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07 Dec 2022, 00:25
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Difficulty:
45%
(medium)
Question Stats:
60% (02:06) correct
40%
(01:40)
wrong
based on 55
sessions
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M, a three digit positive number, can be expressed as 100a + 10b + c, where a, b, c represents the hundreds, tens, and units digit of M, respectively. What is the remainder when M is divided by a ?
(1) a is divisible by 3
(2) b + c = 12
(1) a is divisible by 3
(2) b + c = 12
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
07 Dec 2022, 00:26
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07 Dec 2022, 05:07
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PriyamRathor
(1) a is divisible by 3
So a could be 3, 6 or 9.
Nothing about b or c.
311 is not divisible by 3, but 612 is divisible by 6 or 369 is divisible by 3.
Insufficient
(2) b + c = 12
Nothing about a or exact values of b and c.
8+4=12 and if a=3, then 384 or 348 is divisible by 3.
8+4=12 and if a=5, then 584 or 548 is not divisible by 5.
Insufficient
Combined
a=3,6, or 9
b+c=3+9=4+8=5+7=6+6
If a=3, the answer will be yes as the sum of digits = a+b+c=3+12=15, divisible by 3.
If a=9, the answer is always No as the sum of digits =9+12=21, not divisible by 9.
Insufficient
But let us see what happens in third case.
If a=6, the answer can be yes or no. Yes, when b+c=4+8=6+6 and NO when b+c=3+9=5+7
E
