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# If xy = 12, and x + y = 7, then y could equal which of the following?

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Math Expert
Joined: 02 Sep 2009
Posts: 58431
If xy = 12, and x + y = 7, then y could equal which of the following?  [#permalink]

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24 Jan 2019, 04:02
00:00

Difficulty:

15% (low)

Question Stats:

88% (01:00) correct 12% (01:10) wrong based on 21 sessions

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If xy = 12, and x + y = 7, then y could equal which of the following?

I. 3
II. 4
III. 5

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

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VP
Joined: 31 Oct 2013
Posts: 1465
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If xy = 12, and x + y = 7, then y could equal which of the following?  [#permalink]

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24 Jan 2019, 04:07
Bunuel wrote:
If xy = 12, and x + y = 7, then y could equal which of the following?

I. 3
II. 4
III. 5

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

xy = 12

x + y = 7.

1*12 = 12

2*6 =12

3*4 = 12

4*3 = 12

6*2 = 12.

only pair matched is 3 and 4.

GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5031
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If xy = 12, and x + y = 7, then y could equal which of the following?  [#permalink]

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24 Jan 2019, 05:08
Bunuel wrote:
If xy = 12, and x + y = 7, then y could equal which of the following?

I. 3
II. 4
III. 5

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

xy= 4.3 best match considering we need to get x+y= 7
so
3,4 either can be y
IMO D
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3078
Re: If xy = 12, and x + y = 7, then y could equal which of the following?  [#permalink]

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24 Jan 2019, 05:23

Solution

Given:
• xy = 12
• x + y = 7 ……… (1)

To find:
• The possible value of y

Approach and Working:
• $$(x – y)^2 = 7^2 – 4 * 12 = 1$$
• Implies, x – y = ±1 ……. (2)

Solving two equations, we get,
• 7 – 2y = ±1
• Thus, y = 3 or 4

Hence, the correct answer is Option D

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Re: If xy = 12, and x + y = 7, then y could equal which of the following?   [#permalink] 24 Jan 2019, 05:23
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