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

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

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New post 22 Dec 2014, 09:17
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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 ?

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

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New post 22 Dec 2014, 10:08
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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

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

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New post 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.

Answer is B.

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

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

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New post 23 Dec 2014, 12:00
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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.



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

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New post 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.


The correct answer is B.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: Three friends rented a car for a week and divided the cost equally. Wh [#permalink]

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

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New post 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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