Is this question wrong ?

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Is this question wrong ?

by TkNeo » Sun Feb 03, 2008 9:38 am
If an appliance store sells two sizes of air conditioners, an 8000 BTU air conditioner for $235 and a 14000 BTU air conditioner for $465. If, during a sale, the store sold 3 more of the 8000 BTU models than 14000 BTU models and generated revenue of $3495, how many total air conditioners did it sell.

A: 3
B: 6
C: 9
D: 12
E: 13


I don't have an explanation to the solution but the answer key says C:9

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Re: Is this question wrong ?

by Stuart@KaplanGMAT » Sun Feb 03, 2008 11:24 am
TkNeo wrote:If an appliance store sells two sizes of air conditioners, an 8000 BTU air conditioner for $235 and a 14000 BTU air conditioner for $465. If, during a sale, the store sold 3 more of the 8000 BTU models than 14000 BTU models and generated revenue of $3495, how many total air conditioners did it sell.

A: 3
B: 6
C: 9
D: 12
E: 13


I don't have an explanation to the solution but the answer key says C:9
Let's call the # of 8000 models "x" and the number of 14000 models "y".

x = y + 3

and

235x + 465y = 3495

235 (y + 3) + 465y = 3495

235y + 465y + 705 = 3495

700y = 2790

y = not an integer! That's unpossible!

Let's try backsolving.

If we sold 9 machines, then we sold 6 * 8000 and 3 * 14000 (since there were 3 more of the 8000s sold).

Revenue would be:

6(235) + 3(465) = 1410 + 1395 = 2805. Doesn't match the revenue we need, therefore (c) can't be the right answer.

We need more revenue, so let's try more machines.

There's no even number we can sell and generate 3 more 8000s than 14000s, so let's jump right to (e).

If we sold 13 machines, then we sold 8 * 8000 and 5 * 14000.

Revenue would be:

8(235) + 5(465) = 1880 + 2325 > 4000, so now we have too much revenue.

There's no possible integer answer, so it's an impossible question. Where is it from?
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Re: Is this question wrong ?

by TkNeo » Sun Feb 03, 2008 12:47 pm
Its from peterson's prep...

I have come across wrong question in the past in peterson's tests... Its so annoying to have a wrong question in the test.. wastes a lot of time !

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backsolving

by resilient » Tue Feb 05, 2008 1:17 am
store sold 3 more of the 8000 BTU models than 14000 BTU models ....how did you translate that int y=3b. this is the hard part. also where can i look to get more brushed up on math back solving.
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Re: backsolving

by Stuart@KaplanGMAT » Tue Feb 05, 2008 12:09 pm
Enginpasa1 wrote:store sold 3 more of the 8000 BTU models than 14000 BTU models ....how did you translate that int y=3b. this is the hard part. also where can i look to get more brushed up on math back solving.
The correct translation of "more than" is to use the addition operation.

So, if they sold 3 more Xs than Ys, that means that:

x = y + 3

Backsolving is covered extensively in the Kaplan GMAT materials, I'm not sure about other resources.
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