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If n is a positive integer, which one of the following numbers

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If n is a positive integer, which one of the following numbers [#permalink]

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New post 06 Feb 2016, 12:48
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Question Stats:

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If n is a positive integer, which one of the following numbers must have a remainder of 3 when
divided by any of the numbers 4, 5, and 6?

(A) 12n + 3
(B) 24n + 3
(C) 80n + 3
(D) 90n + 2
(E) 120n + 3

Source: GMAT Math Bible
Spoiler: OA

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Re: If n is a positive integer, which one of the following numbers [#permalink]

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New post 06 Feb 2016, 14:07
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BrainLab wrote:
If n is a positive integer, which one of the following numbers must have a remainder of 3 when
divided by any of the numbers 4, 5, and 6?

(A) 12n + 3
(B) 24n + 3
(C) 80n + 3
(D) 90n + 2
(E) 120n + 3

Source: GMAT Math Bible


Out of the given options, the correct answer will be the one having the divisor a multiple of 4,5,6 in order for all 3 of these give the same remainder.

LCM of 4,5,6 = 60.

Out of the given options only option E can be written in the form of multiple of 60 for the divisor as 2*60*n+3

E is thus the correct answer.

Hope this helps.
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Re: If n is a positive integer, which one of the following numbers [#permalink]

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New post 09 Feb 2016, 20:27
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Hi BrainLab,

This question can be solved by TESTing VALUES and a bit of arithmetic.

We're told that N is a POSITIVE INTEGER. We're asked which of the following numbers MUST have a remainder of 3 when divided by any of the numbers 4, 5, and 6?

Let's TEST N=1

A) 12N + 3 = 15 --> 15/5 = 3r0. This is NOT a match
B) 24N + 3 = 27 --> 27/5 = 5r2. This is NOT a match
C) 80N + 3 = 83 --> 83/6 = 13r5. This is NOT a match
D) 90N + 2 = 92 --> 92/5 = 18r2. This is NOT a match

There's only one answer left...

Final Answer:
Spoiler: ::
E


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Re: If n is a positive integer, which one of the following numbers [#permalink]

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New post 22 Feb 2016, 23:43
12=(2*2*3)n+3
24=(2*2*2*3)n+3
80=(5*2*2*2*2)n+3
90=(5*2*3*3)n+2
120=(5*2*2*2*3)n+3

for 4: all gives remainder 3 exc. D with remainder 0, D out
for 5: A and B gives remainder 0 and 2, respectively, so they out
for 6: E gives remander 3

E
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Re: If n is a positive integer, which one of the following numbers [#permalink]

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New post 09 Apr 2018, 13:08
BrainLab wrote:
If n is a positive integer, which one of the following numbers must have a remainder of 3 when
divided by any of the numbers 4, 5, and 6?

(A) 12n + 3
(B) 24n + 3
(C) 80n + 3
(D) 90n + 2
(E) 120n + 3

Source: GMAT Math Bible


4*5*6=120
E
Re: If n is a positive integer, which one of the following numbers   [#permalink] 09 Apr 2018, 13:08
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