Brent@GMATPrepNow wrote: ↑

Wed Jan 22, 2020 6:42 am

How many integers k are there such that x < k < y?

(1) y – x = 7
(2) y - 10 and x - 1 are consecutive odd integers

Source: www.gmatprepnow.com
Difficulty level: 650-ish
Answer: C

Target question: How many integers k are there such that x < k < y?

Statement 1: y – x = 7
If we assume that x and y are INTEGERS, then we'll incorrectly conclude that statement 1 is sufficient.
However, since we are not given any information stating that x and y are integers, we can come up with cases that yield contradictory answers to the target question.
Here are two such cases: It doesn't even look like you used any more
Case a: y = 10 and x = 3. So k could equal 4,5,6,7,8 or 9. In this case, the answer to the target question is there are 6 integers k such that x < k < y
Case b: y = 10.5 and x = 3.5. So k could equal 4,5,6,7,8,9 or 10. In this case, the answer to the target question is there are 7 integers k such that x < k < y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y - 10 and x - 1 are consecutive odd integers
Even though we're told that we have two consecutive odd integers, we don't know which of them is greater.
Consider these two possible cases:
Case a: y-10 > x-1. Since consecutive odd integers differ by 2, we can write: (y-10) - (x-1) = 2
Simplify to get: y - x - 9 = 2
Add 9 to both sides to get y - x = 11
Since we know that x and y are integers, knowing that y - x = 11 tells us there are 10 integers k such that x < k < y

Case b: y-10 < x-1. Since consecutive odd integers differ by 2, we can write: (x-1) - (y-10) = 2
Simplify to get: x - y + 9 = 2
Subtract 9 from both sides to get: x - y = -7
Multiply both sides by -1 to get: -x + y = 7
Rewrite as: y - x = 7
Since we know that x and y are integers, knowing that y - x = 7 tells us there are 6 integers k such that x < k < y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that y – x = 7
Statement 2 tells us that that x and y are INTEGERS
So the combined statements tell us that there are 6 integers k such that x < k < y
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent