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Three friends rented a car for a week and divided the cost equally. Wh

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Math Expert
Joined: 02 Sep 2009
Posts: 47037
Three friends rented a car for a week and divided the cost equally. Wh [#permalink]

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22 Dec 2014, 09:17
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Difficulty:

35% (medium)

Question Stats:

73% (00:52) correct 27% (01:00) wrong based on 215 sessions

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Tough and Tricky questions: Word Problems.

Three friends rented a car for a week and divided the cost equally. What was the total cost of renting the car ?

(1) If the three friends had kept the car for a second week, they could have obtained the two-week rate, which was 1.5 times the cost of a one-week rental.
(2) If a fourth friend had joined the three friends and the cost had been divided equally among the four friends, the cost to each of the original three would have been reduced by $15 ? Kudos for a correct solution. _________________ Most Helpful Community Reply Manager Joined: 20 Feb 2013 Posts: 76 Location: India GMAT 1: 690 Q49 V34 WE: Information Technology (Computer Software) Re: Three friends rented a car for a week and divided the cost equally. Wh [#permalink] Show Tags 22 Dec 2014, 10:08 4 3 Statement 1: If the three friends had kept the car for a second week, they could have obtained the two-week rate, which was 1.5 times the cost of a one-week rental We don't know the exact value for either week 1 or week 2 -- Insufficient Statement 2: If a fourth friend had joined the three friends and the cost had been divided equally among the four friends, the cost to each of the original three would have been reduced by$15
r/3 - r/4 = 15
r = 180 -- Sufficient

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Manager
Joined: 27 Jan 2013
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Location: United States
Concentration: Entrepreneurship, Marketing
GMAT 1: 730 Q49 V40
GPA: 3.5
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Re: Three friends rented a car for a week and divided the cost equally. Wh [#permalink]

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22 Dec 2014, 20:50
S(1): No information about the $rate of either weeks. Hence no way to determine exact value. Hence Not Sufficient S(2): lets assume total cost is 12x. The initially in the group of 3 the cost to each is 4x. Now with addition of 4th friend cost of each friend is equal to 3x. Hence x=15. Total cost=180$. Hence Sufficient.

Note that we do not need to calculate the answer. looking at B we should realize that we will end up with a equation with 1 variable only. Hence we will definitely get 1 answer only and thus B is sufficient. Working out the exact solution is not required.
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Joined: 29 Oct 2013
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Re: Three friends rented a car for a week and divided the cost equally. Wh [#permalink]

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23 Dec 2014, 06:33
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Bunuel wrote:

Tough and Tricky questions: Word Problems.

Three friends rented a car for a week and divided the cost equally. What was the total cost of renting the car ?

(1) If the three friends had kept the car for a second week, they could have obtained the two-week rate, which was 1.5 times the cost of a one-week rental.
(2) If a fourth friend had joined the three friends and the cost had been divided equally among the four friends, the cost to each of the original three would have been reduced by $15 ? Kudos for a correct solution. St-1. Let the cost of rental for one week be X. Then for two weeks it is 1.5X. No amount details any where so not sufficient St-2. Let X be the cost of rental. Then $$\frac{X}{3}$$ - $$\frac{X}{4}$$ = 15. X can be calculated. Sufficient Ans - B Manager Joined: 21 Aug 2010 Posts: 180 Location: United States GMAT 1: 700 Q49 V35 Re: Three friends rented a car for a week and divided the cost equally. Wh [#permalink] Show Tags 23 Dec 2014, 12:00 2 Bunuel wrote: Tough and Tricky questions: Word Problems. Three friends rented a car for a week and divided the cost equally. What was the total cost of renting the car ? (1) If the three friends had kept the car for a second week, they could have obtained the two-week rate, which was 1.5 times the cost of a one-week rental. (2) If a fourth friend had joined the three friends and the cost had been divided equally among the four friends, the cost to each of the original three would have been reduced by$15 ?

Kudos for a correct solution.

We need to find T = A+B+C; since A=B=C T=3A =>T/3 = A

1) no $value provided - Not sufficient 2) from this t/4 = A and t/3-t/4 =$15 Solving this will give t= $180 - Sufficient Ans B _________________ ------------------------------------- Math Expert Joined: 02 Sep 2009 Posts: 47037 Re: Three friends rented a car for a week and divided the cost equally. Wh [#permalink] Show Tags 24 Dec 2014, 08:20 Bunuel wrote: Tough and Tricky questions: Word Problems. Three friends rented a car for a week and divided the cost equally. What was the total cost of renting the car ? (1) If the three friends had kept the car for a second week, they could have obtained the two-week rate, which was 1.5 times the cost of a one-week rental. (2) If a fourth friend had joined the three friends and the cost had been divided equally among the four friends, the cost to each of the original three would have been reduced by$15 ?

Kudos for a correct solution.

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Manager
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Re: Three friends rented a car for a week and divided the cost equally. Wh [#permalink]

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18 Jan 2016, 11:27
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(2) The fourth guy simply put in 15$for each of the three original guys = 45$. As they all paid the same, they all paid 45\$ - hence total cost 4*45=180.

15 seconds.
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Re: Three friends rented a car for a week and divided the cost equally. Wh [#permalink]

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28 Jan 2017, 14:02
Over to Statement I:

This says that they would have availed a 50% discount for the second week if continued. Not sufficient as it doesn't give us a number. Get rid of A, D

Over to Statement 2:

This compels us write an equation in x, where x is the cost of renting the car for the mentioned week, and our answer too. It translates to (x/3) - (x/4) = 15 and x can be calculated. Sufficient.

Hence B.
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Anaira Mitch

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Joined: 20 Jan 2017
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Re: Three friends rented a car for a week and divided the cost equally. Wh [#permalink]

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27 Jun 2018, 05:57
Oh man I didn't think of the T/3 - T/4=15. But that is easier to my equation set-up.

T/3=C
where C is the cost per person and T is the total of the rental for the week.

T/4=C-15

Therefore:

T=3C and T=4(C-15)

Equate:
3C=4C-60.
C=60
Hence T=180

Regardless, B.
Re: Three friends rented a car for a week and divided the cost equally. Wh   [#permalink] 27 Jun 2018, 05:57
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