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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

86% (01:13) correct
14% (07:53) wrong based on 132 sessions

HideShow timer Statistics

When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 13?

When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 13?

A. 7 B. 21 C. 34 D. 47 E. 55

...

hi,

firstly you can eliminate B, C and D straightway.. all have a difference of 13, so either all 3 can divide or none can.. since we cannot have three answers, all three can be eliminated...

Now X= 143q + 45 = 11*13*q + 45..so we have to make only 45 div by 13..

When a certain number X is divided by 143, the remainder is 45. Which [#permalink]

Show Tags

19 Apr 2016, 10:23

Bunuel wrote:

When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 13?

A. 7 B. 21 C. 34 D. 47 E. 55

Posting a different approach

Least possible value of x is 188

188/13 = 182 and remainder 6

Thus we need 7 more to make the number divisible by 13

Hence answer will be 7 !! _________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

Re: When a certain number X is divided by 143, the remainder is 45. Which [#permalink]

Show Tags

19 Apr 2016, 15:33

1

This post was BOOKMARKED

So the number given is N = 143Q + 45

If this number is divided by 13, the remainder would be R[(143Q + 45)/13]

Since 143 is divisible by 13 , the product 143Q gives no remainder This means the remainder of 45/13 should be the remainder of the entire number N which is 6

To make it divisible by 13 , the smallest number that can be added = 13 - 6 = 7

Re: When a certain number X is divided by 143, the remainder is 45. Which [#permalink]

Show Tags

20 Apr 2016, 14:07

Excellent Question Now if the Question said subtract the answer was 6 or 6- 13p where p is an integer here as it says add => the number must be of the form => 7+13P only A satisfies that..
_________________

Re: When a certain number X is divided by 143, the remainder is 45. Which [#permalink]

Show Tags

04 May 2016, 19:31

the equation becomes- X=143q+45, take the smallest values for q, i.e 0. So now we have 45, nearest multiple is 52(ques. says add), hence the next multiple. 52-45=7.

When a certain number X is divided by 143, the reminder is 45 [#permalink]

Show Tags

03 Oct 2017, 17:44

Mo2men wrote:

When a certain number X is divided by 143, the reminder is 45. Which of the following numbers, if added to X, would result in a number divisible by 13?

1) 7

2) 21

3) 34

4) 47

5) 55

If X = 143a + 45, and a = 1, then

X = (143(1) + 45) = 188

What number could be added to 188 to make it evenly divisible by 13? Obviously, we need a multiple of 13.

(13*13) = 169 --> +13 is (13*14) = 182 --> +13 is (13*15) = 195. Bingo

X = 188. Adding 7 to 188 equals 195, which is divisible by 13.

That is, 188 + 7 = 195

Answer A

Last edited by genxer123 on 03 Oct 2017, 17:58, edited 1 time in total.

When a certain number X is divided by 143, the reminder is 45 [#permalink]

Show Tags

03 Oct 2017, 17:56

Mo2men wrote:

I think you mean either \(\frac{X}{143}\) = a +\(\frac{45}{143}\) or \(X = 143 a + 45\)

Both of your suggestions are more clear than what I have, and certainly more aligned with the division theorem as it is typically written. I'll edit. Thanks!

Re: When a certain number X is divided by 143, the remainder is 45. Which [#permalink]

Show Tags

03 Oct 2017, 21:18

Bunuel wrote:

When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 13?

A. 7 B. 21 C. 34 D. 47 E. 55

x=143+45 143 is a multiple of 13 the next multiple of 13 above 45 is 52 52-45=7 A