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# Is the product of x and y greater than 60?

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Math Expert
Joined: 02 Sep 2009
Posts: 52284
Is the product of x and y greater than 60?  [#permalink]

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25 May 2016, 14:29
00:00

Difficulty:

15% (low)

Question Stats:

72% (00:53) correct 28% (00:39) wrong based on 60 sessions

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Is the product of x and y greater than 60?

(1) The sum of x and y is greater than 60.
(2) Each of the variables is greater than 2.

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Math Expert
Joined: 02 Aug 2009
Posts: 7201
Re: Is the product of x and y greater than 60?  [#permalink]

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25 May 2016, 19:48
Bunuel wrote:
Is the product of x and y greater than 60?

(1) The sum of x and y is greater than 60.
(2) Each of the variables is greater than 2.

Is xy>60?

(1) The sum of x and y is greater than 60.
x could be 0.5 and y= 60......... x+y = 60.5 and xy= 30.......NO
x= 5 y=60.............x+y=65 and xy = 300.......YES
Insuff

(2) Each of the variables is greater than 2.
If x = 5 and y = 5 ....xy=25.....NO
x=10, y=20...........xy=200......YES
Insuff

Combined
x+y > 60 and BOTH x and y are >2.......
the lowest possible value is$$x = 2.00000001$$and then $$y = 60.00000001-2.00000001 = 58$$...
$$xy = 2*58=116..$$
so xy will always be greater than 60
Suff
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Is the product of x and y greater than 60?  [#permalink]

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25 May 2016, 21:11
Bunuel wrote:
Is the product of x and y greater than 60?

(1) The sum of x and y is greater than 60.
(2) Each of the variables is greater than 2.

Is xy > 60?

Statement 1
The sum of x and y is greater than 60
If x = 60 and y = 3, then x + y > 60 and xy > 60 (yes)
If x = 60 and y = 1, then x + y > 60 and xy = 60 (no)
Insufficient

Statement 2
Each of the variables is greater than 2
If x = 60 and y = 3, then xy > 60 (yes)
If x = 2 and y = 3, then xy < 60 (no)
Insufficient

Statement 1 and 2 combined
x > 2, y > 2 and x + y > 60
With these restrictions xy will always be greater than 60. (Irrespective of whether x and y are integers or not)
Hence, sufficient

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Re: Is the product of x and y greater than 60?  [#permalink]

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12 Jan 2019, 15:13
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Re: Is the product of x and y greater than 60? &nbs [#permalink] 12 Jan 2019, 15:13
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