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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: 02 Sep 2009
Posts: 58335
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, 03:04
00:00

Difficulty:

55% (hard)

Question Stats:

63% (02:00) correct 37% (01:24) wrong based on 58 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: 1129
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, 03:33
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.

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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, 03:37
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.

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, 03:37
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