If x < y < z and y – x > 5, where x is an even integer and y and z are GMAT Problem Solving

Question: If x < y < z and y – x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?

A. 6
B. 7
C. 8
D. 9
E. 10

Answer: D

Approach Solution (1):
y < z
y-x < z-x.
Since y-x > 5, we get:
5 < y-x < z-x.
Since y and z are ODD and x is EVEN, y-x = odd-even = ODD and z-x = odd-even = ODD.
Thus, the least possible options are y-x = 7 and z-x = 9.
Correct option: D

Approach Solution (2):
If x is even, then the minimum value of x is 2.
If y - x > 5, then y > 5 + x, so y > 5 + 2, so y > 7. Since y is odd, the minimum y is 9.
If the minimum y is 9, and z > y, then the minimum z is 11 (since z is odd).
So z - x = 11 - 2 = 9
Correct option: D

Approach Solution (3):
Plugging in values is a great approach here, but we have to be careful.
The question stem asks for the least POSSIBLE value of z-x.
After we try one case, we should confirm -- either by using reason or by plugging in a second combination of values -- that there is no way to yield a smaller value for z-x.
Case 2: x=4.
Since y > x+5, y > 9.
Since y must be odd, the minimum value for y = 11.
Since z>y, and z also must be odd, the minimum value for z = 13.
The result:
The minimum value for z-x = 13-4 = 9.
As the second case shows, if we change the value of x, the minimum distances between y and x and between z and x stay the same.
Thus, the least possible value of z-x = 9.
Correct option: D

“If x < y < z and y – x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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