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M28-06

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M28-06  [#permalink]

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New post 16 Sep 2014, 01:28
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  45% (medium)

Question Stats:

62% (00:54) correct 38% (01:01) wrong based on 226 sessions

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Certain rectangle has the length of \(a\) centimeters and the width of \(b\) centimeters, where \(a\) and \(b\) are integers and \(a\geq{b}\). If the area of the rectangle is 36 square centimeters, then how many values of \(a\) are possible?

A. \(4\)
B. \(5\)
C. \(6\)
D. \(7\)
E. \(8\)

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Re: M28-06  [#permalink]

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New post 16 Jan 2017, 10:26
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Math Expert
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Re M28-06  [#permalink]

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New post 16 Sep 2014, 01:28
Official Solution:

Certain rectangle has the length of \(a\) centimeters and the width of \(b\) centimeters, where \(a\) and \(b\) are integers and \(a\geq{b}\). If the area of the rectangle is 36 square centimeters, then how many values of \(a\) are possible?

A. \(4\)
B. \(5\)
C. \(6\)
D. \(7\)
E. \(8\)


The area = \(ab=36=36*1=18*2=12*3=9*4=6*6\), thus \(a\) can take 5 values: 36, 18, 12, 9, and 6.


Answer: B
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Re: M28-06  [#permalink]

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New post 16 Jan 2017, 10:20
How a=6, b=6 is taken as one of the solution...as it was mentioned in Q that this is rectangle...if 6 is taken as a solution then the figure will be square...expert please explain...

Thanks
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Re: M28-06  [#permalink]

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New post 10 Jul 2018, 10:20
I'm confused here because it says a>b, but if 6 and 6 are counted, how do they fit the restriction?
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Re: M28-06  [#permalink]

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New post 10 Jul 2018, 10:30
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Re: M28-06  [#permalink]

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New post 10 Jul 2018, 10:50
How u get dis wrong :shocked
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Re: M28-06  [#permalink]

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New post 18 Oct 2018, 12:24
Bunuel wrote:
Certain rectangle has the length of \(a\) centimeters and the width of \(b\) centimeters, where \(a\) and \(b\) are integers and \(a\geq{b}\). If the area of the rectangle is 36 square centimeters, then how many values of \(a\) are possible?

A. \(4\)
B. \(5\)
C. \(6\)
D. \(7\)
E. \(8\)


Prime factors of 36 = 2^2 * 3^2
Number of factors or 36 = (2+1) * (2+1) = 9

36 and 1
18 and 2
12 and 3
9 and 4
6 and 6 (counted as one factor)

since it is equal to or larger then it is 6,9,12,18, or 36

5 possible values.

Answer choice B
GMAT Club Bot
Re: M28-06   [#permalink] 18 Oct 2018, 12:24
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