Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47032

When a certain number X is divided by 143, the remainder is 45. Which [#permalink]
Show Tags
19 Apr 2016, 03:12
Question Stats:
84% (01:16) correct 16% (06:15) wrong based on 167 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Aug 2009
Posts: 6217

Re: When a certain number X is divided by 143, the remainder is 45. Which [#permalink]
Show Tags
19 Apr 2016, 04:55
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 ... 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..A.7 45 + 7 = 42 YES E. 5545 + 55 = 100 No ans A
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3632
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

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
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Manager
Joined: 12 Jun 2015
Posts: 79

Re: When a certain number X is divided by 143, the remainder is 45. Which [#permalink]
Show Tags
19 Apr 2016, 15:33
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
Correct Option : A



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2646

Re: When a certain number X is divided by 143, the remainder is 45. Which [#permalink]
Show Tags
20 Apr 2016, 14:07



Retired Moderator
Joined: 23 Sep 2015
Posts: 387
Location: France
GMAT 1: 690 Q47 V38 GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)

Re: When a certain number X is divided by 143, the remainder is 45. Which [#permalink]
Show Tags
22 Apr 2016, 11:43
since 143 is divisible by 13, x divided by 13 yields a remainder of 45/13 ==> 6 7 should be added to yield 13. Answer A
_________________
New Application Tracker : update your school profiles instantly!



Current Student
Joined: 15 Mar 2016
Posts: 96
Location: India
Concentration: Operations
WE: Engineering (Other)

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. 5245=7.



Manager
Joined: 16 Mar 2016
Posts: 130
Location: France
GPA: 3.25

Re: When a certain number X is divided by 143, the remainder is 45. Which [#permalink]
Show Tags
05 May 2016, 05:53
X = 143 x k + 45
143 = 11 x 13
the least integer after 45 to be divisible by 13 is 52 (13 x 4 ) = 45 + 7



SC Moderator
Joined: 22 May 2016
Posts: 1825

When a certain number X is divided by 143, the reminder is 45 [#permalink]
Show Tags
Updated on: 03 Oct 2017, 17:58
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
_________________
In the depths of winter, I finally learned that within me there lay an invincible summer.  Albert Camus, "Return to Tipasa"
Originally posted by generis on 03 Oct 2017, 17:44.
Last edited by generis on 03 Oct 2017, 17:58, edited 1 time in total.



SVP
Joined: 26 Mar 2013
Posts: 1719

Re: When a certain number X is divided by 143, the reminder is 45 [#permalink]
Show Tags
03 Oct 2017, 17:50
genxer123 wrote: If \(\frac{X}{143}\) = a + 45, and a = 1, then
X = ((1)143 + 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 I think you mean either \(\frac{X}{143}\) = a +\(\frac{45}{143}\) or \(X = 143 a + 45\)



SC Moderator
Joined: 22 May 2016
Posts: 1825

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!
_________________
In the depths of winter, I finally learned that within me there lay an invincible summer.  Albert Camus, "Return to Tipasa"



VP
Joined: 07 Dec 2014
Posts: 1034

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 5245=7 A




Re: When a certain number X is divided by 143, the remainder is 45. Which
[#permalink]
03 Oct 2017, 21:18






