Bunuel
If \(X\) is a positive integer, what is the remainder of \(\frac{X}{8}\)?
(1) The remainder of \(\frac{X}{16}\) is 2.
(2) The remainder of \(\frac{X}{24}\) is 10.
Target question: What is the remainder when x is divided by 8? Statement 1: When x is divided by 16, the remainder is 2 In other words, x is 2 greater than some multiple of 16
In other words, x = 16k + 2 (for some integer k)
Rewrite this as: x = (
8)(2k) +
2This tells us that x is
2 greater than some multiple of
8This means
we get a remainder of 2 when x is divided by 8Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: When x is divided by 24, the remainder is 10In other words, x is 10 greater than some multiple of 24
In other words, x = 24j + 10 (for some integer j)
In other words, x = 24j + 8 +
2 (for some integer j)
Rewrite this as: x =
8(3j + 1) +
2This tells us that x is
2 greater than some multiple of
8This means
we get a remainder of 2 when x is divided by 8Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
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