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If x < y < z and y-x > 5, where x is an even integer and y [#permalink]
 28 Mar 2012, 02:00
Question Stats:
53% (01:54) correct
46% (01:04) wrong based on 77 sessions
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
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Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]
28 Mar 2012, 02:24
y-x is >5. y is odd and x is even then y-x will be odd. Lowest possible value of y-x is 7.
For lowest possible value of z-x, y and z should be close, it means y and z are consecutive odd integers or z = y + 2.
Hence z-x = y + 2 - x = 7 + 2 = 9.
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Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]
28 Mar 2012, 02:26
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eybrj2 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 We want to minimize z-x, so we need to maximize x. Say z=11=odd, then max value of y will be 9 (as y is also odd). Now, since y-5>x --> 9-5>x --> 4>x, then max value of x is 2 (as x is even). Hence, the least possible value of z-x is 11-2=9. Answer: D.
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Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]
02 Aug 2012, 04:48
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
Y is odd and X is even, so (y - x) has to be odd. ( Y - X ) > 5 means ( Y - X ) can have a value of 7.
Y - X = 7; Y = X + 7
Main equation will become,
X < X + 7 < Z
Subtract X from all,
0 < 7 < Z - X
Since Z is odd and X is even, (Z - X) has to be odd.
As (Z - X) > 7, the least possible value of Z-X will be 9. ANSWER.
- Ravender Singh
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Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]
04 Aug 2012, 21:52
eybrj2 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 Z-x will be odd. therefore, option A, C, E is eliminated. y-x> 5, if x= 2 then Y> 7 (8, 9 etc). so minimum value from z-x is 9
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Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]
19 Dec 2012, 01:27
I did it like this and i am getting 7 as the answer. Kindly tell me where i went wrong.
Given
x<y<z
y-x>5
From the first equation i subtracted x so 0<y-x<z-x
From the second equation multiply by (-1) so -y+x<-5
adding the above 2 i got 0<z-x-5 ie z-x>5
We now that z-x is odd so the next odd number is 7.
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Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]
19 Dec 2012, 03:54
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Re: If x < y < z and y-x > 5, where x is an even integer and y [#permalink]
20 Dec 2012, 12:30
We have:
1) x<y<z
2) y-x>5
3) x=2k (x is an even number)
4) y=2n+1 (y is an odd number)
5) z=2p+1 (z is an odd number)
6) z-x=? least value
z-x=2p+1-2k=2p-2k+1=2(p-k)+1 - that means that z-x must be an ODD number. We can eliminate answer choices A, C and E
we are asked to find the least value, so we have to pick the least numbers
since y is odd and x is even, y-x must be odd. since y-x>5, the least value for y-x must be 7, the least value for x must be 2, and, thus, the least possible value for y must be 9 (y-2=7, y=9)
2<9<z, since z is odd, the least possible value for z is 11
z-x=11-2=9
Answer D
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If x < y < z and y - x > 5, where x is an even integer and y and [#permalink]
23 Apr 2013, 07:33
Acer86 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 The answer i am getting is 7..thought original answer is something else...can someone help me out  Question asks least possible value, thus we can substitute by least possible numbers to get to answer A, C and E are out since they are even Left with B and E y-x>5 which means least value of y-x=7 (since y is odd and x is even, result will be odd) Work back: y= 5 (least value) x= -2 (least value). thus y-x = 5 - (-2) = 7 (least possible odd integer greater than 5) Since z> y, thus least possible value of z = 7 Therefore, z-x = 7 - (-2) = 9 Correct choice D
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If x < y < z and y - x > 5, where x is an even integer and y and
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23 Apr 2013, 07:33
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