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M28-06

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M28-06  [#permalink]

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New post 16 Sep 2014, 00:28
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  45% (medium)

Question Stats:

61% (00:48) correct 39% (00:56) wrong based on 204 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 Sep 2014, 00:28
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M28-06  [#permalink]

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New post 16 Jan 2017, 09:20
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 16 Jan 2017, 09:26
1
spradhan wrote:
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M28-06  [#permalink]

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New post 10 Jul 2018, 09:20
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, 09:30
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Re: M28-06  [#permalink]

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New post 10 Jul 2018, 09:50
How u get dis wrong :shocked
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Re: M28-06  [#permalink]

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New post 18 Oct 2018, 11:24
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 &nbs [#permalink] 18 Oct 2018, 11:24
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M28-06

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