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Math Expert V
Joined: 02 Sep 2009
Posts: 65187
If m and n are prime numbers, is the remainder when 3m is divided by n  [#permalink]

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11 00:00

Difficulty:   65% (hard)

Question Stats: 56% (02:00) correct 44% (02:11) wrong based on 223 sessions

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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

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Math Expert V
Joined: 02 Aug 2009
Posts: 8757
Re: If m and n are prime numbers, is the remainder when 3m is divided by n  [#permalink]

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1
2
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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My bet on B explanation given by chetan2u is perfect.
Current Student D
Joined: 12 Aug 2015
Posts: 2518
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If m and n are prime numbers, is the remainder when 3m is divided by n  [#permalink]

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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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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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Joined: 11 Sep 2015
Posts: 4959
GMAT 1: 770 Q49 V46
If m and n are prime numbers, is the remainder when 3m is divided by n  [#permalink]

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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

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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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This is a very good question which tests you on an important aspect of remainders. When a number ‘x’ is divided by ‘y’ (x>y), the biggest remainder that can be obtained is (y-1). For example, if ‘x’ is divided by 4, the biggest remainder that can be obtained will always be 3.

From the question statement, we know that ‘m’ and ‘n’ are prime numbers. When 3m is divided by n, the remainder cannot be greater than 5 if ‘n’ itself is not greater than 5. This is the trick to understand and solve this question easily.

From statement I alone, we can only figure out that m = 2 or 3 or 5 or 7. We do not have any information about n.
For example, if m = 2 and n = 2, then 3m = 6 and the remainder when 6 (3m) is divided by 2(n) is ZERO; this is not greater than 5. So, the answer to the main question will be a NO.
However, if m = 2 and n = 7, then 3m = 6 and the remainder when 6(3m) is divided by 7(n) is 6; this is greater than 5. The answer to the main question will be a YES.
So, first statement is insufficient. Answer options A and D can be ruled out. Possible answers are B, C and E.

From statement II alone, we know that n is a prime number less than 6. So, n = 2 or 3 or 5. The biggest value of n is 5 and hence, the biggest remainder when 3m is divided by n will be 4, regardless of the value of m.
This is sufficient to answer the main question with a definite NO. Statement II alone is sufficient. The correct answer option is B.

Remember, getting a definite NO is also an acceptable answer in a DS question where the accepted answers are a YES or a NO.

Hope this helps!
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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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_________________ Re: If m and n are prime numbers, is the remainder when 3m is divided by n   [#permalink] 06 Jun 2020, 19:31

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