SwordfishII wrote:

For how many integer values of m is x < m < y ?

(1) x and y are positive integers

(2) y – x = 6

Target question: For how many integer values of m is x < m < y ? Statement 1: x and y are positive integers There are several values of x and y that satisfy statement 1. Here are two:

Case a: x = 1 and y = 3. In this case,

only ONE value of m (m = 2) satisfies the inequality x < m < yCase b: x = 1 and y = 4. In this case,

TWO values of m (m = 2 and m = 3) satisfy the inequality x < m < ySince we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y – x = 6It would SEEM that this statement provides sufficient information.

HOWEVER, the answer to the

target question varies, depending on whether x and y have INTEGER values or whether they have NON-INTEGER values. Here's what I mean:

Case a: x = 1.1 and y = 7.1. (notice that y - x = 7.1 - 1.1 = 6). In this case,

there are 6 values of m (m = 2, 3, 4, 5, 6, and 7) that satisfy the inequality x < m < yCase b: x = 1 and y = 7. (notice that y - x = 7 - 1 = 6). In this case,

there are 5 values of m (m = 2, 3, 4, 5 and 6) that satisfy the inequality x < m < ySince we cannot answer the

target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined When we combine BOTH statements, there is ONLY ONE answer to the

target question If x and y are both integers, AND it is the case that y - x = 6, then

there are 5 values of m that satisfy the inequality x < m < yTo be more specific, if y - x = 6, then y = x + 6

So, the FIVE values of m that satisfy the inequality x < m < y will be: m = x + 1, m = x + 2, m = x + 3, m = x + 4, and m = x + 5

Since we can answer the

target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,

Brent

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