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What is the remainder when m is divided by 3? (1) The remainder when m

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What is the remainder when m is divided by 3? (1) The remainder when m  [#permalink]

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New post 14 Jul 2019, 23:37
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A
B
C
D
E

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85% (01:08) correct 15% (01:26) wrong based on 72 sessions

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Re: What is the remainder when m is divided by 3? (1) The remainder when m  [#permalink]

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New post 14 Jul 2019, 23:58
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Bunuel wrote:
What is the remainder when positive integer m is divided by 3?

(1) The remainder when m is divided by 6 is 2.
(2) The remainder when m is divided by 12 is 2.


Q: What is the remainder when positive integer m is divided by 3?

#1 The remainder when m is divided by 6 is 2.
Take for example x = 6k + 2 => x = 3.(2k) + 2
=> the remainder when positive integer m is divided by 3 = 2
SUFFICIENT

#2 The remainder when m is divided by 12 is 2.
Take for example x = 12k + 2 = 3. (4k) +2
=> the remainder when positive integer m is divided by 3 = 2
SUFFICIENT

IMO D
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Re: What is the remainder when m is divided by 3? (1) The remainder when m  [#permalink]

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New post 16 Jul 2019, 04:01
This is a fairly straightforward question on the concepts of remainders.

When a positive integer is divided by 3, the smallest remainder you can get is 0 and the biggest remainder you can get is 2.

From statement I, when m is divided by 6, the remainder is 2. This means that m can be written as,

m = 6k + 2, where k is the quotient.

When m is divided by 3, 6k will be divisible fully, leaving a remainder of 2. This is a unique value for the remainder.
Statement I alone is sufficient. The possible answer options are A or D. Answer options B, C and E can be eliminated.

From statement II, when m is divided by 12, the remainder is 2. So, m can be written as,

m = 12k + 2, where k is the quotient.

When this m is divided by 3, 12k will be fully divisible, leaving a remainder of 2 again. This is a unique value for the remainder again.
Statement II alone is sufficient. Answer option A can be eliminated.

The correct answer option is D.

Hope this helps!
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Re: What is the remainder when m is divided by 3? (1) The remainder when m  [#permalink]

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New post 12 Mar 2020, 06:49
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Bunuel wrote:
What is the remainder when positive integer m is divided by 3?

(1) The remainder when m is divided by 6 is 2.
(2) The remainder when m is divided by 12 is 2.


Target question: What is the remainder when positive integer m is divided by 3?

Statement 1: The remainder when m is divided by 6 is 2.
This information tells us that m is 2 greater than some of multiple of 6
In other words, we can say: m = 6k + 2 (for some integer k)
We can rewrite this as follows: m = (3)(2k) + 2
Since (3)(2k) is clearly a multiple of 3, we can conclude that (3)(2k) + 2 is 2 greater than some of multiple of 3
So, when we divide (3)(2k) + 2 by 3, the remainder must be 2
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The remainder when m is divided by 12 is 2
The logic here will be identical to the logic used for statement 1.
This information tells us that m is 2 greater than some of multiple of 12
In other words, we can say: m = 12k + 2 (for some integer k)
We can rewrite this as follows: m = (3)(4k) + 2
Since (3)(4k) is clearly a multiple of 3, we can conclude that (3)(4k) + 2 is 2 greater than some of multiple of 3
So, when we divide (3)(4k) + 2 by 3, the remainder must be 2
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

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Re: What is the remainder when m is divided by 3? (1) The remainder when m   [#permalink] 12 Mar 2020, 06:49

What is the remainder when m is divided by 3? (1) The remainder when m

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