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16 Aug 2019, 02:23
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In a group of 60 integers, how many are divisible (with a remainder of 0) by neither 7 nor 13?
(1) Of the 60 numbers, 20 are divisible by 7 but not by 13.
(2) Of the 60 numbers, 30 are divisible by both 7 and 13.
(1) Of the 60 numbers, 20 are divisible by 7 but not by 13.
(2) Of the 60 numbers, 30 are divisible by both 7 and 13.
16 Aug 2019, 02:47
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Statement 1 is insufficient alone as it doesn't mention numbers divisible by 13.
So POE A and D
Statement 2 is insufficient alone as it doesn't consider numbers divisible only by 7 or 13. So POE B.
Statement 1 and 2 together are also not sufficient as it doesn't mention about numbers only divisible by 13 and not 7.
Hence E is the right option
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So POE A and D
Statement 2 is insufficient alone as it doesn't consider numbers divisible only by 7 or 13. So POE B.
Statement 1 and 2 together are also not sufficient as it doesn't mention about numbers only divisible by 13 and not 7.
Hence E is the right option
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17 Sep 2019, 23:36
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Bunuel
In a group of 60 integers, how many are divisible (with a remainder of 0) by neither 7 nor 13?
(1) Of the 60 numbers, 20 are divisible by 7 but not by 13.
(2) Of the 60 numbers, 30 are divisible by both 7 and 13.
(1) Of the 60 numbers, 20 are divisible by 7 but not by 13.
(2) Of the 60 numbers, 30 are divisible by both 7 and 13.
Official Explanation
We have a group of 60 integers that we don't know too much about. It looks like a number properties or prime factorization question, since we are talking about divisibility. But when we glance over the data statements, we think we are talking about overlapping sets, and the divisibility question is merely a disguise. Anyway, we want to know how many of these numbers are divisible neither by 7 nor by 13. If we use the two-set Venn diagram equation, T = G1 + G2 - B + N, then we are looking for N and we have virtually no other information, except that T = 60. On to the statements, separately first.
Statement (1) tells us that G1 - B = 20. We are still missing the value of G2, so this statement is insufficient.
Statement (2) tells us that B = 30. We are missing the values of G1 and G2, so this statement is insufficient.
With both statements, we have B, and we can solve for G1. We are still missing the value of G2, so we cannot solve uniquely for N. The statements together are insufficient.
The correct answer is (E).
