The area of square A is 131 cm^2 greater than the area of square B. If

Question

The area of square A is 131 cm^2 greater than the area of square B. If the lengths of the sides of both squares are integers (in cm), then what is the area of square A?

A. 4096 cm^2
B. 4225 cm^2
C. 4356 cm^2
D. 4489 cm^2
E. 4624 cm^2

Are You Up For the Challenge: 700 Level Questions

Kinshook · Accepted Answer

Given: The area of square A is 131 cm^2 greater than the area of square B.

Asked: If the lengths of the sides of both squares are integers (in cm), then what is the area of square A?

Let the sides of square A be a & side of square B be b cm

a^2 - b^2 = 131 = (a+b)(a-b) 
Since 131 is prime number 
a + b = 131
a - b = 1
a = 66

The area of square A = 66^2 = 4356 cm^2

IMO C

firas92 · Answer

Looking at the answer options, choices B and C have a difference of 131. No reason why the areas shouldn't be 4356 and 4225.

So square A must be the larger of these 2 which gives us the area of square A to be 4356

Answer is (C)

Posted from my mobile device

anniaustin · Answer

We know, A =131 + B
So, B = A - 131, and also this needs to be a perfect square

If A = 4356, then B = 4225, which is a perfect square of  65^2

Answer:  C

ScottTargetTestPrep · Answer

If we let a = the side length of square A and b = the side length of square B, we can create the equation:

a^2 - b^2 = 131

(a + b)(a - b) = 131

Since a and b are integers and 131 is a prime, we see that a + b = 131 and a - b = 1. Adding these two equations, we have:

2a = 132

a = 66

Therefore, the area of square A is 66^2 = 4356.

Answer: C

hiranmay · Answer

The area of square A is 131 cm^2 greater than the area of square B. If the lengths of the sides of both squares are integers (in cm), then what is the area of square A?

A. 4096 cm^2
B. 4225 cm^2
C. 4356 cm^2 -->   correct : a^2=131+b^2=>(a+b)(a-b)=131, because a & b are +ve integers, so (a+b)(a-b)=131*1 (131 is a prime number) i.e. a+b=131 & a-b=1 => a=66 => Area of square A=a^2=66^2=4356 
D. 4489 cm^2
E. 4624 cm^2

Abhishek009 · Answer

Let the sides of the Square A be " a " and the sides of the Square B be " b "

a^2 = b^2 + 131

Or,  a^2 - b^2 = 131

Or,  (a + b)(a - b )= 131*1

Rest approach as shown by  hiranmay

Answer must be (C)

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

The area of square A is 131 cm^2 greater than the area of square B. If

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

The area of square A is 131 cm^2 greater than the area of square B. If

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards