[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
If a rectangle’s length is a+b and its area is (1/a)+(1/b)
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- Max@Math Revolution
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Just a glance at the alternative choices makes us realize that all of them get different values when a=b=3, hence...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´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.
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Since the area of a rectangle equals length times width, the width = area/length. So we have: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
width = [1/a)+(1/b)]/(a+b)
width = [(a + b)/ab]/(a + b)
width = 1/ab
Answer: E
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- Max@Math Revolution
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=>
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
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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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.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 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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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