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If m and n are prime numbers, is the remainder when 3m is divided by n

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If m and n are prime numbers, is the remainder when 3m is divided by n  [#permalink]

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New post 16 Oct 2016, 06:01
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

54% (01:59) correct 46% (02:04) wrong based on 170 sessions

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Re: If m and n are prime numbers, is the remainder when 3m is divided by n  [#permalink]

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New post 16 Oct 2016, 06:37
Bunuel wrote:
If m and n are prime numbers, is the remainder when 3m is divided by n greater than 5?

(1) m <10

(2) n < 6


Hi,

Min value of 3m is 3*2=6 and max can be infinity..
Same value of n can be anything from 2 to infinity..

The value of remainder would mainly depend on the divisor n, since any value equal to or less than the dividend or 3m will leave a remainder less than 3m..
Here to since min value of 3m is 6, dividing by 6 or below will surely have a remainder less than 5...

Let's see the statements
1) m<10...
Say m is 5 ..3m is 15...
When divided by 3, ans is NO, as remainder is 0..
When divided by 19, ans is YES, as remainder is 15
Insuff..

2) n<6...
Min value of 3m is 6..
N can have any value less than 6, so values are 2,3 or 5..
As stated any number above 5 when divided by 5 or less will have a max remainder 4..
So ans is NO always irrespective of value of m..
Suff

B
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Re: If m and n are prime numbers, is the remainder when 3m is divided by n  [#permalink]

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New post 16 Oct 2016, 09:56
My bet on B 8-)
explanation given by chetan2u is perfect.
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Re: If m and n are prime numbers, is the remainder when 3m is divided by n  [#permalink]

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New post 17 Oct 2016, 05:57
1
1
Here we need to check whether the remainder when 3m/n is greater than 5 or not
Statement 1 =>
m<10
m=3
n=3 => remainder =0 => less than 5

m=3
n=31=> remainder = 21=> greater than 5
Hence insuff

Statement 2
n<6
This is an intriguing statement.
We must always remember that remainder is always less then the divisor
hence when the divisor will be <6
max possible value of divisor=5
hence hence the remainder will be always less than 5
ie=> 0,1,2,3,4

Hence Sufficient to state here that the remainder will always be less than 5
Hence B
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If m and n are prime numbers, is the remainder when 3m is divided by n  [#permalink]

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New post 22 Oct 2016, 04:16
Bunuel wrote:
If m and n are prime numbers, is the remainder when 3m is divided by n greater than 5?

(1) m <10

(2) n < 6


FROM 1

3M<30 THUS 3 M ( 6, 9, 15, 21, 27) ... NO INFO ABOUT N ... INSUFF

FROM 2

N ( 2,3,5) ... insuff

but since remainder has to be less than divisor then r has to be less than 5 .. suff
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If m and n are prime numbers, is the remainder when 3m is divided by n  [#permalink]

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New post 24 Mar 2018, 06:18
Top Contributor
Bunuel wrote:
If m and n are prime numbers, is the remainder when 3m is divided by n greater than 5?

(1) m <10

(2) n < 6


Target question: When 3m is divided by n, is the remainder greater than 5?

Given: m and n are prime numbers

Statement 1: m < 10
Let's TEST some values.
There are several values of m and n that satisfy statement 1. Here are two:
Case a: m = 2 and n = 7. Here 3m = 6, so 3m divided by n is the same as 6 divided by 7, in which case the remainder is 6. In other words, the answer to the target question is YES, the remainder IS greater than 5
Case b: m = 3 and n = 7. Here 3m = 9, so 3m divided by n is the same as 9 divided by 7, in which case the remainder is 2. In other words, the answer to the target question is NO, the remainder is NOT greater than 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n < 6
Useful rule: When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0

Statement 2 tells us we are dividing by a value that is 5 is less. So, the remainder must be 4 or less
This means the answer to the target question is NO, the remainder is NOT greater than 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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If m and n are prime numbers, is the remainder when 3m is divided by n &nbs [#permalink] 24 Mar 2018, 06:18
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If m and n are prime numbers, is the remainder when 3m is divided by n

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