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# What is the value of x+y, if x and y are real numbers? (1) x-y = 4

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DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1342
Location: India
What is the value of x+y, if x and y are real numbers? (1) x-y = 4  [#permalink]

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23 Jul 2018, 21:13
00:00

Difficulty:

55% (hard)

Question Stats:

35% (01:06) correct 65% (01:49) wrong based on 23 sessions

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What is the value of x+y, if x and y are real numbers?

(1) x-y = 4

(2) (x+y)^2 = 16
RC Moderator
Status: Perfecting myself for GMAT
Joined: 22 May 2017
Posts: 436
Concentration: Nonprofit
Schools: Haas '21
GPA: 4
WE: Engineering (Computer Software)
Re: What is the value of x+y, if x and y are real numbers? (1) x-y = 4  [#permalink]

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23 Jul 2018, 22:17
To find the value of x + y

Statement 1

x - y = 4

=> x can be 6 y can be 2 => x + y can be 8
=> x can be 7 y can be 3 => x + y can be 10

Statement 1 is not sufficient

Statement 2

$$(x + y)^2 = 16$$

=> x can be 2 y can be 2 => x + y can be 4
=> x can be -2 y can be -2 => x + y can be -4

Statement 2 is not sufficient

Combining statements 1 and 2

from statement 1, we have x = y + 4

$$(x + y)^2 = 16$$

=> $$(2y + 4)^2 = 16$$

=> (2y + 4) = 4 or (2y + 4) = -4

=> y = 0 or y = -4

=> x = 4 or x = 0

=> x + y can be either 4 or -4

Statements 1 and 2 together are not sufficient

Hence option E
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Re: What is the value of x+y, if x and y are real numbers? (1) x-y = 4 &nbs [#permalink] 23 Jul 2018, 22:17
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