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16 Sep 2014, 01:25
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If \(-3 < x < 5\) and \(-7 < y < 9\), which of the following represents the range of all possible values of \(y-x\)?
A. \(-4 \lt y-x \lt 4\)
B. \(-2 \lt y-x \lt 4\)
C. \(-12 \lt y-x \lt 4\)
D. \(-12 \lt y-x \lt 12\)
E. \(4 \lt y-x \lt 12\)
A. \(-4 \lt y-x \lt 4\)
B. \(-2 \lt y-x \lt 4\)
C. \(-12 \lt y-x \lt 4\)
D. \(-12 \lt y-x \lt 12\)
E. \(4 \lt y-x \lt 12\)
16 Sep 2014, 01:25
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Official Solution:
If \(-3 < x < 5\) and \(-7 < y < 9\), which of the following represents the range of all possible values of \(y-x\)?
A. \(-4 \lt y-x \lt 4\)
B. \(-2 \lt y-x \lt 4\)
C. \(-12 \lt y-x \lt 4\)
D. \(-12 \lt y-x \lt 12\)
E. \(4 \lt y-x \lt 12\)
To obtain the maximum value of \(y-x\), consider the maximum value of \(y\) and the minimum value of \(x\): \(9-(-3)=12\);
To obtain the minimum value of \(y-x\), consider the minimum value of \(y\) and the maximum value of \(x\): \(-7-(5)=-12\);
Therefore, the range of all possible values of \(y-x\) lies between \(-12\) and \(12\): \(-12 < y-x < 12\).
Alternatively, we can approach the problem in the following way. We know that \(-3 < x < 5\) and \(-7 < y < 9\).
Add \(y < 9\) to \(-3 < x\) to get \(y - 3 < 9 + x\), which can be rearranged as \(y - x < 12\). This gives the upper bound for the value of \(y-x\).
Add \(-7 < y\) to \(x < 5\) to get \(-7 + x < y + 5\), which can be rearranged as \(-12 < y - x\). This gives the lower bound for the value of \(y-x\).
Thus, we establish that \(-12 < y - x < 12\).
Answer: D
If \(-3 < x < 5\) and \(-7 < y < 9\), which of the following represents the range of all possible values of \(y-x\)?
A. \(-4 \lt y-x \lt 4\)
B. \(-2 \lt y-x \lt 4\)
C. \(-12 \lt y-x \lt 4\)
D. \(-12 \lt y-x \lt 12\)
E. \(4 \lt y-x \lt 12\)
To obtain the maximum value of \(y-x\), consider the maximum value of \(y\) and the minimum value of \(x\): \(9-(-3)=12\);
To obtain the minimum value of \(y-x\), consider the minimum value of \(y\) and the maximum value of \(x\): \(-7-(5)=-12\);
Therefore, the range of all possible values of \(y-x\) lies between \(-12\) and \(12\): \(-12 < y-x < 12\).
Alternatively, we can approach the problem in the following way. We know that \(-3 < x < 5\) and \(-7 < y < 9\).
Add \(y < 9\) to \(-3 < x\) to get \(y - 3 < 9 + x\), which can be rearranged as \(y - x < 12\). This gives the upper bound for the value of \(y-x\).
Add \(-7 < y\) to \(x < 5\) to get \(-7 + x < y + 5\), which can be rearranged as \(-12 < y - x\). This gives the lower bound for the value of \(y-x\).
Thus, we establish that \(-12 < y - x < 12\).
Answer: D
General Discussion
earnit
Joined: 06 Mar 2014
Last visit: 21 Dec 2016
Posts: 161
Given Kudos: 84
Location: India
Schools: INSEAD Jan '16 Tepper '16 ISB '16 Simon '18 (A)
GMAT Date: 04-30-2015
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16 Sep 2014, 10:42
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Bunuel
This question is good but it would be interesting to see a question with the same guidelines as to find the range of values but with the variables x/y or both with inclusive numbers like -3<=x<5 and -7<y<=9.
Also if possible, kindly suggest similar problems.
