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15 Jul 2019, 00:37
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D
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Difficulty:
5%
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Question Stats:
88% (01:02) correct
12%
(01:20)
wrong
based on 217
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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.
(1) The remainder when m is divided by 6 is 2.
(2) The remainder when m is divided by 12 is 2.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
15 Jul 2019, 00:58
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Bunuel
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
16 Jul 2019, 05:01
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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!
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!
