IMO the answer should be C.
Given x<m<y,
Consider two cases:
A) x=0.5 then y=6.5, then the number of integer values of m will be 6 ie, {1,2,3,4,5,6}; and
B) x=1 then y=7, then the number of integer values of m will be 5 ie, {2,3,4,5,6}

hm interesting, thank you for the response

This is a copy of OG13 following question:


Discussed here: how-many-integers-n-are-there-such-that-r-n-s-166396.html

Similar questions to practice:
how-many-integers-are-there-between-c-and-d-1-neither-c-115561.html
how-many-integers-are-there-such-that-v-n-w-129065.html

P.S. Please provide the OA's when posting. Thank you.
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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

Cheers,
Brent
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