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A merchant discounted the sale price of a coat and the sale price of a

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

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16 Oct 2018, 02:19
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Difficulty:

65% (hard)

Question Stats:

46% (01:46) correct 54% (01:48) wrong based on 69 sessions

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A merchant discounted the sale price of a coat and the sale price of a sweater. Was the discount in dollars on the coat greater than that on the sweater?

(1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater

(2) Before the discounts, the sale price of the coat was \$10 less than the sale price of the sweater

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Re: A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

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16 Oct 2018, 09:00
Each statement is individually insufficient, Since sale price is not mentioned in S1 and Discount is not mentioned in S2.

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Re: A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

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16 Oct 2018, 15:21
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1
Bunuel wrote:
A merchant discounted the sale price of a coat and the sale price of a sweater. Was the discount in dollars on the coat greater than that on the sweater?

(1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater

(2) Before the discounts, the sale price of the coat was \$10 less than the sale price of the sweater

Target question: Was the discount in dollars on the coat greater than that on the sweater?

Statement 1: The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater
No information about the PRICES before the discount.
NOT SUFFICIENT

Statement 2: Before the discounts, the sale price of the coat was \$10 less than the sale price of the sweater
No information about the PERCENT DISCOUNTS.
NOT SUFFICIENT

Statements 1 and 2 combined
Let x = the PRE-DISCOUNT price of a coat
So, x + 10 = the PRE-DISCOUNT price of a sweater

Let p= the percent discount on a sweater
So, p + 2 = the percent discount on a coat

So, the dollar discount on the sweater = (p/100)(x + 10 )
And the dollar discount on the coat = [(p + 2)/100](x)

So, the question becomes: "Is [(p + 2)/100](x) > (p/100)(x + 10 )?"
Multiply both sides by 100 to get: Is (p + 2)(x) > (p)(x + 10)?
Expand both sides to get: Is px + 2x > px + 10p?
Subtract px from both sides to get: Is 2x > 10p?
And for kicks, let's divide both sides by 2 to get: Is x > 5p?
In other words, Is the PRE-DISCOUNT price of a coat greater than 5 times the percent discount on a sweater?

Since we can't answer this question with certainty, the correct answer is E.
If you're not convinced, check out these two possible cases:

Case a: The pre-discount coat price is \$100, and there a 4% discount on the coat. Total discount = 4% of \$100 = \$4.00
The pre-discount sweater price \$110, and there a 2% discount on the coat. Total discount = 2% of \$110 = \$2.20. In this case, the answer to the target question is YES, the coat discount IS greater than the sweater discount

Case b: The pre-discount coat price is \$1, and there a 3% discount on the coat. Total discount = 3% of \$1 = \$0.03
The pre-discount sweater price \$11, and there a 1% discount on the coat. Total discount = 1% of \$11 = \$0.11. In this case, the answer to the target question is NO, the coat discount is NOT greater than the sweater discount

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
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Re: A merchant discounted the sale price of a coat and the sale price of a   [#permalink] 16 Oct 2018, 15:21
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