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If a rectangle’s length is a+b and its area is (1/a)+(1/b)

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by Max@Math Revolution » Tue Oct 16, 2018 11:30 pm

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[Math Revolution GMAT math practice question]

If a rectangle's length is a+b and its area is (1/a)+(1/b), what is its width?

A. 1
B. a+b
C. ab
D. 1/(a+b)
E. 1/ab
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by rrnicky » Wed Oct 17, 2018 12:59 am
Length *width=area
(a+b)*width= 1/a + 1/b
= (a+b)/ab
width = 1/ab
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by fskilnik@GMATH » Wed Oct 17, 2018 5:43 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If a rectangle's length is a+b and its area is (1/a)+(1/b), what is its width?

A. 1
B. a+b
C. ab
D. 1/(a+b)
E. 1/ab
Just a glance at the alternative choices makes us realize that all of them get different values when a=b=3, hence...

Let´s explore this PARTICULAR CASE!
$${\rm{rectangle}}\,\,\left\{ \matrix{
\,{\rm{length}} = \,\,6 \hfill \cr
\,{\rm{area}} = \,\,{2 \over 3} \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,?\,\,\left( {{\rm{target}}} \right)\,\,\,\, = \,\,\,\,{{\,\,{2 \over 3}\,\,} \over 6}\,\, = \,\,{1 \over 9}\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( E \right)$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by swerve » Wed Oct 17, 2018 3:26 pm
Length give is (a+b)
Area = (1/a + 1/b)
Area of rectangle = Length * Width
(1/a + 1/b) = (a+b) * Width
Width = 1/ab
Option E.

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by Scott@TargetTestPrep » Thu Oct 18, 2018 5:15 pm
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If a rectangle's length is a+b and its area is (1/a)+(1/b), what is its width?

A. 1
B. a+b
C. ab
D. 1/(a+b)
E. 1/ab
Since the area of a rectangle equals length times width, the width = area/length. So we have:

width = [1/a)+(1/b)]/(a+b)

width = [(a + b)/ab]/(a + b)

width = 1/ab

Answer: E

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by Max@Math Revolution » Thu Oct 18, 2018 11:56 pm
=>
Let x be the width of the rectangle. Then
x(a+b) = 1/a + 1/b = (a+b)/ab.
Thus, x = 1/ab.

Therefore, the answer is E.
Answer: E
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by GMATGuruNY » Fri Oct 19, 2018 4:05 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If a rectangle's length is a+b and its area is (1/a)+(1/b), what is its width?

A. 1
B. a+b
C. ab
D. 1/(a+b)
E. 1/ab
Let a=b=0.5, implying that the rectangle's length = a+b = 0.5+0.5 = 1 and that its area = (1/0.5) + (1/0.5) = (10/5) + (10/5) = 2+2 = 4.
Since the rectangle has an area of 4 and a length of 1, its width = 4.
The correct answer must yield a value of 4 when a=b=0.5.
Only E works:
1/ab = 1/(0.5 * 0.5) = 1/(0.25) = 100/25 = 4.

The correct answer is E.
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