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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If x < y < z and y - x > 5, where x is an even integer and y and z are
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05 Nov 2021, 07:30
05 Nov 2021, 07:30
Expert Reply
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Question Stats:
50% (01:12) correct
50% (01:29) wrong based on 8 sessions
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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
A. 6
B. 7
C. 8
D. 9
E. 10
If x < y < z and y - x > 5, where x is an even integer and y and z are
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08 Nov 2021, 19:47
08 Nov 2021, 19:47
1
\(x < y < z\) & \(y - x > 5\)
\(x\) even & \(y , z\) are odd
We need to find the least difference, so we will take the least value.
Let's take \(x = 2\) so \(y > 7\)
\(y = 9\) & \(z = 11\)
The least value for \(z - x = 9\)
Answer D
\(x\) even & \(y , z\) are odd
We need to find the least difference, so we will take the least value.
Let's take \(x = 2\) so \(y > 7\)
\(y = 9\) & \(z = 11\)
The least value for \(z - x = 9\)
Answer D
Re: If x < y < z and y - x > 5, where x is an even integer and y and z are
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21 Jul 2022, 00:28
21 Jul 2022, 00:28
Solution -
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
The 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 D
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
The 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 D
