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# M28-06

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Math Expert
Joined: 02 Sep 2009
Posts: 47977

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16 Sep 2014, 01:28
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Difficulty:

55% (hard)

Question Stats:

57% (00:49) correct 43% (01:13) wrong based on 30 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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Math Expert
Joined: 02 Sep 2009
Posts: 47977

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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.

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Intern
Joined: 24 May 2014
Posts: 14
Location: India
Concentration: General Management, Operations
WE: Engineering (Energy and Utilities)

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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
Math Expert
Joined: 02 Sep 2009
Posts: 47977

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16 Jan 2017, 10:26
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

The point is that a square is also a rectangle - all squares are rectangles but not every rectangle is a square.
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Intern
Joined: 01 Jul 2017
Posts: 3

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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?
Math Expert
Joined: 02 Sep 2009
Posts: 47977

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10 Jul 2018, 10:30
Lisapizzola wrote:
I'm confused here because it says a>b, but if 6 and 6 are counted, how do they fit the restriction?

It says a >= b, not a > b.
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Manager
Joined: 07 Feb 2017
Posts: 170

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10 Jul 2018, 10:50
How u get dis wrong
Re: M28-06 &nbs [#permalink] 10 Jul 2018, 10:50
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# M28-06

Moderators: chetan2u, Bunuel

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