By what percent was the price of a certain television set di

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By what percent was the price of a certain television set discounted for a sale?

(1) The price of the television set before it was discounted for the sale was 25 percent greater than the discounted price.
(2) The price of the television set was discounted by $60 for the sale.

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by ceilidh.erickson » Wed Mar 15, 2017 6:03 am

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There are several strategies we could use here: algebra or testing numbers. I'll demonstrate the latter first:

Target question: By what percent was the price of a certain television set discounted for a sale?

(1) The price of the television set before it was discounted for the sale was 25 percent greater than the discounted price.

Test 1:
Before discount: $125
Discounted: $100
Percent decrease: 20%

Test 2:
Before discount: $12,500 (crazy price for a tv, but who cares?)
Discounted: $10,000
Percent decrease: 20%

If we get the same answer when we test numbers of different orders of magnitude, we can assume it is SUFFICIENT.

(2) The price of the television set was discounted by $60 for the sale.
Test 1:
Before discount: $100
Discounted: $40
Percent decrease: 60%

Test 2:
Before discount: $10,000
Discounted: $9,940
Percent decrease: 0.6%

Two different answers ==> INSUFFICIENT.

The answer is A.
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by GMATGuruNY » Wed Mar 15, 2017 6:03 am

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NandishSS wrote:By what percent was the price of a certain television set discounted for a sale?

(1) The price of the television set before it was discounted for the sale was 25 percent greater than the discounted price.
(2) The price of the television set was discounted by $60 for the sale.
Statement 1:
Case 1: Discounted price = $4, original price = $4 + (25% of $4) = 4+1 = $5.
Since the price decreases from $5 to $4 -- a discount of $1 -- the discount percentage = (discount)/(original price) * 100 = (1/5)(100) = 20%.

Case 2: Discounted price = $8, original price = $8 + (25% of $8) = 8+2 = $10.
Since the price decreases from $10 to $8 -- a discount of $2 -- the discount percentage = (discount)/(original price) * 100 = (2/10)(100) = 20%.

Since the discount percentage is THE SAME in each case, SUFFICIENT.

Statement 2:
Since the original price is unknown, it is not possible to determine the discount percentage.
INSUFFICIENT.

The correct answer is A.
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by ceilidh.erickson » Wed Mar 15, 2017 6:11 am

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To set this up algebraically, assign variables:
x = old price before discount
y = new price after discount

If we want to know the PERCENT CHANGE from the old price to the new price, we can write that as:
(x - y)/x = ?

Simplify that by splitting the fraction:
(x/x) - (y/x) = ?
1 - (y/x) = ?

Since this is DS, we would have sufficient information to answer the question if we knew the value of the ratio y/x.

Target question: y/x = ?

(1) The price of the television set before it was discounted for the sale was 25 percent greater than the discounted price.
Translate:
x = 1.25y
(1/1.25) = y/x
We have a value for the ratio y/x. SUFFICIENT.

(2) The price of the television set was discounted by $60 for the sale.
Translate:
y = x - 60
We have a DIFFERENCE between the two variables, but we can't get a RATIO.
INSUFFICIENT.

The answer is A.

You may start to notice this trend in DS: when a question asks for a PROPORTION (percent, ratio, fraction) and no concrete values are given, another proportion is often sufficient (as in #1). A concrete value alone (as in #2) will not help to answer a proportion question, if not other values are given.
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by ceilidh.erickson » Wed Mar 15, 2017 6:14 am

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by [email protected] » Wed Apr 04, 2018 7:36 pm

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Hi All,

We're asked by what PERCENT was the price of a certain television set discounted for a sale. This question can be approached in a number of different ways; at it's heart though, the concept involves Percent Change (which is a relationship between two values).

1) The price of the television set before it was discounted for the sale was 25 percent greater than the discounted price.

If the price of the television was 25% GREATER than the discounted price, then we can organize the the two prices in the following way:

Discounted Price = X
Regular Price = (1.25)(X)

Since the Regular Price is 'locked in' at 25% greater, we can use the Percentage Change Formula to calculate the Percent Decrease in price:

Percent Change = (New - Old)/(Old) = (X - 1.25X)/(1.25X) = (-.25X)/(1.25X) = -1/5 = -20% = a 20% decrease.
Fact 1 is SUFFICIENT

(2) The price of the television set was discounted by $60 for the sale.

With the information in Fact 2, we don't know the Regular Price nor the Discounted Price.
IF....
Regular Price = $60 and Discounted Price = $0, then the Percent Decrease is (60 - 0)/(60) = 60/60 = 1 = 100% discount
Regular Price = $120 and Discounted Price = $60, then the Percent Decrease is (120 - 60)/(120) = 60/120 = 1/2 = 50% discount
Fact 2 is INSUFFICIENT

Final Answer: A

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by [email protected] » Tue Apr 10, 2018 10:26 am

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NandishSS wrote:By what percent was the price of a certain television set discounted for a sale?

(1) The price of the television set before it was discounted for the sale was 25 percent greater than the discounted price.
(2) The price of the television set was discounted by $60 for the sale.
We need to determine the percent discount of the television.

Statement One Alone:

The price of the television set before it was discounted for the sale was 25 percent greater than the discounted price.

We can let n = the regular price and d = the discounted price:

1.25d = n

d = n/1.25

d = 100n/125 = n(100/125) = n(4/5)

So the television was discounted 20%.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

The price of the television set was discounted by $60 for the sale.

Since we do not know the regular price of the television, statement two alone is not sufficient to answer the question.

Answer: A

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