GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 14 Jul 2020, 15:19

### 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: 503
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, 16:47
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.

VP
Joined: 29 Jun 2017
Posts: 1053
Re: A positive integer is divisible by 9 if and only if the sum of its  [#permalink]

### Show Tags

27 Dec 2018, 20:51
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.
Manager
Joined: 21 Aug 2019
Posts: 132
Re: A positive integer is divisible by 9 if and only if the sum of its  [#permalink]

### Show Tags

30 Jan 2020, 02:05
I took n=1
so equation became:
25*10^1 + k * 10^2(1) = 0
=250 + 100k = 0
= 50 (5 + 2k) = 0
now plug in values and check for answers
= 5 + 2(47)
=5+94
=99

is my approach correct?
_________________
I don't believe in giving up!
Intern
Joined: 19 Jan 2019
Posts: 47
Re: A positive integer is divisible by 9 if and only if the sum of its  [#permalink]

### Show Tags

05 Feb 2020, 11:38
25*10^n+K*10^2n ---> assuming n=1 as it will have least impact when adding digits (10(25+10K))
substitute k values from option (10(25+470))--> 4950 ___ adding digits 18 hence e
Manager
Joined: 12 Oct 2015
Posts: 235
GMAT 1: 700 Q47 V39
GPA: 3
WE: Accounting (Accounting)
A positive integer is divisible by 9 if and only if the sum of its  [#permalink]

### Show Tags

17 Feb 2020, 11:01
A very simple approach.

_________________
Winners dont make excuses.

350--> 700

https://gmatclub.com/forum/700-q47-v39-ir-7-awa-246682.html
Intern
Joined: 01 Sep 2011
Posts: 14
Re: A positive integer is divisible by 9 if and only if the sum of its  [#permalink]

### Show Tags

03 Mar 2020, 01:28
stonecold wrote:
Excellent Question
Here Taking out 10^n common => 100k+25 must be divisible by 9
checking values (try and start with last in such questions of plugging in values ) we get => E

After Taking out 10^n
the expression would be,
10^n(25+k.10^n))
Re: A positive integer is divisible by 9 if and only if the sum of its   [#permalink] 03 Mar 2020, 01:28

Go to page   Previous    1   2   [ 26 posts ]