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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
Think about it this way: x < y < z
The difference between y and x is more than 5 so it is at least 6. But x is even and y is odd so their difference would be odd. Hence the diff between them will be at least 7.
Now z is greater than y by at least 2 (since z is odd too), hence diff between x and z is at least 9.
Answer (D)
Hey Karishma, this is how I solved the question. Let me know if my approach was right.
The question says least. Therefore the distance between the 3 should be minimum. I took the smallest odd numbers i.e 3 and 5 as y and z respectively.
Now the question just states integers. Thus the closest even number satisfying the condition is -4 (3-(-4)=7). Thus I simply subtracted -4 from 5= 5-(-4)= 9.
I just wanted to know if I should continue with this logic in similar questions are is the same a wrong approach.