A clock store sold a certain clock to a collector for 20 per

[estarkman1030]

I am taking a practice test and I am confused about one answer to a question...

"A clock store sold a certain clock to a collector for 20 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 50 percent of what the collector had paid. The shop then sold the clock again at a profit of 80 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $100, for how much did the shop sell the clock the second time?


$270

$250

$240

$220

$200"

The explanation states that the answer is $270 for the following reason:

"If p is the price that the shop originally paid for the clock, then the price that the collector paid was 1.2p (to yield a profit of 20%). When the shop bought back the clock, it paid 50% of the sale price, or (.5)(1.2)p = .6p. When the shop sold the clock again, it made a profit of 80% on .6p or (1.8)(.6)p = 1.08p.

The difference between the original cost to the shop (p) and the buy-back price (.6p) is $100.
Therefore, p - .6p = $100. So, .4p = $100 and p = $250.

If the second sale price is 1.08p, then 1.08($250) = $270. (Note: at this point, if you recognize that 1.08p is greater than $250 and only one answer choice is greater than $250, you may choose not to complete the final calculation if you are pressed for time.)

The correct answer is A."

From ManhattanGMAT CAT1 Question 33/37

I do not understand how we arrived at 1.08 after this part "When the shop sold the clock again, it made a profit of 80% on .6p or (1.8)(.6)p = 1.08p."

Any advice?

Thanks

[tim]

So I assume you've figured out how to arrive at .6p as the buy-back price (let me know if you need help with that). If you want to sell something at 80% profit, that means you are getting the price you paid plus 80% of that price, in other words 180% of the price, which means you will multiply by 1.80. Multiplying 1.80 by .6p gives you the 1.08p that was described in the solution.

[estarkman1030]

Thank you very much Tim!

[RonPurewal]

glad we could help.

in the future, be sure to post these things in the correct folder. (this folder is for problems from the GMAT PREP software; there are separate folders for MGMAT problems.)
thanks.