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

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Magoosh GMAT Instructor
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The original price of an item is discounted 20%. A customer buys the [#permalink]

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New post 05 May 2016, 15:48
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E

Difficulty:

  25% (medium)

Question Stats:

83% (01:35) correct 17% (01:51) wrong based on 153 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 :-)

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Re: The original price of an item is discounted 20%. A customer buys the [#permalink]

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New post 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

Answer: E
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The original price of an item is discounted 20%. A customer buys the [#permalink]

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New post 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: \(\frac{1}{2}x + $1.90\)

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


Answer E
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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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