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

This topic has 4 expert replies and 0 member replies

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

Post Wed Mar 15, 2017 5:54 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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.

    Source: OG 16

    OA:A

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    Post Wed Mar 15, 2017 6:03 am
    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.

    _________________


    Ceilidh Erickson
    Manhattan Prep GMAT & GRE instructor
    EdM in Mind, Brain, and Education
    Harvard Graduate School of Education


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    Thanked by: NandishSS, gmatdestroyer13
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    Post Wed Mar 15, 2017 6:03 am
    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.

    _________________
    Mitch Hunt
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    Post Wed Mar 15, 2017 6:11 am
    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.

    _________________


    Ceilidh Erickson
    Manhattan Prep GMAT & GRE instructor
    EdM in Mind, Brain, and Education
    Harvard Graduate School of Education


    Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
    Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

    Thanked by: NandishSS, gmatdestroyer13
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    Post Wed Mar 15, 2017 6:14 am

    _________________


    Ceilidh Erickson
    Manhattan Prep GMAT & GRE instructor
    EdM in Mind, Brain, and Education
    Harvard Graduate School of Education


    Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
    Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

    Thanked by: NandishSS, gmatdestroyer13
    Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.

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