For a sales promotion, a dog food producer produces packages

Question

For a sales promotion, a dog food producer produces packages with 40 percent more dog food than the regular-size package and sells the larger package for the same price as the usual price of the regular-size package. Compared to the regular-size package at its usual price, approximately what percent less is the price per ounce of the larger package of dog food?

A. 25%
B. 29%
C. 37.5%
D. 40%
E. 60%

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Attachment:

2024-01-27_13-51-20.png

gmatophobia · Accepted Answer

Regular-size Package

Assume

Quantity = 100 ounce 
 Price = $100 
 Price per ounce =  \frac{100}{100}  = $1 per ounce

Promotional Package

The promotional package has 40% more dog food.

Quantity = 100*1.4 = 140 ounce 
 Price = $100 
 Price per ounce =  \frac{100}{140}  = $  \frac{5}{7}  per ounce

Price Difference =  1 - \frac{5}{7} = \frac{2}{7}

Required Percentage =  \frac{\frac{2}{7}}{1}*100  =  \frac{2}{7}*100

If the denominator were 8,

Required Percentage = \frac{2}{8}*100 = 25 %

Hence, our answer will be greater than 25% but close to it. From the available options, the closest value is 29%.

Option B

MartyMurray · Answer

For a sales promotion, a dog food producer produces packages with 40 percent more dog food than the regular-size package and sells the larger package for the same price as the usual price of the regular-size package. Compared to the regular-size package at its usual price, approximately what percent less is the price per ounce of the larger package of dog food?

A. 25%
B. 29%
C. 37.5%
D. 40%
E. 60%

Show Spoiler

Attachment:

2024-01-27_13-51-20.png

Let the normal size in ounces be S and the normal price be P.

The price per ounce for the normal size is P/S.

The price per ounce of the larger size is P/1.4S.

So, the percentage difference is the following:

(P/1.4S - P/S)/(P/S)

Simplifying, we get the following:

1/1.4 - 1 = 10/14 - 14/14 = -4/14 = -2/7

1/7 is a little less than 15%. So, 2/7 is around 29%.

A. 25%
B. 29%
C. 37.5%
D. 40%
E. 60%

Correct answer:  B

ShuGMATTutor · Answer

Ok lets dumb this down for us. "A problem well defined is halfway through to the solution - Kidlins law"

Visualization  
 Now lets imagine this situation more clearly - in "real" terms 
 Lets assume the package used to be 10oz being sold at $100 and now they are selling 14oz for $100.

Translation  
 So lets compare the per oz rates  
 earlier - $100/10 = $10 per oz 
now - $100/14 per oz   (dont simplify till the end)

Approach  
 Lets just now lets calculate the change in price 
 (old-new)/old - check below image

Conclusion & Estimation  
 So the percentage come to around 200/7 - which we know its less than 30% and it is greater than 25% - thus the only workable answer for us 29%

Shu "TheGMATTutor" 
    T  he GMAT concepts are relatively basic   , but they require a deep understanding to tackle nuanced questions effectively. So  lets dumb it down for us . This is    not just a math and English test   —it is a    deductive test designed to assess your problem-solving skills

KarishmaB · Answer

Assume numbers that simplify calculations.

Say the regular package quantity is 100 ml so large package quantity is 140 ml. 
Say usual price of regular package is $140 (not $100 because then price per unit will become a fraction) and that stays the same for the large package.

So price per unit for regular package is $1.4 and for the large package is $1.

So the price per unit for large package is less by approximately  \frac{.4}{1.4} * 100 = \frac{2}{7} * 100 = 28.56%  (percent fraction equivalent taught us that 1/7 = 14.28)

Percent fraction equivalents are discussed here:  https://youtu.be/HxnsYI1Rws8

Answer (B)

bumpbot · Answer

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For a sales promotion, a dog food producer produces packages

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