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Math Expert V
Joined: 02 Sep 2009
Posts: 55684
A dealer originally bought 15 identical cars. If each car was sold for  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 72% (02:07) correct 28% (02:31) wrong based on 34 sessions

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A dealer originally bought 15 identical cars. If each car was sold for q dollars, which was 60 percent above the original cost per car, then in terms of q, what was the total cost of the cars, in dollars, to the dealer?

A. q/250
B. 5q/8
C. 75q/8
D. 9q/10
E. 24q

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Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3373
Location: India
GPA: 3.12
A dealer originally bought 15 identical cars. If each car was sold for  [#permalink]

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Bunuel wrote:
A dealer originally bought 15 identical cars. If each car was sold for q dollars, which was 60 percent above the original cost per car, then in terms of q, what was the total cost of the cars, in dollars, to the dealer?

A. q/250
B. 5q/8
C. 75q/8
D. 9q/10
E. 24q

Since the car was sold for q dollars which was 1.6 times the cost, the cost of the car would be $$\frac{q}{1.6}$$

Since he bought 15 identical cars, the cost of the cars would be $$15*\frac{q}{1.6} = \frac{150q}{16} = \frac{75q}{8}$$(Option C)
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Senior SC Moderator V
Joined: 22 May 2016
Posts: 2899
Re: A dealer originally bought 15 identical cars. If each car was sold for  [#permalink]

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Bunuel wrote:
A dealer originally bought 15 identical cars. If each car was sold for q dollars, which was 60 percent above the original cost per car, then in terms of q, what was the total cost of the cars, in dollars, to the dealer?

A. q/250
B. 5q/8
C. 75q/8
D. 9q/10
E. 24q

Another approach: assign values.
When you see fractions in answer choices, choose small values.
Almost always, if chosen values are small, the fractional answers can be assessed quickly.

Sell price is 60 percent above cost. SP = 1.6 * cost price
Use two integers. 5 * 16 = 80, so 5 * 1.6 = 8
You could also use cost = $10 and SP =$16

Let cost = $5 per car Then Sell Price =$5 * 1.6 = $8 So q =$8
Total cost = ($5 * 15) =$75

With q = 8, find the answer that yields $75 Eliminate A, B, and D immediately. Their numerators and denominators make their results much too small: $$\frac{8}{250}$$, $$\frac{40}{8}$$, and $$\frac{72}{10}$$, respectively Eliminate E, too. 24 * 8 will not yield an answer whose units digit is 75 (And 24 * 8 > 160, more than twice what we need) Check C) 75q/8 $$(75 * 8) = (150 * 4) = 600$$ (double one factor and halve the other) $$\frac{600}{8}= \frac{300}{4} = \frac{150}{2}$$=$75. Correct.

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Tell me, what is it you plan to do with your one wild and precious life? -- Mary Oliver Re: A dealer originally bought 15 identical cars. If each car was sold for   [#permalink] 05 Jan 2018, 09:48
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