Lee is buying apples to make pies. The apples cost $1 per pound and

Question

Lee is buying apples to make pies. The apples cost $1 per pound and each pie requires 3 cups of peeled and cored apple. Lee estimates that each apple loses 1/5th of its weight when it is peeled and cored and that 2 cups of peeled and cored apples weigh 1 pound. Based on estimates, which of the following represents the cost, in dollars, of the apples for p pies?

$ \frac{3p}{10 }$

$\frac{4p}{10}$

$\frac{6p}{5}$

$ \frac{3p}{2}$

$\frac{15p}{8}$

A.   \frac{3p}{10 }

B.  \frac{4p}{10}

C.  \frac{6p}{5}

D.   \frac{3p}{2}

E.  \frac{15p}{8}

RCARC · Accepted Answer

for making 1 pie,
2 cups = 1 pound 
1 pie = 3 cups
3 cups = 1.5 pound
1 pound apples lose 1/5 or 20% of its weight to become 4/5.
x pound apples lose x/5 or 20% of its weight to become 4x/5.
4x/5 = 1.5pound
x = 1.5*5/4 = 15/8 pounds

chetan2u · Answer

2 cups of peeled and cored apples weigh 1 pound, so 3 cups of peeled and cored apples would weigh 1.5 pound.

What exactly comes out of one pound apple = 0.8 pound of peeled apple.
or 1 pound of peeled apple =  \frac{1}{0.8}  of apples.
So, 1.5 pound peeled apple will require  \frac{1}{0.8}*1.5  or  \frac{15}{8} of apples.
Thus, one pie requires  \frac{15}{8}  pounds of apples.
=> 'p' pies will require  p*\frac{15}{8} of apples.

E

Archit3110 · Answer

cost per apple is $1
total 3 cups peeled cored apples required
weight loss is 1/5th
4/5 is what we will have per apple
let apples used be x
4x/5 is total weight of apple 
given 2 cups of peeled and cored apples = 1 pound
8x/5 is weight per pound
cost per apple will be 
each pie requires 3 cups so for p pies 3p cups required
8x/5 = 3p
x = 15p/8

PB005 · Answer

given:
cost of 1 pound of apples: $1
1 pie = 3 cups Peeled+cored (p+c) apples
1/5 wt lost during p+c => 4/5 wt remained per apple
2 cups p+c apples = 1 pound

to find: 
cost to buy apples to make p pies

soln:
1 pie = 3 cups => 1.5 pound of p+c apples =>1.5*(5/4) pounds of unpeeled and cored apples = 15/8 pounds (=$15/8 cost)
so, for p pies: $ p*15/8

jasminepuri · Answer

I got 1.5 lbs required for 2 cups. Then,
I did (1.5) * (1+1/5), i.e., adding 1/5 to account for the lost apples. Can anyone explain why that is wrong?

nicksteele · Answer

1 pound of regular apples = $1
1 pie = 3 cups of P&C apples

Each regular apples loses 1/5th of its weight after peeling and coring --> remaining weight = 4/5th

1 pound of regular apples = 4/5 pound of P&C apples
1 pound of P&C apples = 5/4 pounds of regular apples
1 pound of P&C apples = 2 cups
2 cups of P&C apples = 5/4 pounds of regular apples

Making the number of cups equal
(1 pie = 3 cups of P&C apples ) x2
(2 cups of P&C apples = 5/4 pounds of regular apples) x3

2 pie = 6 cups of P&C apples
6 cups of P&C apples = 15/4 pounds of regular apples

Cost per pound = $1
Cost per 15/4 pound = $15/4

Substituting P for 2 in answer choices

E) 15p/8 --> 15*2/8 = 15/4

nguyenpham1309 · Answer

1.5 lbs is of peeled and cored apples, which already lost 1/5 weight compared to the original whole apples.

"Lee estimates that each apple loses 1/5th of its weight when it is peeled and cored". We translate this sentence one by one:
=> (full) each apple = (1-1/5) * cored and peeled apples
=> each apple = cored and peeled *4/5 => 1.5*4/5 (not 6/5 as what you are writing)

juancarlos12 · Answer

Try to follow an order to solve this type of problem, otherwise it may get a bit confusing.

Cost(appl)=$1/pound  
1 pound appl= $1 --(0) 
  1pie=3cups PCappl --(1)

1appl=(1-1/5) PCappl --weight
1appl=4/5 PCappl --weight 
5/4 appl= 1 PCappl   --weight ---(2)

2cups PCappl = 1 pound PCappl 
 1 cup PCappl =1/2 pound PCappl ---(3)

which of the following represents the cost, in dollars, of the apples for p pies?
 Use formula (1) 
 
 p pies= 3p  cups PCappl   
 Use formula (3) 
 
 p pies= 3p*1/2  pound PCappl   
 Use formula (2)  
 
 p pies= 3p*1/2*5/4  pound appl   
 Use formula (0) 
 
 p pies= 3p*1/2*5/4 *$1
p pies= $15p/8

KarishmaB · Answer

When you have a variable in the options, one easy way to handle the question is to take a value for the variable. 
So say I want to bake 1 pie. p = 1. If I do that, each option will give me a different value so I am good.

1 pie needs 3 cups of peeled and cored apples. 
2 cups of peeled and cored apples weigh 1 pound. So 3 cups will weigh 1.5 pounds. So I need 1.5 pounds (or 3/2) of peeled and cored apples.

