Harvis Wheels rents 64 vehicles, most of them minivans

Question

Harvis Wheels rents 64 vehicles, most of them sedans and the rest minivans. At Harvis Wheels, a sedan costs 60 percent less to rent than a minivan. On one particular day, every Harvis Wheels vehicle was rented, generating $3,910 in revenue. If the daily rental rate for a sedan is a two-digit integer, how much revenue came from the minivans that day?

(A) $1,150
(B) $1,610
(C) $2,300
(D) $2,760
(E) $2,890

Show Answer

Official Answer

B

(A) $1,150
(B) $1,610
(C) $2,300
(D) $2,760
(E) $2,890

HarshavardhanR · Answer

Here is one way to solve this. I look forward to seeing quicker solves on this one! https://gmatclub.com/forum/download/file.php?id=89480 --- Harsha GMAT-Club-Forum-rctswm2f.png

simranatwork · Answer

please give a simple easy to understand solution

egmat · Answer

Hi simranatwork,

Happy to lay this out step by step. The trick is to turn the words into a rate relationship, then let the answer choices do the heavy lifting.

Step 1: Translate "60% less"

A sedan costs  60% less  than a minivan, so a sedan is  40%  of the minivan rate. Flip that around:

- minivan rate =  2.5 x  sedan rate

So if the sedan rate is s, the minivan rate is 2.5s.

Step 2: Set up counts

Let the number of sedans be n. Then minivans =  64  - n, and since  most  are sedans, n >  32 . Total revenue:

- sedan revenue = n · s
- minivan revenue = (64 - n) · 2.5s

Step 3: Use the choices - and watch s cancel

Each answer choice  is  the minivan revenue, so the sedan revenue is  3910  - (choice). Now take the ratio of the two revenues:

minivan rev / sedan rev = 2.5s(64 - n) / (s · n) = 2.5(64 - n) / n

Notice s  cancels  - the ratio depends only on n. That's what makes this clean.

Test choice B ($1,610):  sedan revenue =  3910  -  1610  =  2300 .

1610  /  2300  = 0.7 = 2.5( 64  - n) / n =>  160  - 2.5n = 0.7n => n =  50

That gives  50  sedans (yes, >  32 ) and  14  minivans. Then s =  2300  /  50  =  46  - a  two-digit integer , exactly as required. Check:  14  x (2.5 x  46 ) =  14  x  115  =  1610 . ✓

Why the others fail

Run the same ratio on A, C, D, E and every one gives a  non-integer  number of sedans (or fewer than  33  sedans). Only  B  produces whole vehicles  and  a two-digit sedan rate - that two-digit clue is the filter that pins down the answer.

So the minivans brought in  $1,610 .

Answer: B

kevincan · Answer

Let s be the number of sedans. Then there are 64 − s minivans. We know s > 32 because most of the vehicles are sedans.

A sedan costs 60% less to rent than a minivan, so the sedan rental rate is 2/5 of the minivan rental rate. Thus, if the sedan rental rate is c, the minivan rental rate is 5c/2.

Therefore,

3910 = sc + (64 − s)(5c/2)

Multiplying by 2:

7820 = 2sc + 320c − 5sc

7820 = c(320 − 3s)

Now factor 7820:

7820 = 2 × 2 × 5 × 391

Since

391 = 202 − 9 = 23 × 17,

we have

7820 = 2 × 2 × 5 × 17 × 23.

Since s > 32 and c > 0, 320 − 3s is a positive factor of 7820 that is less than 224.

The relevant factor is 170:

320 − 3s = 170

3s = 150

s = 50.

Thus there are 50 sedans and 14 minivans.

Also,

c = 7820/170 = 46.

The minivan rental rate is

(5/2)(46) = 115.

Therefore, the revenue from the minivans was

14 × 115 = $1,610.

Answer: (B) $1,610

Harvis Wheels rents 64 vehicles, most of them minivans

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Harvis Wheels rents 64 vehicles, most of them minivans

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards