When the price of oranges is lowered by 40%, 4 more oranges

Question

When the price of oranges is lowered by 40%, 4 more oranges can be purchased for $12 than can be purchased for the original price. How many oranges can be purchased for 24 dollars at the original price?

(A) 8
(B) 12
(C) 16
(D) 20
(E) 24

(A) 8
(B) 12
(C) 16
(D) 20
(E) 24

Bunuel · Accepted Answer

Say  x  is the original price of an orange, then:

xn=12 ;
and 
 0.6x*(n+4)=12  -->  x(n+4)=20  -->  xn+4x=20  -->  12+4x=20  -->  x=2 .

So, for 24 dollars 24/2=12 oranges can be purchased at the original price of $2.

Answer: B.

heygmat · Answer

are there any other ways?

law258 · Answer

Set up:

12/p = x
12/0.60 = x+4

Manipulate and plug the first equation into the second --> you'll find p = $2

Thus $24/$2 per orange = 12 oranges

gracie · Answer

let r=number of oranges purchased originally
 /(12/r)=.6
r/(r+4)=.6
r=6 oranges
$12/6=$2 per orange
$24/$2=12 oranges
B

stonecold · Answer

Here is what i did in this question =>

Let the price of each orange be $x
Hence for $12 => we can buy => 12/x oranges

Now new price => x(1-40/100) => $0.6x
Hence for $12 we could now buy => 12/0.6x

As per the given information => 12/x+4=12/0.6x
Hence 12+4x/x=20/x
=> 12+4x=20
=>x=2

So the price of each orange is $2

Now for 24 dollars => we can buy => 1/2*24=12 oranges

SMASH THAT B.

gmatzpractice · Answer

12/(.6x)=12/x+4
20=12+4x
x=2
24/2

Answer B

ScottTargetTestPrep · Answer

We use the equation: price per item x no. of items = total cost. Here, we let p = the original price of an orange and q = the original number of oranges purchased. We can create the equation for the original total cost:

pq = 12

q = 12/p

After the orange’s price is lowered, we have that 0.6p = the new (reduced) price of an orange and (q + 4) = the new number of oranges that can be purchased at the reduced price. Our new equation for total cost is:

(0.6p)(q + 4) = 12

0.6pq + 2.4p = 12

Substituting for q, we have:

0.6p(12/p) + 2.4p = 12

7.2 + 2.4p = 12

2.4p = 4.8

p = 2

That is, each orange is $2. So for $24, we can buy 24/2 = 12 oranges.

Answer: B

ScottTargetTestPrep · Answer

Let P denote the price per orange (before discount) and Q denote the number of oranges that can be bought for $12 (before discount). We can create the equations:

P * Q = 12

Q = 12/P

and

0.6P * (Q + 4) = 12

0.6PQ + 2.4P = 12

Substituting, we have:

0.6P * 12/P + 2.4P = 12

7.2 + 2.4P = 12

2.4P = 2.8

P = 2, so for 24 dollars, 12 oranges can be purchased.

Answer: B

BrentGMATPrepNow · Answer

The price of oranges is lowered by 40%  
Let  x  = the ORIGINAL price per orange (in dollars)
So,  0.6x  = the REDUCED price per orange

4 more oranges can be purchased for $12 than can be purchased for the original price.  
Let's start with a "word equation"

(number of oranges that can be purchased for $12 at the REDUCED price)  = ( number of oranges that can be purchased for $12 at the ORIGINAL price ) + 4
Substitute values to get: 12/ 0.6x  = 12/ x  + 4 
Multiply both sides of the equation by x to get: 12/0.6 = 12 + 4x
Simplify: 20 = 12 + 4x
Subtract 12 from both sides: 8 = 4x
Solve: x = 2
In other words, the ORIGINAL price per orange is  $2

How many oranges can be purchased for 24 dollars at the ORIGINAL price?  
24/ 2  = 12 oranges

Answer: B

Target4bschool · Answer

Let x be the original price per orange. 
Suppose, we buy y oranges, then, 
xy =12

Now, after reduction: 
0.6x (y+4) =12
0.6xy + 2.4x = 12
0.6*12 + 2.4x =12
x=2

So, total number of oranges which can be bought = 24/2 = 12

KarishmaB · Answer

Here is how one can do it without any variables: We know, Revenue = Price * Quantity So if price becomes 60% i.e. 3/5, the quantity will become 5/3 to retain the same total amount of $12. New quantity of oranges : Old quantity of oranges = 5:3 The difference of 2 on ratio scale is actually 4 oranges so multiplier is 2. Hence we can now purchase 10 oranges in $12 where initially we could purchase only 6 oranges for $12. So initially we could purchase 12 oranges for $24. Answer (B) Check: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... of-ratios/ to understand the ratios and multiplier.

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

When the price of oranges is lowered by 40%, 4 more oranges

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

When the price of oranges is lowered by 40%, 4 more oranges

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