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Math Expert V
Joined: 02 Aug 2009
Posts: 8587
What is the value of |x| + |y| + xy, where x and y are integers?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 57% (01:05) correct 43% (01:04) wrong based on 212 sessions

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What is the value of |x| + |y| + xy, where x and y are integers?

(1) $$xy=17$$
(2) $$x=\sqrt{17^2}$$

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Re: What is the value of |x| + |y| + xy, where x and y are integers?  [#permalink]

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2
St1: xy = 17 is prime --> x * y = 1 * 17 or -1 * -17.

|x| + |y| + xy = 1 + 17 + 17 = 35.

Sufficient

St2: Clearly insufficient as we do not know the value of y.

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Re: What is the value of |x| + |y| + xy, where x and y are integers?  [#permalink]

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1
chetan2u wrote:
What is the value of |x| + |y| + xy, where x and y are integers?
(1) $$xy=17$$
(2) $$x=\sqrt{17^2}$$

|x| + |y| + xy

(1) $$xy=17$$

Since x and y are integers x and y can have values -1, -17 or vice versa or 1,17 or vice versa.

Irrespective of the sign |x| and |y| will be +ve.

1+17+17= 35 Sufficient.

2) $$x=\sqrt{17^2}$$

We don't know the value of y. Not sufficient.

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Math Revolution GMAT Instructor V
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Re: What is the value of |x| + |y| + xy, where x and y are integers?  [#permalink]

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There are 2 variables ( x and y) in the original condition. Hence, there is high chance that C is the correct answer. Using both the condition 1) and the condition 2), we get x=17, y=1. The answers are unique and the conditions are sufficient. However, since this is one of key questions, an integer question, we need to apply the common mistake type 4(A).
In case of the condition 1), from (x,y)=(1,17),(17,1),(-1,-17),(-17,-1), the answer is always |x|+|y|+xy=35. The answer is unique and the condition is sufficient. Hence, the correct answer is A.
Attachments variable approach's answer probability.jpg [ 219.74 KiB | Viewed 2192 times ]

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Re: What is the value of |x| + |y| + xy, where x and y are integers?  [#permalink]

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_________________ Re: What is the value of |x| + |y| + xy, where x and y are integers?   [#permalink] 08 Aug 2019, 12:49

# What is the value of |x| + |y| + xy, where x and y are integers?   