Bunuel wrote:

If a and b are positive integers, is a/b = 5/8 ?

(1) 1/2 < a/b < 2/3

(2) b = 8

Kudos for a correct solution.

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 = 5/8Since 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 = 5/8Since 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 5/8Since we can answer the

target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,

Brent

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Brent Hanneson – Founder of gmatprepnow.com