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Percentages - Query

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Percentages - Query

by MI3 » Sun May 22, 2011 2:30 am
Q. Henry purchased 3 items during a sale. He received a 20 percent discount off the regular price of the most expensive item of a 10 percent discount off the regular price of each of the other 2 items. Was the total discount of these three items greater than 15 percent of the sum of the regular prices of the 3 items?
(1) The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20
(2) The regular price of the least expensive item was $15

IMO answer should be A, am i correct?

Thanks,
M
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Source: — Data Sufficiency |
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by GMATGuruNY » Sun May 22, 2011 4:08 am
MI3 wrote:Q. Henry purchased 3 items during a sale. He received a 20 percent discount off the regular price of the most expensive item of a 10 percent discount off the regular price of each of the other 2 items. Was the total discount of these three items greater than 15 percent of the sum of the regular prices of the 3 items?
(1) The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20
(2) The regular price of the least expensive item was $15

IMO answer should be A, am i correct?

Thanks,
M
This is a weighted average question. Very little math is needed.
If we replace discount with solution, here is the same question:

A 20% solution is combined with a 10% solution. Is the percentage in the resulting mixture greater than 15%?

If we use equal amounts of the 20% solution and the 10% solution, the resulting solution will be exactly 15%.
Thus, to yield a solution that is more than 15%, we must use more of the 20% solution and less of the 10% solution.

Applying the same logic to the DS question above, in order for the total discount to be greater than 15%, the price of the most expensive item (the "20% solution") must be greater than the sum of the prices of the other 2 items (the "10% solution").

Rephrased, the question is asking:

Was the price of the most expensive item greater than the sum of the prices of the other 2 items?

Statement 1: The regular price of the most expensive item was $50, and the regular price of the next most expensive
item was $20.
The combined prices of the other 2 items cannot be greater than 20+20 = 40.
Thus, the $50 price of the most expensive item is greater than the sum of the prices of the other 2 items.
Sufficient.

Statement 2: The regular price of the least expensive item was $15.
No way to determine whether the price of the most expensive item is greater than the sum of the prices of the other 2 items.
Insufficient.

The correct answer is A.
Last edited by GMATGuruNY on Sun May 22, 2011 6:20 am, edited 1 time in total.
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by badresh70 » Sun May 22, 2011 5:30 am
Hi Mitch,

Can you please explain it in some different manner or may be with another example.
I did not understood from the current example.

Thanks,
Badresh
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by GMATGuruNY » Sun May 22, 2011 6:16 am
badresh70 wrote:Hi Mitch,

Can you please explain it in some different manner or may be with another example.
I did not understood from the current example.

Thanks,
Badresh
To illustrate why statement 1 is sufficient:
The most expensive item = 50.
20% discount = .2*50 = 10.

The maximum sum of the prices of the 2 other items = 20+20 = 40.
10% discount = .1*40 = 4.
20% discount + 10% discount = 10+4 = 14.
Total of the regular prices = 50+20+20 = 90.
A 15% discount would be = .15*90 = 13.5.
Since 14>13.5, the total discount is greater than 15%.

The prices of the other 2 items can only be decreased, since the next most expensive item can't be more than $20.

Let the sum of the prices of the 2 other items = 20+10 = 30.
10% discount = .1*30 = 3.
20% discount + 10% discount = 10+3 = 13.
Total of the regular prices = 50+20+10 = 80.
A 15% discount would be = .15*80 = 12.
Since 13>12, the total discount is greater than 15%.

Notice that as the sum of the prices of the other 2 items decreases, the difference between the total discount and the 15% discount increases.

Thus, the total discount will always be greater than 15%.
Last edited by GMATGuruNY on Mon May 23, 2011 11:21 am, edited 1 time in total.
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by MI3 » Mon May 23, 2011 11:15 am
Thank you for both the explanations, very useful.
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