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The remainder obtained by the division of two numbers by a common divi

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Bunuel
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The remainder obtained by the division of two numbers by a common divi [#permalink] New post   16 Nov 2021, 06:00
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The remainder obtained by the division of two positive integers by a common divisor are 33 and 47 respectively. However when the sum of these two numbers is divided by the same divisor, the remainder obtained is only 30. What is the divisor?

A. 20
B. 30
C. 40
D. 50
E. 65
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D
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Re: The remainder obtained by the division of two numbers by a common divi [#permalink] New post   16 Nov 2021, 06:22
Option (D) in my opinion.

Let the two positive no.s be x and y.

Let the common divisor be a.

Given:
x = a*k1 + 33. Implies x > 33
y = a*k2 + 47. Implies x > 47

Adding both gives, x + y = a (k1*k2) + 80.

But, given that the sum of two no.s leaves a remainder of 30 only when divided by a.
It can be possible only when a = 50.
Because, then, x + y = 50(k1*k2) + 50 + 30, will leave the remainder 30 when divided by 30 (for a > 47).
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Re: The remainder obtained by the division of two numbers by a common divi [#permalink] New post   30 Dec 2021, 05:36
Given x = Dq1 + 33
and y = Dq2 + 47
and x + y = Dm + 80

Dq1 + Dq2 - Dm = 50
D(q1 + q2 -M) = 50
this means D is a multiple of 50, and by option only D is 50 and other are not a mutliple of 50. hence D.
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Re: The remainder obtained by the division of two numbers by a common divi [#permalink] New post   03 Apr 2024, 05:05
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­↧↧↧ Detailed Video Solution to the Problem ↧↧↧



The remainder obtained by the division of two positive integers by a common divisor are 33 and 47 respectively.

Since the remainder obtained by dividing two numbers by a divsior is 33 and 47
=> Divisor will be more than 47

For simplicity let's say the two numbers are 33 and 47.

However when the sum of these two numbers is divided by the same divisor, the remainder obtained is only 30.

=> Remainder of (33+47)/divisor = Remainder of 80/divisor = 30
=> Divisor can be 50 as 80/50 remainder is 30

So, Answer will be D
Hope it helps!

Watch the following video to MASTER Remainders
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gmatclubot
Re: The remainder obtained by the division of two numbers by a common divi [#permalink]
03 Apr 2024, 05:05
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