Oct 15 12:00 PM PDT  01:00 PM PDT Join this live GMAT class with GMAT Ninja to learn to conquer your fears of long, kooky GMAT questions. Oct 16 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 25 Jan 2010
Posts: 99
Location: Calicut, India

Two numbers when divided by a divisor leave reminders of 248
[#permalink]
Show Tags
23 Nov 2011, 09:14
Question Stats:
75% (02:19) correct 25% (02:32) wrong based on 602 sessions
HideShow timer Statistics
Two numbers when divided by a divisor leave reminders of 248 and 372 respectively. The reminder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor. A. 276 B. 552 C. 414 D. 1104 E. 2202
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
If u think this post is useful plz feed me with a kudo




Manager
Joined: 29 Oct 2011
Posts: 143
Concentration: General Management, Technology
GPA: 3.76

Re: Numbers #3
[#permalink]
Show Tags
23 Nov 2011, 09:57
Fun question.
Say the two numbers are x and y, and divisor is a.
x divided by a leaves a remainder of 248. This means that x = a*N + 248, where N is the integer result of the division. y divided by a leaves a remainder of 372. This means that x = a*K + 372, where K is the integer result of the division.
x+y divided by a leaves a remainder of 68. This means that x = a*M + 68, where M is the integer result of the division.
From definitions above:
x+y = (a*N + 248) + (a*K + 372) = a*(N+K) + 620.
a*(N+K) + 620 = a*M + 68 552 = a*(MNK)
We know that M, N, and K are integers and that a must be at least 373 (to leave a 372 remainder). The only possible value for (MNK) is 1.
Therefore, a = 552. B.




Manager
Joined: 25 Jan 2010
Posts: 99
Location: Calicut, India

Re: Numbers #3
[#permalink]
Show Tags
23 Nov 2011, 10:58
cleetus wrote: Two numbers when divided by a divisor leave reminders of 248 and 372 respectively. The reminder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor. A) 276 B) 552 C) 414 D 1104 E) 2202 Thanks kostyan5. My approach is similar to that of urs. This is how i did it. Let the 2 numbers be X and Y; Let D= Divisor X = D*N+248 , N = Quotient got when X is divided by divisor R Y = D*K+372 , K = Quotient got when Y is divided by divisor R X+Y = (D*N+248) + (D*K+372) = D(N+K)+620 = D(N+K+552/D)+68 As N+K+552/D must be an integer, D must be a factor of 552. As any divisor is greater than the reminder, D>372 So D=552 Answe B
_________________
If u think this post is useful plz feed me with a kudo



Intern
Joined: 25 Aug 2011
Posts: 19
Concentration: Entrepreneurship, General Management
GMAT Date: 01312012

Re: Numbers #3
[#permalink]
Show Tags
30 Jan 2012, 21:55
kostyan5 wrote: Fun question.
Say the two numbers are x and y, and divisor is a.
x divided by a leaves a remainder of 248. This means that x = a*N + 248, where N is the integer result of the division. y divided by a leaves a remainder of 372. This means that x = a*K + 372, where K is the integer result of the division.
x+y divided by a leaves a remainder of 68. This means that x = a*M + 68, where M is the integer result of the division.
From definitions above:
x+y = (a*N + 248) + (a*K + 372) = a*(N+K) + 620.
a*(N+K) + 620 = a*M + 68 552 = a*(MNK)
We know that M, N, and K are integers and that a must be at least 373 (to leave a 372 remainder). The only possible value for (MNK) is 1.
Therefore, a = 552. B. ok, "a" must be at least 373, but then why not 414 instead of 552? Thanks!



Math Expert
Joined: 02 Sep 2009
Posts: 58332

Re: Numbers #3
[#permalink]
Show Tags
31 Jan 2012, 02:21
Saurajm wrote: kostyan5 wrote: Fun question.
Say the two numbers are x and y, and divisor is a.
x divided by a leaves a remainder of 248. This means that x = a*N + 248, where N is the integer result of the division. y divided by a leaves a remainder of 372. This means that x = a*K + 372, where K is the integer result of the division.
x+y divided by a leaves a remainder of 68. This means that x = a*M + 68, where M is the integer result of the division.
From definitions above:
x+y = (a*N + 248) + (a*K + 372) = a*(N+K) + 620.
a*(N+K) + 620 = a*M + 68 552 = a*(MNK)
We know that M, N, and K are integers and that a must be at least 373 (to leave a 372 remainder). The only possible value for (MNK) is 1.
Therefore, a = 552. B. ok, "a" must be at least 373, but then why not 414 instead of 552? Thanks! If we follow kostyan5's way we get 552=a*(MNK) > (MNK)=integer=552/a, no other value from the answer choices will yield an integer for this expression except 552 and 276, and as a>372 then a=552. Hope it's clear.
_________________



Intern
Joined: 17 Jan 2012
Posts: 41

Re: Two numbers when divided by a divisor leave reminders of 248
[#permalink]
Show Tags
31 Jan 2012, 03:24
Once we know that a=552/ (MNK),
Can we say that a < or = 552. And since 372 is one of the remainders (eliminates A. 276) the only possibility is 552 itself.



