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Bunuel
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Several persons rented a car for $30. If there had been one more perso 06 May 2019, 21:02
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

85% (01:35) correct 15% (02:04) wrong based on 68 sessions

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Several persons rented a car for $30. If there had been one more person in the group, it would have cost each person $1 less. How many people were in the group originally?

A. 5
B. 6
C. 10
D. 12
E. 15
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A
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Several persons rented a car for $30. If there had been one more perso 06 May 2019, 23:24
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30/x = (30/x+1) + 1
=> x = 5

Option (A).
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Several persons rented a car for $30. If there had been one more perso 25 Jun 2019, 03:05
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GyanOne

can you maybe further explain? I got the answer right by seeing the relation between 5 & 6, but wanted to be able to solve it with an equation as well. I just can not figure out how to solve it, like you did. Thanks a lot!
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Several persons rented a car for $30. If there had been one more perso 09 Jul 2019, 07:16
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GyanOne

can you maybe further explain? I got the answer right by seeing the relation between 5 & 6, but wanted to be able to solve it with an equation as well. I just can not figure out how to solve it, like you did. Thanks a lot!

\(\frac{30}{x}=(\frac{30}{x+1})+1\) (multiply by \(x\))

\(30=(\frac{30x}{x+1})+x\) (multiply by \(x+1\))

\(30x+30=30x+x^2+x\)

--> \(x^2+x-30\) (then solve for \(x\))

\((x-5)*(x+6)\) \(x\) needs to be positive based on the question and logic. So only \(x=5\) makes sense, therefore (A).

This techniques helps in solving quadratic equations quickly: https://gmatclub.com/forum/how-to-solve-quadratic-equations-factor-quadratic-equations-241297.html
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Several persons rented a car for $30. If there had been one more perso 10 Jul 2019, 17:23
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Bunuel
Several persons rented a car for $30. If there had been one more person in the group, it would have cost each person $1 less. How many people were in the group originally?

A. 5
B. 6
C. 10
D. 12
E. 15


We can let n = the number of people originally in the group, so 30/n represents the amount that each person originally had to pay. We can create the equation:

30/n = 30/(n + 1) + 1

Multiplying by n(n + 1):

30(n + 1) = 30n + n(n + 1)

30n + 30 = 30n + n^2 + n

n^2 + n - 30 = 0

(n + 6)(n - 5) = 0

n = -6 or n = 5,

Since n can’t be negative, so n = 5.

Answer: A
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