GMAT CLUB OLYMPICS: On a market, two merchants sold total of 100 pinea

Question

On a market, two merchants sold total of 100 pineapples and earned the same amount of money. If the first merchant had sold the second merchants pineapples at first merchant's price per pineapple, he would earned $15 and if the second merchant had sold the first merchants pineapples at second merchant's price per pineapple, he would earned $\$6\frac{2}{3}$. How many pineapples did the second merchant sell ?

A. 20
B. 30
C. 40
D. 60
E. 80

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A. 20
B. 30
C. 40
D. 60
E. 80

M37-60

Bunuel · Accepted Answer

Official Solution:

On a market, two merchants sold total of 100 pineapples and earned the same amount of money. If the first merchant had sold the second merchants pineapples at first merchant's price per pineapple, he would earned $15 and if the second merchant had sold the first merchants pineapples at second merchant's price per pineapple, he would earned $\$6\frac{2}{3}$. How many pineapples did the second merchant sell ?

A. 20
B. 30
C. 40
D. 60
E. 80

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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A.  20 
B.  30 
C.  40 
D.  60 
E.  80

Say the first merchant sold  x  pineapples at  $a  per pineapple and the second merchant sold  y  pineapples at  $b  per pineapple.
 
They earned the same amount, so:  xa = yb . This gives:  \frac{a}{b} = \frac{y}{x} .
 
If the first merchant had sold the second merchants pineapples at first merchant's price per pineapple, he would earned  $15 :  ya=15 ;
 
If the second merchant had sold the first merchants pineapples at second merchant's price per pineapple, he would earned  $6\frac{2}{3} :  xb=\frac{20}{3} 
 
Divide:  ya=15  by  xb=\frac{20}{3}  to get:  \frac{y}{x}*\frac{a}{b}=\frac{9}{4} 
 
Substitute  \frac{a}{b} = \frac{y}{x}  into  \frac{y}{x}*\frac{a}{b}=\frac{9}{4}  to get  \frac{y}{x}*\frac{y}{x}=\frac{9}{4} ;
 
 (\frac{y}{x})^2=\frac{9}{4} ;
 
 \frac{y}{x}=\frac{3}{2} ;
 
Since  x+y=100 , then  x=40  and  y=60 .

Answer: D

Kinshook · Answer

Given: On a market, two merchants sold total of 100 pineapples and earned the same amount of money. If the first merchant had sold the second merchants pineapples at first merchant's price per pineapple, he would earned $15 and if the second merchant had sold the first merchants pineapples at second merchant's price per pineapple, he would earned  \$6\frac{2}{3} .

Asked: How many pineapples did the second merchant sell ?

Let the pineapples sold by second merchant be x.
Pineapples sold by first merchant = 100 - x

Let the first merchant's price per pineapple be p1 and second merchant's price per pineapple be p2.

On a market, two merchants sold total of 100 pineapples and earned the same amount of money.
p1 (100-x) = p2 x 
p1 /p2 = x/(100-x) (1)

If the first merchant had sold the second merchants pineapples at first merchant's price per pineapple, he would earned $15.
x p1 = 15 (2)

if the second merchant had sold the first merchants pineapples at second merchant's price per pineapple, he would earned  \$6\frac{2}{3} 
(100-x)p2 = 6 2/3 = 20/3 (3)

(2)/(3)

xp1/(100-x)p2 = 15*3/20 = 9/4
{x/(100-x)}^2 = 9/4 
x/(100 - x) = 3/2 
2x = 300 - 3x
5x = 300
x = 300/5 = 60

IMO D

sumitkrocks · Answer

Let us assume 
First merchant sold x Pineapples at a $ per peace
second merchant sold y Pineapples at b $ per peace

x+ y =100 
also 
ax = by (they earn equal amounts)

ay = 15 
bx = \frac{20}{3}

\frac{ay}{bx}  = 15* \frac{3}{4}
 
 \frac{y}{x =3/2} 
y = 60

(D) is correct

JonShukhrat · Answer

Initially both merchants earned an equal amount. However, when the second merchant sold the pineapples of the first at his own price, his revenue decreased. This means that the second merchant initially sold more number of pineapples than the first, and for a lower price than that of the first. Since overall number is 100, the second initially sold more than 50. Only D and E give us such value. Let’s try D.

Second: 60 for Y each
First: 40 for X each

then 40*Y=20/3 so x=1/6
then 60*X = 15 so x = ¼

Let’s check: 60*1/6=10
40*1/4=10
10=10

So D

Second: 60 for Y each 
First: 40 for X each

then 40*Y=20/3 so x=1/6
then 60*X = 15 so x = ¼

Let’s check: 60*1/6=10
40*1/4=10
10=10

So D

ctio90 · Answer

let
a = qty of 1st merchant
b = qty of 2nd merchant
x = price of 1st merchant
y = price of 2nd merchant

a + b = 100 
b.x = 15 ; b = 15/x
a.y = 20/3 ; a = 20/3y
 find b?

a.x = b.y ------> the two merchants earn same amount of money
(20/3y) . x = (15/x) . y 
20.x^2 = 45.y^2
4.x^2 = 9.y^2
2x = 3y ; x = 3y/2

again use, a.x = b.y
3y.a/2 = b.y --- > eliminate y
3.a = 2.b

a = 40,  b = 60 
check a + b = 100

neutronstar · Answer

It is very difficult to solve question by building an equation. So I decided to apply plug and check approach.

Creating a matrix with 3 columns can be easier. Check image below for 5 step process. After following the process for option A & B it was clear that number of fruits sold by 2nd merchant should be more than number of fruits sold by 1st merchant. Hence, logically, answer should be between D & E. While plugging, 15 is a factor of 60 so I tried option D first in the 5 step process below. Option D is the correct answer.

bumpbot · Answer

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GMAT CLUB OLYMPICS: On a market, two merchants sold total of 100 pinea

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GMAT CLUB OLYMPICS: On a market, two merchants sold total of 100 pinea

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