16
(C) 23
(D) 35
(E) 47

In this question regardless of the value of n we will have units digit of 0

So we are concerned with how 2+5+k adds up to a number divisible by 9

if we take 2+5+4+7 = 18 a number divisible by 9.

Director
Joined: 29 Jun 2017
Posts: 740
Re: A positive integer is divisible by 9 if and only if the sum of its  [#permalink]

### Show Tags

27 Dec 2018, 21:51
A positive integer is divisible by 9 if and only if the sum of its digits is divisible by 9. If n is a positive integer, for which of the following values of k is $$25*10^n + k*10^{2n}$$ divisible by 9?

(A) 9
(B) 16
(C) 23
(D) 35
(E) 47

is this from official source.
this is hard. many person do it wrongly

because k*10^2n has at least 1 number more than 25*10^n, we know that the sume of the two number will be
K25*10^x
for exam ple if k=52
the sume will be
5225*10^n

ONLY THIS CASE HAPPEN, we can add the digit, and find the answer is E.
Re: A positive integer is divisible by 9 if and only if the sum of its   [#permalink] 27 Dec 2018, 21:51

Go to page   Previous    1   2   [ 22 posts ]

Display posts from previous: Sort by