Hi,
I have this as an inequality:
a/b > b/c
Mathematically, can we cross multiply to make it ac > b^2 ??
I have this as an inequality:
a/b > b/c
Mathematically, can we cross multiply to make it ac > b^2 ??
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a/b > b/c - inequality
Source: Beat The GMAT — Problem Solving |
Yes you can provided both b and c are positive.
If atleast one of them is negative , the sign of inequality will change.
If atleast one of them is negative , the sign of inequality will change.
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Stuart@KaplanGMAT
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Hi,pesfunk wrote:Hi,
I have this as an inequality:
a/b > b/c
Mathematically, can we cross multiply to make it ac > b^2 ??
you have to be very careful when manipulating inequalities that involve variables.
Remember, when you multiply or divide both sides by a negative, you have to swap the inequality. Since we don't know the sign of b or c, it's NOT safe to cross multiply.
Let's pick numbers to illustrate the danger:
a/b > b/c
if a=4, b=2 and c=-2, our original inequality holds, since:
4/2 > 2/-2
2 > -1
However, if we cross multiply as you suggested:
ac > b^2
(4)(-2) > 2^2
-8 > 4
which most certainly isn't true.
Consequently, you cannot simply cross-multiply (or divide) inequalities by variables with unknown signs.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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