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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7115
GMAT 1: 760 Q51 V42
GPA: 3.82
If a rectangle’s length is a+b and its area is (1/a)+(1/b), what is it  [#permalink]

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16 Oct 2018, 01:03
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15% (low)

Question Stats:

88% (01:16) correct 12% (01:15) wrong based on 31 sessions

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[Math Revolution GMAT math practice question]

If a rectangle’s length is $$a+b$$ and its area is $$(\frac{1}{a})+(\frac{1}{b})$$, what is its width?

$$A. 1$$
$$B. a+b$$
$$C. ab$$
$$D. \frac{1}{(a+b)}$$
$$E. \frac{1}{ab}$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 26 Feb 2017 Posts: 89 Location: India GPA: 3.99 Re: If a rectangle’s length is a+b and its area is (1/a)+(1/b), what is it [#permalink] Show Tags 16 Oct 2018, 01:09 Length given 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 is the correct answer Posted from my mobile device Senior PS Moderator Status: It always seems impossible until it's done. Joined: 16 Sep 2016 Posts: 747 GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: If a rectangle’s length is a+b and its area is (1/a)+(1/b), what is it [#permalink] Show Tags 16 Oct 2018, 01:34 MathRevolution wrote: [Math Revolution GMAT math practice question] If a rectangle’s length is $$a+b$$ and its area is $$(\frac{1}{a})+(\frac{1}{b})$$, what is its width? $$A. 1$$ $$B. a+b$$ $$C. ab$$ $$D. \frac{1}{(a+b)}$$ $$E. \frac{1}{ab}$$ The area is given as a sum of two fractions - let us find this sum. $$(\frac{1}{a})+(\frac{1}{b}) = (\frac{b}{ab} + \frac{a}{ab}) = \frac{(a+b)}{ab}$$ since the length is $$(a+b)$$ width must be Area/length ... $$\frac{(a+b)}{ab} * \frac{1}{(a+b)}$$ Thus width is = $$\frac{1}{ab}$$ Hence Option (E) is our choice. Best, Gladi _________________ Regards, Gladi “Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back) GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 911 Re: If a rectangle’s length is a+b and its area is (1/a)+(1/b), what is it [#permalink] Show Tags 17 Oct 2018, 06:49 MathRevolution wrote: [Math Revolution GMAT math practice question] If a rectangle’s length is $$a+b$$ and its area is $$(\frac{1}{a})+(\frac{1}{b})$$, what is its width? $$A. 1$$ $$B. a+b$$ $$C. ab$$ $$D. \frac{1}{(a+b)}$$ $$E. \frac{1}{ab}$$ 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) Our high-level "quant" preparation starts here: https://gmath.net Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7115 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If a rectangle’s length is a+b and its area is (1/a)+(1/b), what is it [#permalink] Show Tags 18 Oct 2018, 01:12 => Let $$x$$ be the width of the rectangle. Then $$x(a+b) = \frac{1}{a} + \frac{1}{b} = \frac{(a+b)}{ab}.$$ Thus, $$x = \frac{1}{ab}.$$ Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: If a rectangle’s length is a+b and its area is (1/a)+(1/b), what is it   [#permalink] 18 Oct 2018, 01:12
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