M28-06

Question

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

Bunuel · Answer

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, given by  ab , equals  36 . We can express  36  as the product of several pairs of integers:  36=36 *1=18*2=12*3=9*4=6*6 . Consequently,  a  can assume five values:  36, 18, 12, 9,  and  6 .
 
Note that this is not a Geometry question. While it uses basic knowledge of lines and figures, it is not testing geometry knowledge. There are 8 questions within GMAT Prep Focus Edition that use similar principles.  Here is one example .

Answer: B

spradhan · Answer

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

Bunuel · Answer

The point is that a square is also a rectangle - all squares are rectangles but not every rectangle is a square.

Lisapizzola · Answer

I'm confused here because it says a>b, but if 6 and 6 are counted, how do they fit the restriction?

Bunuel · Answer

It says a >= b, not a > b.

gmatzpractice · Answer

How u get dis wrong

Salsanousi · Answer

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

TheMBmonster · Answer

We know that the area is 36

36 is 2^2 *3^2 .

The number of factors is product of the "exponents + 1" . --> (2 +1) (2+1) = 9 factors of 36

{1,2,3,4,6,9,12,18,36} Just in case

9/2+1= 5 factor pairs

Sanity check: 36 is a perfect square so there will be an  odd  amount of factor pairs.

Each pair is a set of a and b
 
Therefore the answer is 5

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Vikramaditya00 · Answer

I think this is a  high-quality  question and I agree with explanation. Calculated as 4 complete forgot about a>=b in the process of calculations

swarrangi · Answer

This is a great question that’s helpful for learning. Geometry is not a part of Gmat FE

Bunuel · Answer

Note that this is not a Geometry question. While it uses basic knowledge of lines and figures, it is not testing geometry knowledge. There are 8 questions within GMAT Prep Focus Edition that use similar principles.  Here is one example .

Check these two topics:

GMAT Syllabus for Focus Edition  
  Geometry Tested on GMAT Focus?

While specific geometry knowledge is not tested on GMAT Focus, not everything involving shapes, volumes, or areas requires specialized geometry knowledge. The area of a square or rectangle, the volume of a cube or rectangular solid, and the Pythagorean theorem are not considered specific geometry knowledge by the GMAT and can still be tested. Moreover, a question can involve shapes but test another area, such as combinations or other topics. There are several  questions involving these concepts in the GMAT Prep Focus mocks .

The chapter on coordinate geometry, including planes and slopes, is still present in the recent Official Guides. That said, it is tested to a much smaller extent. For example, you might see some questions involving graphs, either in Problem Solving or in Data Insights graph-based questions. However, those usually fall under the functions category rather than pure coordinate geometry, so they typically won’t involve distance calculations, angles, or similar topics.

M28-06

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