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# If Peter spends \$460 on three pairs of shoes, how much did the least

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Math Expert
Joined: 02 Sep 2009
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If Peter spends \$460 on three pairs of shoes, how much did the least  [#permalink]

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18 Jul 2016, 08:17
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Difficulty:

25% (medium)

Question Stats:

80% (01:25) correct 20% (01:18) wrong based on 92 sessions

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If Peter spends \$460 on three pairs of shoes, how much did the least expansive shoes cost?

(1) The ratio between the most expansive shoes to the least expansive shoes is 3 to 1.
(2) The ratio between the least expansive shoes to all the other ones is 1 to 5.

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Re: If Peter spends \$460 on three pairs of shoes, how much did the least  [#permalink]

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18 Jul 2016, 19:25
Total = 460; Least expensive shoes = ?

St1: The ratio between the most expansive shoes to the least expansive shoes is 3 to 1. --> Clearly insufficient as we do not know the price of the middle one.

St2: The ratio between the least expansive shoes to all the other ones is 1 to 5. --> Least : Other = 1 : 5
Least = 1/6 * 460.
Sufficient

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Re: If Peter spends \$460 on three pairs of shoes, how much did the least  [#permalink]

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19 Jul 2016, 01:59
x+y+z=460 (x is the least expensive, then y, then z)

1) x+y+3x=460-->4x+y=460
insufficient

2) x+5x=460, then x=76.67
sufficient

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Re: If Peter spends \$460 on three pairs of shoes, how much did the least  [#permalink]

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18 Jan 2018, 14:31
Bunuel wrote:
If Peter spends \$460 on three pairs of shoes, how much did the least expansive shoes cost?

(1) The ratio between the most expansive shoes to the least expansive shoes is 3 to 1.
(2) The ratio between the least expansive shoes to all the other ones is 1 to 5.

We are given that Peter spends \$460 on three pairs of shoes and need to determine the price of the least expensive pair of shoes.

Statement One Alone:

The ratio between the most expensive shoes to the least expensive shoes is 3 to 1.

Since we do not have any information regarding the 2nd cheapest pair of shoes we cannot determine the cost of the least expensive shoes. Statement one is not sufficient to answer the question.

Statement Two Alone:

The ratio between the least expensive shoes to all the other ones is 1 to 5.

We can create the equation:

x + 5x = 460

6x = 460

x = 76.6

Thus, the least expensive shoes were 76.60 dollars.

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Re: If Peter spends \$460 on three pairs of shoes, how much did the least   [#permalink] 18 Jan 2018, 14:31
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