If Peter spends $460 on three pairs of shoes

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

If Peter spends $460 on three pairs of shoes

by BTGmoderatorDC » Tue Jan 16, 2018 6:11 am

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.

Can some experts find the correct statement in this?

OA B

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Source: Beat The GMAT — Data Sufficiency | Tue Jan 16, 2018 6:11 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Wed Jan 17, 2018 2:50 am

lheiannie07 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.

Can some experts find the correct statement in this?

OA B

Say the prices of the three shoes are $x, $y and $z; the most expensive shoes is $x and the least expensive one is $z. We know that x + y + z = 460.
We need to get the value of $z.

(1) The ratio of the most expensive shoes to the least expansive shoes is 3 to 1.

=> x/z = 3/1. Can't get the value of z. Insufficient.

(2) The ratio of the least expensive shoes to all the other ones is 1 to 5.

=> z/(x + y) = 1/5

z/(460 - z) = 1/5

5z = 460 - z

6z = 460 => z = 460/6 = $73.67. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Jan 18, 2018 1:44 pm

lheiannie07 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.

Answer: B

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