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02 Mar 2022, 03:00
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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.
Are You Up For the Challenge: 700 Level Questions
(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
kungfury42
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02 Mar 2022, 16:15
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(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.
26 Jul 2025, 08:24
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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
