A rectangular with dimensions 24 inches by 42 inches . . .

[Vincen]

A rectangular with dimensions 24 inches by 42 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares?

a) 4 inches
b) 6 inches
c) 7 inches
d) 8 inches
e) 10 inches

The OA is B.

How can I find the correct answer? Can any expert give me some help? Please.

[EconomistGMATTutor]

Hello Vincen.

Let's take a look at your question.

We need to divide the rectangle in many squares of equal size. The dimensions are 24 by 42 inches.

We just need to calculate the greatest common factor of 24 and 42. So $$24=2^3\cdot3\ and\ 42=2\cdot3\cdot7.$$ Then $$GCF\left(24,42\right)=2\cdot3=6.$$ SO, we can divide the rectangle in squares of side 2 inches, 3 inches or 6 inches.

As 2 inches and 3 inches are not in the options, the correct option is B .

I hope this explanation may help you. Regards.

[[email protected]]

Hi Vincen,

We're told that a rectangular with dimensions 24 inches by 42 inches is to be divided into SQUARES of EQUAL size. We're asked to find the answer that COULD be a length of a side of the squares. We can solve this question by TESTing THE ANSWERS.

To start, the word 'could' means that there's more than one possible answer - but only one of the five answer choices will 'fit' what we're told. We're thinking about SQUARES and we're meant to use the ENTIRE rectangle - so there can't be any 'leftover' space. Thus, whatever the dimension of the square ends up being, a multiple of that dimension MUST cover the entire 24 inches and 42 inches of the rectangle.

Only 3 of the answer choices divide evenly into 24 (4, 6 and 8). Eliminate Answers C and E.
Of those 3 remaining answers, only one divides evenly into 42 (6). Eliminate Answers A and D.
Thus, the squares must be 6x6 --> and that would yield 28 squares in the given rectangle (these last couple of steps are technically unnecessary, but prove the correct answer).

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

A rectangular with dimensions 24 inches by 42 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares?

a) 4 inches
b) 6 inches
c) 7 inches
d) 8 inches
e) 10 inches

The OA is B.

How can I find the correct answer? Can any expert give me some help? Please.

The side length of squares must be a common factor of 24 and 42. Since only 6 (of all the given choices) is a common factor of 24 and 42, choice B is the correct answer.

Answer: B

[Saupayan]

The term square means all of it's sides should be equal in length. Let's call that length L
Now we are told that N number of such squares will fit in the rectangle measuring 24x42.
This means that 24 is a multiple of L, and 42 is also a multiple of L. In other words L is a common factor of 24 as well as 42. What we need to do is to find L.

One way would be to list out all the prime factors of 24 and 42...
24 = 2x2x2x3
42 = 2x3x7
We see that 2 and 3 are common factors in both. So, L can be 2,3 or 6(i.e. 2x3). Remember, 1 is always implicit.

An alternative would be to find the GCF of 24 and 42, and find all its factors.
GCF(24,42) = 6
Factors of 6 = 1,2,3,6

Now look at the answer choices, and pick the right one.