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
OA D
Source: Official Guide
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If x < y < z and y - x > 5, where x is an even inte
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Since x must be even, let x=0.BTGmoderatorDC wrote: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
To minimize z-x, we must minimize the distance between z and x.
Plugging x=0 into y-x > 5, we get:
y-0 > 5
y > 5
Since y must be odd, the least possible value for y is 7.
Plugging y=7 into z > y, we get:
z > 7
Since z must be odd, the least possible value for z is 9.
Result:
z-x = 9-0 = 9
The correct answer is D.
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Since y < z and y and z are odd integers, the smallest value that z can be, in terms of y, is z = y + 2BTGmoderatorDC wrote: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
OA D
Source: Official Guide
Since y - x > 5 and x is an even integer and y is an odd integer, the smallest difference between y and x is 7, so we have y - x = 7).
Therefore, the smallest difference between z and x is z - x = (y + 2) - x = (y - x) + 2 = 7 + 2 = 9.
Answer: D
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