The price of a box of Red Valley cereal

Question

The price of a box of Red Valley cereal has increased by 60 percent over the past 20 years. However , the manufacturer has reduced two of the three interior dimensions of the rectangular box by 20 percent each, leaving the third dimension unchanged .

By approximately what percent has the price per unit volume of the cereal increased over the past 20 years?

A. 80%
B. 100%
C. 120%
D. 150%
E. 160%

Edskore · Answer

Great problem to test your understanding of Percent and Volume reasoning — a concept that trips up a lot of students on Problem Solving (PS) because they rush to work with the price directly and forget that the volume of the box has also changed.

Key concept being tested: Percent change applied to multi-dimensional quantities (volume = length × width × height).

Here's the step-by-step solution:

Step 1 — Set up the original volume.
Let the original dimensions be L, W, and H. So original volume V = L × W × H.

Step 2 — Calculate the new volume.
The manufacturer reduces two of the three dimensions by 20% each, leaving the third unchanged. So new volume = (0.8L) × (0.8W) × H = 0.64 × L × W × H = 0.64V.

Step 3 — Calculate the new price.
Price increased by 60%, so new price = 1.6P.

Step 4 — Compare price per unit volume.
Original price per unit volume = P/V
New price per unit volume = 1.6P / 0.64V = 2.5 × (P/V)

Step 5 — Calculate the percent increase.
Percent increase = (2.5 − 1) / 1 × 100% = 150%.

Answer: D (150%)

Common trap: Most students pick B (100%) because they see "60% price increase" and a "20% reduction in dimensions" and try to do 60/0.20 = 300... or they forget that TWO dimensions shrink, not one. If only one dimension shrank by 20%, new volume would be 0.8V, and the answer would be 1.6/0.8 = 2.0, i.e., 100% increase. The question says TWO dimensions shrink, making the new volume 0.64V — not 0.8V.

Takeaway: Whenever a "price per unit" problem involves a geometric container, always calculate the new volume first before touching the price ratio.

— Kavya | GMAT Focus 725 (99th percentile)

abhiramkrishna · Answer

Let original Price = 100
Lets assume length, width and height of the box be L, B and H
Therefore original box volume = L × W × H

After 20 years Price increased by 60%
new price = old price x 1.6 = 100 × 1.6 = 160

Dimensions: Two dimensions reduced 20%: multiplier = 0.8 each
Third dimension unchanged

L new = L (no change in one dimension)
W new = 0.8 W
H new = 0.8 H

So new volume multiplier:
V new = L × ( 0.8 W ) × ( 0.8 H ) = 0.64 × ( L W H )

Now lets compute price per unit volume

Original price per unit volume: 100 / L W H

New price per unit volume: 160/(0.64 x L W H) = (160/0.64) × (1/L W H) = 250 × (1/L W H)

So New per-unit = 250 , Old per-unit = 100

Percent increase (250 − 100)/100 × 100 % = 150 % increase
 be careful here  100 → 250 is 2.5 times, but the question is to find the % increase
So the price per unit volume increased by 150% (it is 2.5 times the old rate)

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NupurNeha123 · Answer

Great explanation

egmat · Answer

Let's break this into two parts: what happened to the PRICE, and what happened to the VOLUME.

STEP 1: The Price 
Say the original price was  100 . A  60%  increase means the new price is  160 .

STEP 2: The Volume 
A rectangular box has  3  dimensions: length, width, and height.  Volume = length × width × height .

Let's say the original dimensions are  10  ×  10  ×  10 , giving an original volume of  1000 .

Two dimensions were each reduced by  20% . A  20%  reduction means each becomes  80%  of what it was, so  8  instead of  10 . The third dimension stays at  10 .

New volume =  8  ×  8  ×  10  =  640

So the volume shrank to  64%  of the original.

STEP 3: Price Per Unit Volume 
This is simply Price ÷ Volume.

Original price per unit volume =  100  /  1000  =  0.10 
New price per unit volume =  160  /  640  =  0.25

STEP 4: Find the Percent Increase 
Change =  0.25  -  0.10  =  0.15 
Percent increase =  0.15  /  0.10  =  1.50  =  150%

Answer: D

Key Insight:    The key trap here: Don't just add 60% + 20% + 20% to get 100%. That's the most common wrong answer (B).   Percent changes don't simply add  — you must calculate the actual new volume and new price, then find the ratio. The sneaky part is that the box got SMALLER while the price went UP, so you're paying way more per unit of granola than the  60%  price hike suggests.

luisdicampo · Answer

Deconstructing the Question

The price of the box increased by   60\%  , so the new price is   1.6P  .

Two of the three dimensions were reduced by   20\%  , so each of those dimensions becomes   0.8   of the original. The third dimension stays the same.

Since volume is the product of the three dimensions, we first find the new volume factor, then compare price per unit volume.

Step-by-step

Let the original price be   P   and the original volume be   V  .

New price is

1.6P

New volume is

(0.8)(0.8)(1)V = 0.64V

Original price per unit volume is

\frac{P}{V}

New price per unit volume is

\frac{1.6P}{0.64V}

Compare new to old:

\frac{\frac{1.6P}{0.64V}}{\frac{P}{V}} = \frac{1.6}{0.64} = 2.5

So the new price per unit volume is   2.5   times the old one.

Percent increase is

(2.5 - 1)\cdot 100\% = 150\%

Answer: D

The price of a box of Red Valley cereal

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The price of a box of Red Valley cereal

Prep Toolkit

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

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