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# Is xy < 17 ? (1) x < 0 and y > 0. (2) x ≤ 3 and 2 ≤ y ≤ 5.

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Math Expert
Joined: 02 Sep 2009
Posts: 52296
Is xy < 17 ? (1) x < 0 and y > 0. (2) x ≤ 3 and 2 ≤ y ≤ 5.  [#permalink]

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26 Feb 2017, 08:14
00:00

Difficulty:

25% (medium)

Question Stats:

82% (01:01) correct 18% (00:25) wrong based on 51 sessions

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Is xy < 17 ?

(1) x < 0 and y > 0.
(2) x ≤ 3 and 2 ≤ y ≤ 5.

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Re: Is xy < 17 ? (1) x < 0 and y > 0. (2) x ≤ 3 and 2 ≤ y ≤ 5.  [#permalink]

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26 Feb 2017, 21:32
Bunuel wrote:
Is xy < 17 ?

(1) x < 0 and y > 0.
(2) x ≤ 3 and 2 ≤ y ≤ 5.

Question: Is xy < 17?

Statement 1: x < 0 and y > 0.
Since x is negative and y is positive hence, xy will always be negative hence
SUFFICIENT

Statement 2: x ≤ 3 and 2 ≤ y ≤ 5
The maximum value of xy will be when x is 3 and y is 5
i.e. Maximum xy = 15 which is less than 17, Hence
SUFFICIENT

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Re: Is xy < 17 ? (1) x < 0 and y > 0. (2) x ≤ 3 and 2 ≤ y ≤ 5.  [#permalink]

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26 Feb 2017, 21:49
Ans is A
As from statement 1
x is negative and y is positive so xy<0 which is less than 17
But from statement 2
x can be positive or negative while y is always positive so not sufficient.

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Intern
Joined: 17 Sep 2016
Posts: 44
GMAT 1: 640 Q44 V35
Re: Is xy < 17 ? (1) x < 0 and y > 0. (2) x ≤ 3 and 2 ≤ y ≤ 5.  [#permalink]

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05 Mar 2017, 08:09
Ans D
1 is sufficient as obvious.
2 shows max positive value of x is 15. sufficient.
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Re: Is xy < 17 ? (1) x < 0 and y > 0. (2) x ≤ 3 and 2 ≤ y ≤ 5.  [#permalink]

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05 Mar 2017, 12:00
1
awdxzs wrote:
Ans is A
As from statement 1
x is negative and y is positive so xy<0 which is less than 17
But from statement 2
x can be positive or negative while y is always positive so not sufficient.

Sent from my iPhone using GMAT Club Forum

Go a little further with the cases you tested for statement 2. The error you've made here is a classic one: assuming that something is insufficient, without actually writing out the specific cases that show it's insufficient.

Here, if you write out the cases, here's what happens:

Case 1:
x = 2
y = 3

xy = 6 which is less than 17, so the answer is 'yes'

Case 2:
x = -100
y = 3

xy = -300 which is less than 17, so the answer is 'yes'

It's true that xy can be either positive or negative, but both the positive and negative answers actually give you the same answer to the question asked. All negative numbers are smaller than 17, after all.
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Re: Is xy < 17 ? (1) x < 0 and y > 0. (2) x ≤ 3 and 2 ≤ y ≤ 5. &nbs [#permalink] 05 Mar 2017, 12:00
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