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# Is y>0?

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Math Expert
Joined: 02 Sep 2009
Posts: 55670

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21 Aug 2017, 21:49
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Difficulty:

35% (medium)

Question Stats:

64% (01:04) correct 36% (01:20) wrong based on 133 sessions

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Is y>0?

(1) x^2−y^2=0

(2) x^2+y^2=0

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Joined: 18 Aug 2016
Posts: 617
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38

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Updated on: 21 Aug 2017, 23:23
1
Bunuel wrote:
Is y>0?

(1) x^2−y^2=0

(2) x^2+y^2=0

(1) no information about x hence not sufficient

(2) only possible when x=y=0

Sufficient
B

P.S. Second attempt
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Thanks
Luckisnoexcuse

Originally posted by Luckisnoexcuse on 21 Aug 2017, 22:56.
Last edited by Luckisnoexcuse on 21 Aug 2017, 23:23, edited 1 time in total.
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Joined: 06 Feb 2016
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21 Aug 2017, 23:20

statement 1: x^2-y^2=0; x^2=y^2. there can be infinite numbers where x=y, satisfying statement 1. INSUFFICIENT.

statement 2: x^+y^2=0; x^2=-y^2. as this can never be true except x=y=0 (as square of a number cannot be negative). So we have a definite answer i.e. no. SUFFICIENT.

Thanks
Swapnil Varshney
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22 Aug 2017, 06:43
Is y>0?

(1) x^2−y^2=0

(2) x^2+y^2=0

statement 1

x^2−y^2=0
x^2−y^2 => ( x+y ) ( x-y ) = 0

x+y = 0 and x-y = 0
x = -y and x = y ( no information about x and y ) Insuff.

statement 2

x^2+y^2=0

Now, one thing we know from here that x^2 will always be positive and y^2 will always be positive
So, Sum of two positives can only be zero if both of them are zero.
Hence sufficient . y = 0

Regards

SandySilva
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Joined: 19 Oct 2017
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06 Sep 2018, 06:35
1
Hi guys,

How come does x or y becomes only 0 in condition (2) ?

If X is (-2)^1/2 and Y is (2)^1/2, X^2 + Y^2 becomes 0.

Thus, Y could be either (2)^1/2 or 0.

Can anyone explain it?

Thank you.
Math Expert
Joined: 02 Sep 2009
Posts: 55670

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06 Sep 2018, 20:55
jayjune wrote:
Hi guys,

How come does x or y becomes only 0 in condition (2) ?

If X is (-2)^1/2 and Y is (2)^1/2, X^2 + Y^2 becomes 0.

Thus, Y could be either (2)^1/2 or 0.

Can anyone explain it?

Thank you.

The square of a number is non-negative, so it's 0 or positive.

x^2 + y^2 = (non-negative) + (non-negative) = (0 or positive) + (0 or positive).

If x^2 or y^2 were positive the sum would be positive too, thus both of them is 0: x^2 = y^2 = 0 --> x = y = 0.

P.S. Even roots from negative numbers is not defined on the GMAT. All numbers on the GMAT are by default real numbers.
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Joined: 19 Oct 2017
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09 Sep 2018, 22:24
Bunuel wrote:
jayjune wrote:
Hi guys,

How come does x or y becomes only 0 in condition (2) ?

If X is (-2)^1/2 and Y is (2)^1/2, X^2 + Y^2 becomes 0.

Thus, Y could be either (2)^1/2 or 0.

Can anyone explain it?

Thank you.

The square of a number is non-negative, so it's 0 or positive.

x^2 + y^2 = (non-negative) + (non-negative) = (0 or positive) + (0 or positive).

If x^2 or y^2 were positive the sum would be positive too, thus both of them is 0: x^2 = y^2 = 0 --> x = y = 0.

P.S. Even roots from negative numbers is not defined on the GMAT. All numbers on the GMAT are by default real numbers.

Thanks for your explanation Mr. Bunuel.

But I cant still get it how square of x or y cannot be negative number.

In example, if we square 'Root (-3)', it can be calculated as below.

(Root (-3))^2 = (Root (3) * i)^2 = 3 * i^2 = 3 * (-1) = -3
--> (i denotes imaginary number)

Do you mean even though above negative number can come out from the square of any number, GMAT allows only real numbers without any additional condition stated in every questions?

Math Expert
Joined: 02 Sep 2009
Posts: 55670

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09 Sep 2018, 23:04
jayjune wrote:
Bunuel wrote:
jayjune wrote:
Hi guys,

How come does x or y becomes only 0 in condition (2) ?

If X is (-2)^1/2 and Y is (2)^1/2, X^2 + Y^2 becomes 0.

Thus, Y could be either (2)^1/2 or 0.

Can anyone explain it?

Thank you.

The square of a number is non-negative, so it's 0 or positive.

x^2 + y^2 = (non-negative) + (non-negative) = (0 or positive) + (0 or positive).

If x^2 or y^2 were positive the sum would be positive too, thus both of them is 0: x^2 = y^2 = 0 --> x = y = 0.

P.S. Even roots from negative numbers is not defined on the GMAT. All numbers on the GMAT are by default real numbers.

Thanks for your explanation Mr. Bunuel.

But I cant still get it how square of x or y cannot be negative number.

In example, if we square 'Root (-3)', it can be calculated as below.

(Root (-3))^2 = (Root (3) * i)^2 = 3 * i^2 = 3 * (-1) = -3
--> (i denotes imaginary number)

Do you mean even though above negative number can come out from the square of any number, GMAT allows only real numbers without any additional condition stated in every questions?

$$\sqrt{negative}$$ is UNDEFINED on the GMAT.

All numbers are real by default. So, NO complex numbers (imaginary numbers).
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Re: Is y>0?   [#permalink] 09 Sep 2018, 23:04
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