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If x and y are positive integers, what is the value of x + y?

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Math Expert
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V
Joined: 02 Sep 2009
Posts: 50623
If x and y are positive integers, what is the value of x + y?  [#permalink]

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New post 02 May 2018, 00:33
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

73% (01:39) correct 27% (01:42) wrong based on 73 sessions

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e-GMAT Representative
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Joined: 04 Jan 2015
Posts: 2203
Re: If x and y are positive integers, what is the value of x + y?  [#permalink]

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New post 02 May 2018, 01:05

Solution



Given:
• x and y are positive integers

To find:
• The value of x + y

Analysing Statement 1

    • As per the information given in Statement 1, xy = 36
      o From this statement, we cannot conclude the value of x and y individually as there exist multiple possibilities (like x = 1, y = 36; or, x = 4, y = 9 etc.)

    • Hence, Statement 1 is not sufficient to answer

Analysing Statement 2

    • As per the information given in Statement 2, y ≥ x + 6
      o From this statement, we can only say y – x ≥ 6
    • We cannot conclude the value of x and y individually as there exist multiple possibilities (like x = 1, y = 7; or, x = 2, y = 8 etc.)
    • Hence, Statement 2 is not sufficient to answer

Combining Both Statements

    • From 1st statements, xy = 36
      o x=1, y= 36 and y=1, x= 36
      o x=2, y= 18 and y=2, x= 18
      o x=3, y= 12 and y=3, x= 12
      o x=4, y=9 and y=4, x=9
      o x=6, y=6 and y=6, x=6

• From statement 2: y – x ≥ 6

By combining both the statements, the values of x and y that satisfies are:
      o x=1, y= 36
      o x=2, y= 18
      o x=3, y= 12
Since we cannot get a unique value of x and y, hence, the correct answer is Option E.

Answer: E
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Re: If x and y are positive integers, what is the value of x + y?  [#permalink]

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New post 27 Aug 2018, 05:03
Bunuel wrote:
If x and y are positive integers, what is the value of x + y?

(1) xy = 36
(2) y >= x + 6


(1+2) Insufficient:

Take (x,y) = (1,36) to answer 37
Take (x,y) = (2,18) to answer 20

The above follows the notations and rationale taught in the GMATH method.
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Re: If x and y are positive integers, what is the value of x + y? &nbs [#permalink] 27 Aug 2018, 05:03
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