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# The original price of an item is discounted 20%. A customer buys the

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4488
The original price of an item is discounted 20%. A customer buys the  [#permalink]

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05 May 2016, 15:48
00:00

Difficulty:

25% (medium)

Question Stats:

79% (02:14) correct 21% (02:24) wrong based on 172 sessions

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The original price of an item is discounted 20%. A customer buys the item at this discounted price using a $20-off coupon. There is no tax on the item, and this was the only item the customer bought. If the customer paid$1.90 more than half the original price of the item, what was the original price of the item?

(A) $61 (B)$65

(C) $67.40 (D)$70

(E) $73 Word problems are tricky, but there are various strategies that make them more approachable. For a discussion of GMAT word problems, as well as the OE for this question, see: Intro to GMAT Word Problems, Part 1: Translating from Word to Math Mike _________________ Mike McGarry Magoosh Test Prep Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939) Retired Moderator Joined: 13 Apr 2015 Posts: 1679 Location: India Concentration: Strategy, General Management GMAT 1: 200 Q1 V1 GPA: 4 WE: Analyst (Retail) Re: The original price of an item is discounted 20%. A customer buys the [#permalink] ### Show Tags 05 May 2016, 19:49 Let x be the original price of the item Discounted price = 0.8x Payment made by the customer after using the$20 coupon = 0.8x - 20

0.8x - 20 = x/2 + 1.9
1.6x - 40 = x + 3.8
0.6x = 43.8
6x = 438
x = 73

Senior SC Moderator
Joined: 22 May 2016
Posts: 2911
The original price of an item is discounted 20%. A customer buys the  [#permalink]

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28 Dec 2017, 08:00
mikemcgarry wrote:
The original price of an item is discounted 20%. A customer buys the item at this discounted price using a $20-off coupon. There is no tax on the item, and this was the only item the customer bought. If the customer paid$1.90 more than half the original price of the item, what was the original price of the item?

(A) $61 (B)$65

(C) $67.40 (D)$70

(E) $73 Word problems are tricky, but there are various strategies that make them more approachable. For a discussion of GMAT word problems, as well as the OE for this question, see: Intro to GMAT Word Problems, Part 1: Translating from Word to Math Mike x = original price Price is equal to: 1) the price that is discounted 20% = .80x, and 2) -$20, from a $20-off coupon Together: $$.80x - 20$$ Price is also equal to: 1) half the original price, plus 2)$1.90
Together: $$\frac{1}{2}x + 1.90$$

$$.80x + 20 =\frac{1}{2}x - 1.90$$
$$\frac{8}{10}x + 20 = \frac{5}{10}x + 1.90$$
$$8x + 200 = 5x + 19$$
$$3x = 219$$
$$x = 73$$

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The original price of an item is discounted 20%. A customer buys the   [#permalink] 28 Dec 2017, 08:00
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