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# Quants - Problems

Author Message
Director
Affiliations: SAE
Joined: 11 Jul 2012
Posts: 513
Location: India
Concentration: Strategy, Social Entrepreneurship
GMAT 1: 710 Q49 V37
GPA: 3.5
WE: Project Management (Energy and Utilities)

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12 Sep 2012, 22:54
A no when divided by D gives remainder 7 and when divided by 3D gives remainder 20.
What will be the remainder when twice the number is divided by 3D?

a.1
b.40.
c.27
d.13
e.can' be determined
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)

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13 Sep 2012, 01:13
1
KUDOS
getgyan wrote:
A no when divided by D gives remainder 7 and when divided by 3D gives remainder 20.
What will be the remainder when twice the number is divided by 3D?

a.1
b.40.
c.27
d.13
e.can' be determined

Denote our number by N. Then we can write:
N = DQ + 7, where Q is a non-negative integer. Necessarily 7 < D.
N = 3Dq + 20, where q is also a non-negative integer, and 20 < 3D.
From the above two equations, we can deduce that DQ + 7 = 3Dq + 20, or D(Q - 3q) = 13.
It follows that D must be a factor of 13, and since D > 7, then D must be equal to 13.

From the second equality, multiplying by 2, we obtain 2N = 6 * 13q + 40 = (3 * 13)*(2q) + 3 * 13 + 1, which means that the remainder when 2N is divided by 3D = 3 * 13 is 1.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Director
Affiliations: SAE
Joined: 11 Jul 2012
Posts: 513
Location: India
Concentration: Strategy, Social Entrepreneurship
GMAT 1: 710 Q49 V37
GPA: 3.5
WE: Project Management (Energy and Utilities)

### Show Tags

13 Sep 2012, 01:29
getgyan wrote:
A no when divided by D gives remainder 7 and when divided by 3D gives remainder 20.
What will be the remainder when twice the number is divided by 3D?

a.1
b.40.
c.27
d.13
e.can' be determined

Hey !

Kudos to you.

Thanks!
_________________

First Attempt 710 - http://gmatclub.com/forum/first-attempt-141273.html

Re: Quants - Problems   [#permalink] 13 Sep 2012, 01:29
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# Quants - Problems

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