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

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

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New post 26 Feb 2017, 08:14
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

73% (00:40) correct 27% (00:11) wrong based on 47 sessions

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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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New post 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

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

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New post 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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New post 05 Mar 2017, 12:00
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Expert's post
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.


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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.   [#permalink] 05 Mar 2017, 12:00
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