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Difficulty:
55%
(hard)
Question Stats:
56% (01:42) correct
44%
(01:33)
wrong
based on 126
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How many of the three different positive integers a, b, and c are divisible by 7?
(1) The product of a, b, and c is divisible by 3, but only c is divisible by 21.
(2) Each of the three positive integers is divisible by 3, but only c is divisible by 21.
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(1) The product of a, b, and c is divisible by 3, but only c is divisible by 21.
(2) Each of the three positive integers is divisible by 3, but only c is divisible by 21.
Are You Up For the Challenge: 700 Level Questions
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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kungfury42
Joined: 07 Jan 2022
Last visit: 31 May 2023
Posts: 580
Schools: NUS '25 (A)
GMAT 1: 740 Q51 V38
GPA: 4
Products:
(A) c = 21k tells us that c is a multiple of 7. Also with a*b*c = 3m and c = 21k, clearly a*b*c = 21p but now we don't know anything about a and b except that they are not multiples of 21. But they might as well be multiples of 7 such as 14, 35, 49 etc. or could be just some other prime numbers. Since we cannot comment on the nature of a and b, we cannot exactly determine how many out of a, b, and c will be divisible by 7. Insufficient.
(B) If all of a, b, and c are divisible by 3, and only c is divisible by 21, it means only c is divisible by 7 and a and b are not, because had they been, then they too would've been multiples of 21 and it would not be just c alone. Sufficient.
Hence, B.
(B) If all of a, b, and c are divisible by 3, and only c is divisible by 21, it means only c is divisible by 7 and a and b are not, because had they been, then they too would've been multiples of 21 and it would not be just c alone. Sufficient.
Hence, B.
What does "but only" mean in I? "The product of a, b, and c is divisible by 3, but only c is divisible by 21." Some other thing is not divisible by 21. What is it? Good question but I think this should be rephrased
Posts: 78
It means only C is divisible by 21.
Say if a and b are not multiples of 3, but the product abc will still be divisible by 3, because c is divisible by 21 (which is 3 * 7).
Say if a and b are not multiples of 3, but the product abc will still be divisible by 3, because c is divisible by 21 (which is 3 * 7).
srik410
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