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02 Sep 2022, 05:10
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E
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Difficulty:
55%
(hard)
Question Stats:
60% (01:27) correct
40%
(01:06)
wrong
based on 100
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What is the remainder when positive integer x is divided by 6?
(1) 15x is divisible by 2.
(2) 15x is divisible by 3.
(1) 15x is divisible by 2.
(2) 15x is divisible by 3.
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:
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02 Sep 2022, 05:28
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E?
15x is divisible by 2 tells that x is an even, but does not tell if x is also divisible by 3. Hence not sufficient to determine the remainder. Could be multiple values.
15x is divisible by 3 does not tell if x alone is divisible by 3 and 2 or not, hence multiple values for remainder possible.
Posted from my mobile device
15x is divisible by 2 tells that x is an even, but does not tell if x is also divisible by 3. Hence not sufficient to determine the remainder. Could be multiple values.
15x is divisible by 3 does not tell if x alone is divisible by 3 and 2 or not, hence multiple values for remainder possible.
Posted from my mobile device
Updated on: 12 Sep 2022, 11:37
Originally posted by sanjitscorps18 on 02 Sep 2022, 07:23.
Last edited by sanjitscorps18 on 12 Sep 2022, 11:37, edited 1 time in total.
Last edited by sanjitscorps18 on 12 Sep 2022, 11:37, edited 1 time in total.
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Bunuel
(1) 15x is divisible by 2.
This implies x is even hence possible values of x are 2, 4, 6, 8 .......
2 divided by 6 leaves remainder 2
4 divided by 6 leaves remainder 4
6 divided by 6 leaves the remainder 0
--> Insufficient
(2) 15x is divisible by 3
x can take values of 1, 2, 3, 4 ......
All will leave the remainder 0
--> Insufficient
Taking both statements together we see that x has common values at even numbers, hence we get values of x = 2, 4, 6....
For all these values the remainder would always be 0
IMO Option E
