How many of the numbers x, y, and z are positive if each of

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

by BTGmoderatorDC » Mon Jul 30, 2018 4:38 pm

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How many of the numbers x, y, and z are positive if each of these numbers is less than 10?

(1) x + y + z = 20
(2) x + y = 14

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Source: Beat The GMAT — Data Sufficiency | Mon Jul 30, 2018 4:38 pm

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

by Jay@ManhattanReview » Tue Jul 31, 2018 12:01 am

BTGmoderatorDC wrote:How many of the numbers x, y, and z are positive if each of these numbers is less than 10?

(1) x + y + z = 20
(2) x + y = 14

Let's take each statement one by one.

(1) x + y + z = 20

Let's maximize two of x, y and z so that we have the minimum possible value of the third number; this is an attempt to see if the third one turns out to be negative.

Say x = y = 9.99 (maximum possible value)

=> x = 0.01 (minimum possible value)

=> All three are positive. Sufficient.

(2) x + y = 14

No information about z. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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