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# If x & y are integers and y = x^2 + x^3, is y < 0? (1) x < 0 (2) y < 1

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
If x & y are integers and y = x^2 + x^3, is y < 0? (1) x < 0 (2) y < 1  [#permalink]

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09 Oct 2018, 02:04
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:03) correct 39% (01:22) wrong based on 50 sessions

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If x & y are integers and y = x^2 + x^3, is y < 0?

(1) x < 0
(2) y < 1

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Joined: 07 Dec 2017
Posts: 890
Re: If x & y are integers and y = x^2 + x^3, is y < 0? (1) x < 0 (2) y < 1  [#permalink]

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09 Oct 2018, 02:33
Bunuel wrote:
If x & y are integers and y = x^2 + x^3, is y < 0?

(1) x < 0
(2) y < 1

1) let's say x=-1: in this case, y = 1 -1 = 0 ===> the answer is no!
But now let's try another number: say x=-2: in this case, y =4-8=-4 ==> the answer is yes!
We've used the data to get two contradicting answers - insufficient! eliminate A & D

2) if y is an integer smaller than 1, it is either negative (meaning the answer is yes) or zero (meaning it is no). As we've just seen, it can be both given the above expression, and this data gives us no tools to decide which - insufficient! Eliminate B.

Combined: (1) tells us y can be either negative or zero. (2) tells us the same. neither adds any information to the other. insufficient! Eliminate C.

E is our answer.
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Re: If x & y are integers and y = x^2 + x^3, is y < 0? (1) x < 0 (2) y < 1  [#permalink]

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09 Oct 2018, 02:37
Bunuel wrote:
If x & y are integers and y = x^2 + x^3, is y < 0?

(1) x < 0
(2) y < 1

Statement 1:

x<0.

let x be -1.

In this case y = 0.

Not Sufficient.

Statement 2;

y<1.

y could be 0 , -100.

Not sufficient.

Combining both statements :

If y is less than 1 and x<0 , y could be 0 , -100 - 5..........

Still NOT sufficient.

The best answer is E.
Re: If x & y are integers and y = x^2 + x^3, is y < 0? (1) x < 0 (2) y < 1   [#permalink] 09 Oct 2018, 02:37
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# If x & y are integers and y = x^2 + x^3, is y < 0? (1) x < 0 (2) y < 1

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