If a and b are positive integers, is a/b = 5/8 ?
(1) 1/2 < a/b < 2/3
(2) b = 8
Source: Princeton Review
If a and b are positive integers, is
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Target question: Is a/b = 5/8
Given: a and b are positive integers
Statement 1: 1/2 < a/b < 2/3
In other words, 0.5 < a/b < 0.6666...
5/8 = 0.625, so 5/8 is between 1/2 and 2/3.
However, there are infinitely many other fractions between 1/2 and 2/3, so there's no way to say for certain that a/b = 5/8
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: b = 8
We have no idea what the value of a is, so there's no way to determine whether a/b = 5/8
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that 1/2 < a/b < 2/3
Statement 2 tells us that b = 8
Since a must be a POSITIVE INTEGER, we can test some values.
a cannot = 1, 2, 3 or 4, because these cases yield a fraction, a/b, that's not greater than 1/2
a cannot = 6, 7, 8 ...., because these cases yield a fraction, a/b, that's not less than 2/3
So, we can be certain that a EQUALS 5, which means a/b definitely EQUALS 5/8
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C