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Math Expert V
Joined: 02 Sep 2009
Posts: 59182

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Difficulty:   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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Math Expert V
Joined: 02 Sep 2009
Posts: 59182

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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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Math Expert V
Joined: 02 Sep 2009
Posts: 59182

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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  S
Joined: 24 May 2014
Posts: 12
Location: India
Concentration: General Management, Operations
WE: Engineering (Energy and Utilities)

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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
Intern  B
Joined: 01 Jul 2017
Posts: 3

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I'm confused here because it says a>b, but if 6 and 6 are counted, how do they fit the restriction?
Math Expert V
Joined: 02 Sep 2009
Posts: 59182

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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  S
Joined: 07 Feb 2017
Posts: 175

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How u get dis wrong Director  G
Joined: 19 Oct 2013
Posts: 511
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)

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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. Re: M28-06   [#permalink] 18 Oct 2018, 12:24
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# M28-06

Moderators: chetan2u, Bunuel  