Intern
Joined: 27 Apr 2012
Posts: 1

Re: Numbers #3
[#permalink]
Show Tags
11 May 2012, 20:33
kostyan5 wrote: Fun question.
Say the two numbers are x and y, and divisor is a.
x divided by a leaves a remainder of 248. This means that x = a*N + 248, where N is the integer result of the division. y divided by a leaves a remainder of 372. This means that x = a*K + 372, where K is the integer result of the division.
x+y divided by a leaves a remainder of 68. This means that x = a*M + 68, where M is the integer result of the division.
From definitions above:
x+y = (a*N + 248) + (a*K + 372) = a*(N+K) + 620.
a*(N+K) + 620 = a*M + 68 552 = a*(MNK)
We know that M, N, and K are integers and that a must be at least 373 (to leave a 372 remainder). The only possible value for (MNK) is 1.
Therefore, a = 552. B. Why did you decide the a must be at least 373 and not 248? That's the other remainder.



Math Expert
Joined: 02 Sep 2009
Posts: 58332

Re: Numbers #3
[#permalink]
Show Tags
12 May 2012, 02:43
elaskova wrote: kostyan5 wrote: Fun question.
Say the two numbers are x and y, and divisor is a.
x divided by a leaves a remainder of 248. This means that x = a*N + 248, where N is the integer result of the division. y divided by a leaves a remainder of 372. This means that x = a*K + 372, where K is the integer result of the division.
x+y divided by a leaves a remainder of 68. This means that x = a*M + 68, where M is the integer result of the division.
From definitions above:
x+y = (a*N + 248) + (a*K + 372) = a*(N+K) + 620.
a*(N+K) + 620 = a*M + 68 552 = a*(MNK)
We know that M, N, and K are integers and that a must be at least 373 (to leave a 372 remainder). The only possible value for (MNK) is 1.
Therefore, a = 552. B. Why did you decide the a must be at least 373 and not 248? That's the other remainder. Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is nonnegative integer and always less than divisor).So, the divisor mus be greater than both remainders, which means that a>372. Also check this: twonumberswhendividedbyadivisorleaveremindersof123645.html#p1036863Hope it helps.
_________________



Intern
Joined: 25 Sep 2012
Posts: 1

Re: Numbers #3
[#permalink]
Show Tags
06 Oct 2012, 06:32
A rule to solve all similar problems 
If two numbers, say a & b, are divided by the same divisor (d) leaving remainders r1 & r2.
Then the remainder (R), when Sum (a+b) / d = (r1+r2)  d. Note  If R becomes negative, then R = (r1+r2) only.
Hence Solution to the above problem 
d = 68, r1 = 248, r2 = 372 so Remainder R when Sum (a+b) / 68 = (248+372)  68 = 620  68 = 552
Note  Difference (ab) is exactly divisible by the same divisor (d).
Hope it helps.



SVP
Joined: 06 Sep 2013
Posts: 1572
Concentration: Finance

Re: Two numbers when divided by a divisor leave reminders of 248
[#permalink]
Show Tags
17 Dec 2013, 15:33
cleetus wrote: Two numbers when divided by a divisor leave reminders of 248 and 372 respectively. The reminder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor.
A. 276 B. 552 C. 414 D. 1104 E. 2202 Easy, why 68 if the sum of the remainders is 248+372=620? Cause the divisor is eating the other part. Then the divisor is 62068=552 Answer is A Cheers! J



Manager
Joined: 28 Apr 2014
Posts: 195

Re: Two numbers when divided by a divisor leave reminders of 248
[#permalink]
Show Tags
01 May 2014, 03:05
jlgdr wrote: cleetus wrote: Two numbers when divided by a divisor leave reminders of 248 and 372 respectively. The reminder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor.
A. 276 B. 552 C. 414 D. 1104 E. 2202 Easy, why 68 if the sum of the remainders is 248+372=620? Cause the divisor is eating the other part. Then the divisor is 62068=552 Answer is A Cheers! J you mean B !!. Answer given is correct but option marked is incorrect. This was the smartest approach of the lot and I used the same.. If 620 is equating to 68 , what was the remaining amount ( 620  68). This added one unit to divisor



Manager
Joined: 21 Jun 2016
Posts: 75
Location: India

Re: Two numbers when divided by a divisor leave reminders of 248
[#permalink]
Show Tags
12 Jul 2016, 04:27
friends... I have a question ... Why (MNK) has to be one.... In other words why the answer is 552 and not 1104...



Manager
Joined: 29 May 2017
Posts: 125
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability

Re: Two numbers when divided by a divisor leave reminders of 248
[#permalink]
Show Tags
26 Oct 2018, 05:24
VeritasKarishmahi....i did this question as follows: x: dp + 248 y: dq + 372 x+y: dr + 68 setting p,q,r as 1, I get 2d + 620 equals d + 68 solving for d i get 552 Note: i have attempted similar questions like and just ignored the negative sign. Am wondering if you can pin point a pitfall in this approach? and please tell me why the answers are correct.. regards



Intern
Joined: 03 Nov 2018
Posts: 3

Re: Two numbers when divided by a divisor leave reminders of 248
[#permalink]
Show Tags
05 Nov 2018, 00:28
248+372=620
62068=552( answer )
Posted from my mobile device




Re: Two numbers when divided by a divisor leave reminders of 248
[#permalink]
05 Nov 2018, 00:28






