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Manager  Joined: 25 Jan 2010
Posts: 99
Location: Calicut, India
Two numbers when divided by a divisor leave reminders of 248  [#permalink]

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33 00:00

Difficulty:   35% (medium)

Question Stats: 75% (02:19) correct 25% (02:32) wrong based on 602 sessions

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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

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Manager  Joined: 29 Oct 2011
Posts: 143
Concentration: General Management, Technology
Schools: Sloan '16 (D)
GMAT 1: 760 Q49 V44 GPA: 3.76
Re: Numbers #3  [#permalink]

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3
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*(M-N-K)

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 (M-N-K) is 1.

Therefore, a = 552. B.
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Manager  Joined: 25 Jan 2010
Posts: 99
Location: Calicut, India
Re: Numbers #3  [#permalink]

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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
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Intern  Joined: 25 Aug 2011
Posts: 19
Concentration: Entrepreneurship, General Management
GMAT Date: 01-31-2012
Re: Numbers #3  [#permalink]

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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*(M-N-K)

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 (M-N-K) is 1.

Therefore, a = 552. B.

ok, "a" must be at least 373, but then why not 414 instead of 552? Thanks!
Math Expert V
Joined: 02 Sep 2009
Posts: 58332
Re: Numbers #3  [#permalink]

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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*(M-N-K)

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 (M-N-K) 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*(M-N-K) --> (M-N-K)=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.
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Intern  Joined: 17 Jan 2012
Posts: 41
GMAT 1: 610 Q43 V31 Re: Two numbers when divided by a divisor leave reminders of 248  [#permalink]

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1
Once we know that a=552/ (M-N-K),

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]

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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*(M-N-K)

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 (M-N-K) 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 V
Joined: 02 Sep 2009
Posts: 58332
Re: Numbers #3  [#permalink]

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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*(M-N-K)

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 (M-N-K) 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 non-negative integer and always less than divisor).

So, the divisor mus be greater than both remainders, which means that a>372.

Also check this: two-numbers-when-divided-by-a-divisor-leave-reminders-of-123645.html#p1036863

Hope it helps.
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Intern  Joined: 25 Sep 2012
Posts: 1
Re: Numbers #3  [#permalink]

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5
4
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 (a-b) 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]

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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 620-68=552

Cheers!
J Manager  Joined: 28 Apr 2014
Posts: 195
Re: Two numbers when divided by a divisor leave reminders of 248  [#permalink]

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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 620-68=552

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]

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friends... I have a question ...
Why (M-N-K) has to be one....
In other words why the answer is 552 and not 1104...
Manager  B
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]

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hi....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]

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248+372=620

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