When an apple is peeled and cored, it loses 1/5th of its weight i.e. it becomes 4/5th of its actual weight. 
This 3/2 pounds is 4/5th of actual apple weight so actual apple weight is (3/2) * (5/4) = 15/8

So I need 15/8 pounds of actual apples which means a cost of $15/8 (since cost of apples is $1/pound)

p = 1 gives me 15/8 in option (E).

Answer (E)

abhichatur · Answer

KarishmaB  I ended up making the mistake where I was saying that 1 pound of unpeeled apples mean 1.2 pounds of peeled apples. While I figured out the mistake by seeing the solutions, what can I change in the thought process/procedure that I never get that wrong again.

KarishmaB · Answer

It is a common error. Before you take a percentage, always think about what the base is. If it is 10%, then 10% of what?

Check the discussion here:  https://youtu.be/HxnsYI1Rws8

abhichatur · Answer

Thank you Karishma. That was helpful

Dbrunik · Answer

Hey im still having a hard time understanding why we multiply by 5/4 and not 4/5. can you help me visualize this ? if we have 1.5 pounds that we need, the apples we get will only be 80% of what we pay. what am i missing here? cost = price apples * quantity where the price stays the same, 1$ per pound, and quantity of 1.5 pounds which is reduced by 1/5. ?

chetan2u

2 cups of peeled and cored apples weigh 1 pound, so 3 cups of peeled and cored apples would weigh 1.5 pound.

What exactly comes out of one pound apple = 0.8 pound of peeled apple.
or 1 pound of peeled apple =  \frac{1}{0.8}  of apples.
So, 1.5 pound peeled apple will require  \frac{1}{0.8}*1.5  or  \frac{15}{8} of apples.
Thus, one pie requires  \frac{15}{8}  pounds of apples.
=> 'p' pies will require  p*\frac{15}{8} of apples.

E

Kinshook · Answer

poddarritika98

Lee is buying apples to make pies. The apples cost $1 per pound and each pie requires 3 cups of peeled and cored apple. Lee estimates that each apple loses 1/5th of its weight when it is peeled and cored and that 2 cups of peeled and cored apples weigh 1 pound.

Based on estimates, which of the following represents the cost, in dollars, of the apples for p pies?

The cost of apples = $1 per pound
The cost of peeled and cored apples = $1/(1-1/5) = $1/(4/5) = $1.25 per pound
1 cups of peeled and cored apples weight = .5 pound
1 pie require 3 cups of peeled and cored apples weighing = 3*.5 = 1.5 pound
The cost of 1 pie = $1.25*1.5 = 5/4*3/2 = $15/8 
The cost of p pies = $15p/8

IMO E

DanTheGMATMan · Answer

Tricky word problem. Figure out how many pounds of apples you need to buy to make 3 cups of peeled and cored apples:

https://www.youtube.com/watch?v=leO_utC4pj8

Ggt1234 · Answer

Hi Dbrunik,

So 3/2 pounds of cored apples is required. An apple loses 4/5 of its weight after it is cored. Hence an apple is 4/5 of its weight after being cored. Now how do we convert 3/2 pounds of cored apple to apple?
So here X pounds of 4/5 fresh apples = 3/2 pounds of cored apples. so x= 3/2 * 5/4 = 15/8

nabz2024 · Answer

Dimension analysis or unit conversion - but this is a really tricky problem because of the apples losing weight after being peeled and cored.

We want to ultimately know how much money needs to be spent on apples to make p pies.

? $ on apples for p pies can be written as... (pca = peeled and cored apples)

= ($1 / 1 lb. reg aps) *  (1 lb. reg aps / (4/5) lb. of pca)  * (1 lb. of pca / 2 cups pca) * (3 cups pca / 1 pie) * (p pies)

Think of it as (in english):
 
 $1 for 1 pound of regular apples 
  1 pound of regular apples for 4/5 pounds of peeled and cored apples  
 1 pound of peeled and cored apples for 2 cups of peeled and cored apples 
 3 cups of peeled and cored apples for 1 pie 
 we are making p pies

Cancel out units so you are left with just dollars (because the question is asking for how much money) and notice the  4/5 flips  because it was in the denominator:

Fractions rewritten => ($1/1)* (5/4) *(1/2)*(3/1)*p = $ 15p/8

GMAT2025champ · Answer

1 pie = 3 cups
P pies= 3p cups

2 cups = 1 pound
3p cups = 3/2p pounds

But 3/2p is net after 1/5 weight loss; (1/5=20%) so;

3/2p = 80%
 ? = 100%

cross multiply 100/80 * 3/2p= 5/4 * 3/2p = 15/8p

HarshavardhanR · Answer

1 pie needs 3 cups of peeled and cored apples. 
 So, p pies need 3p cups of peeled and cored apples. 
 2 cups of peeled and cored apples weigh 1 pound. 
 Then, 3p cups of peeled and cored apples weigh 3p/2 pounds. 
 But remember - it is the whole apple that is bought at $1/pound, not a peeled and cored apple. 
 We know that 4/5 pound of peeled and cored apple comes from 1 pound of apple. 
 Then, 3p/2 pounds of peeled and cored apple will come from 15p/8 pounds of whole apples. 
 Finally, 1 pound of apples costs $1. So, 15p/8 pounds of apples will cost $ 15p/8.

So, p pies will incur a cost of $ 15p/8 for the apples.

---
Harsha

Lee is buying apples to make pies. The apples cost $1 per pound and

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

Lee is buying apples to make pies. The apples cost $1 per pound and

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