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

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

(1) x and y are positive integers
(2) y - x = 6

Which of the statements is sufficient?

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by mbawisdom » Tue Mar 06, 2018 4:27 pm
lheiannie07 wrote:For how many integer values of m is x < m < y ?

(1) x and y are positive integers
(2) y - x = 6

Which of the statements is sufficient?

OA C
(1) not sufficient as we do not know the actual values of x and y, or its span. If x and y were 1 and 3, m could only be 2 [1 INTEGER], but if x and y were 1 and 4, m could be 2 or 3 [2 INTEGERS].
(2) not sufficient as we don't know if x and y are only integers. If x and y were 1 and 7, m could be 2, 3, 4, 5, 6 [5 INTEGERS], but if x and y were 1.4 and 7.4, m could be 2, 3, 4, 5, 6, 7 [6 INTEGERS].

(1) and (2) together: sufficient, we know the span of x and y and that they are both integers, using the logic above we know that the answer is 5 integers.

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by Brent@GMATPrepNow » Thu Mar 08, 2018 10:30 am
lheiannie07 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 < y
Case b: x = 1 and y = 4. In this case, TWO values of m (m = 2 and m = 3) satisfy the inequality x < m < y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y - x = 6
It 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 < y
Case 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 < y
Since 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 < y
To 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

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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