In measuring the sides of a rectangle, one side is taken 8% in excess

Question

In measuring the sides of a rectangle, one side is taken 8% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements.

A. 3.5%
B. 2.4% 
C. 3%
D. 5%
E. 2.6%

b2bt · Accepted Answer

Percentage Change Formula
if there are two succesive changes to a quantity ( as in this case ) you can solve it by a simple formula
 net change = a + b + \frac{ab}{100} 
e.g. net change of to increase of 50% =  50 + 50 + \frac{2500}{100} = 125 
net change of increase in 8% and decrease of 5 % =  8 - 5 -\frac{8*5}{100} = 2.6

sanman · Answer

Let the sides of the rectangle be a and b.

actual area of the rectangle without error = ab

New side a ( 8% in excess) = a+0.08a = 1.08a
New side b ( 5% in deficit) = b-0.05b = 0.95b

Area of the new rectangle = (1.08a)(0.95b)= (1.0260)ab
say a=1 and b=1
area of the original rectangle = 1
area of the new rectangle = 1.026
change in the area calculation = .026
error percentage in the area calculated = 2.6%

Let me know otherwise.
Cheers

Bunuel · Answer

Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000.

Now, the area obtained with wrong measurements would be 108*95=10,260, which is 2.6% greater than the actual area.

Answer: E.

JeffTargetTestPrep · Answer

We can let the original area = LW. Thus, the new area is:

1.08L x 0.95W = 1.026LW

Thus, the error percentage is 0.026 = 2.6 percent.

Answer: E

hemantbafna · Answer

We will take for ease of calculations that length increased and breadth decreased
Excess of 8% in length= (108) l

Deficit in breadth = (095)b

Therefore new area= (1.08) l * (95)b=102.60
Which is difference of 2.6%
 E

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.

In measuring the sides of a rectangle, one side is taken 8% in excess

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

In measuring the sides of a rectangle, one side is taken 8% in excess

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