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NamaySharma
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If x < y < z and y - x > 5, where x is an even integer and y and z are 30 Nov 2021, 23:02
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VeritasKarishma
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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)
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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.
Thanks in advance!
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If x < y < z and y - x > 5, where x is an even integer and y and z are 01 Dec 2021, 23:13
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NamaySharma
VeritasKarishma
eybrj2
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.
Thanks in advance!
Show more

Yes, the approach is perfectly fine though if I am taking numbers, I would much rather take non negative numbers. Calculations with negative numbers are just more prone to errors. So if I know x is less than y, I would take y to be a greater odd number. Or I would much rather start with x = 0 ( an even integer).

Also, if you would like to direct a question to me, please tag me as VeritasKarishma. I would normally miss an untagged reply to my post.
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If x < y < z and y - x > 5, where x is an even integer and y and z are 24 Jun 2024, 12:57
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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

WE can take x= -2 (since it is not mentioned that it is a positive integer)
then y can be taken as 5 so that 5- (-2)>5

z can be taken as 7 so 7-(-2)= 9
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If x < y < z and y - x > 5, where x is an even integer and y and z are 30 Jun 2025, 14:46
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Since the question does not specify y&z being distinct integers, why can we ignore the possibility of y&z being equal?
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If x < y < z and y - x > 5, where x is an even integer and y and z are 30 Jun 2025, 14:48
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Timaisweg
Since the question does not specify y&z being distinct integers, why can we ignore the possibility of y&z being equal?
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We ARE given that x, y, and z are distinct numbers. Check below:

Quote:
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?
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If x < y < z and y - x > 5, where x is an even integer and y and z are 21 Aug 2026, 22:53
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Since the difference between y-x is more than 5 (assume at least 6), it means y has to be a number >5 and given x is even and y is odd.

For calculating the least value for z-x, we have to minimise the values of z and maximise x, but here x is even and the difference between y and x has to more than 5, so assuming some values for ease of understanding,

x = 2;
y = 9;
z = 11; z-x = 9

x=4;
y = 11;
z= 13; z-x = 9

Answer (D)
eybrj2
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

PS25302.01
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Bunuel
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