A rectangular box of laundry detergent was redesigned so that its

Question

A rectangular box of laundry detergent was redesigned so that its height was increased by 10%, its length was decreased by 10%, and its width was increased by 1%. What was the resulting percentage change in the volume of the box?

(A) 1% less
(B) 0.01% less
(C) No change
(D) 0.01% greater
(E) 1% greater

(A) 1% less
(B) 0.01% less
(C) No change
(D) 0.01% greater
(E) 1% greater

Catman · Answer

Length = 10L , Width = 10W , Height = 10H

Old Volume V=  10L*10W*10H

New Length  L_n  = 9L
New Width  W_n  = 10.1W
New Height  H_n  = 11H

New Volume =  9L*10.1W*11H

Change in Volume =  (9L*10.1W*11H)  -  (10L*10W*10H)  = -0.1LWH (Decrease in Volume)

% Change in Volume =   \frac{-0.1LWH }{ 1000LWH}*100

% Change in Volume= 0.01%less

Kinshook · Answer

Given: A rectangular box of laundry detergent was redesigned so that its height was increased by 10%, its length was decreased by 10%, and its width was increased by 1%.

Asked: What was the resulting percentage change in the volume of the box?

V = l w h
V' = .9l 1.01w 1.1h = .9*1.01*1.1 lwh = .9999 lwh = .9999 V = (1-.0001)V = (100% - .01%)V

IMO B

Bhide · Answer

Got this question in my Official Mock 4 of FE. Is'nt this q testing geometry concepts which is excluded from FE syllabus ?
 bb   gmatophobia   Bunuel

illegallyblonde · Answer

Nope. This is a percentage question. Tests you on the % change formula: Final Value - Initial Value/Initial Value x 100

sayan640 · Answer

KarishmaB  , Any quick method like this formulae i.e x + y + x*y / 100 which we can use for two variables with simulataneous increase and decrease . But here we have three variables . What can be done in this case ?  MartyMurray

KarishmaB · Answer

Use the concept of Percentages. Volume = LBH NewVolume = (\frac{9}{10} * L) * (\frac{101}{100} * W) * (\frac{11}{10} * H) NewVolume = \frac{9999}{10000} * LBH = \frac{99.99}{100} LBH Hence there is a decrease of .01% Answer (B) Here are some discussions on Percentages: https://youtu.be/HxnsYI1Rws8 https://anaprep.com/arithmetic-successi ... e-changes/ https://anaprep.com/arithmetic-markup-discount-profit/

chini · Answer

sayan640  we can do the question using the quick method using the formula i.e   x + y +     \frac{x*y}{100}  
but we need to do it twice

first with the height and length, which comes to  10 - 10 +  \frac{10*-10}{100}    which comes to  -1%

then we equate this -1% change with the width that is +1% 
so it comes to   -1 + 1 +  \frac{1*-1}{100}    which comes to  -0.01%  which is your answer

giuseppemvn · Answer

Volume = Height * Length * Width

So

New Volume = Height * \frac{11}{10} * Length * \frac{9}{10} * Width * \frac{101}{100}

Which can be written as

New Volume = Volume * (\frac{11}{10} * \frac{9}{10} * \frac{101}{100} )

Therefore

New Volume = Volume * \frac{9999}{10000}

Or

New Volume = Volume * (1 - \frac{1}{10000})

The change in volume is a decrease of  \frac{1}{10000}  or  0,01 %.

Answer B.

pete789 · Answer

Each dimensional change is like a percent change to the volume of the box. 
3 successive percent changes:

The first two changes: (a-b+((a)(-b)/100))
Box(10-10+((10)(-10)/100))= (-1)Box

So final change = -Box(1-(99/100)= -Box(1/100) = 1% decrease in the box's volume

Goldenfuture · Answer

Appl successive % change formula - this should reduce answer time to 50seconds.

A rectangular box of laundry detergent was redesigned so that its

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

A rectangular box of laundry detergent was redesigned so that its

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