Is x

Question

Is x < y?

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

fra · Answer

St.1- can be rearranged as x^2 (x^2-y^2) and -(x+y) are both negative so their division must be positive. (x^2-y^2)/-(x+y)> 0 (x+y)(x-y)/-(x+y)> 0 -(x-y)> 0 x-y <0 So x

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Bunuel · Answer

Is x < y? Is x < y? --> is x - y < 0? (1) x^2 - y^2 < 0 --> x^2 |x|<|y|. Not sufficient. Consider: (x, y)=(1, -2) and (x, y)=(1, 2). (2) -x - y < 0 --> x+y>0. The sum of two numbers is greater than 0, from this we cannot say which one is greater. Consider (x, y)=(1, 2) and (x, y)=(2, 1). Not sufficient. (1)+(2) From (1) we have that (x-y)(x+y)<0 and from (2) we have that x+y>0, thus x-y<0. Sufficient. Answer: C.

gauravkaushik8591 · Answer

x^2 - y^2 < 0 --> x^2>y^2

is that a typo or did you mean that?

Bunuel · Answer

Yes, it was a typo. Edited. Thank you.

GSBae · Answer

This question is also very easily solved algebraically.

1)  x^2 - y^2 <0. (x+y)(x-y) <0 . One of these is negative, so either x+y<0 , which means that  x<-y , or  x<y . Two options; not sufficient.

2)  -x-y<0 . Not sufficient.

Using number 2), we can multiply by a negative to see that  x+y>0 . Now using option 1, this means that x-y must be less than 0. Therefore,  x-y<0  and  x<y . Sufficient.

Answer: C

itisSheldon · Answer

Veritas Prep OFFICIAL EXPLANATION

Explanation: (1) The values 2 and 3 will give us a YES answer to the question stem, but the values 2 and -3 will give us a response of NO. Another way to approach this is to realize that you can factor the left hand side of the inequality to get (x - y)(x + y) < 0. This means that either the first term, (x - y), is negative or the second term, (x + y), is negative, but not both. If the first term is negative, then YES is answer to the question. However, if the second term is negative, the answer could be YES or NO. Accordingly, this statement is insufficient.

(2) You can simplify this by multiplying both sides by -1, which means you need to flip the direction of the inequality. You'll now have x + y > 0. This, however, doesn't tell us which value is larger, and this statement is insufficient.

Together, we know that (x - y)(x + y) < 0 and x + y > 0. This means that x - y < 0 . Remember, for the product of two values to be negative, one of them and only one of them must be negative. Because we know that (x + y) must be positive, then (x - y) < 0. Simply adding to each side of that inequality, we find that x < y, and know that the statements together are sufficient. Accordingly, the answer is C.

ScottTargetTestPrep · Answer

Statement One Alone: \Rightarrow x^2 - y^2 < 0 We can conclude from this statement that the absolute value of y is greater than the absolute value of x, however, this is not sufficient to determine whether x < y. For instance, if x = 1 and y = 2, then x < y and the answer to the question is yes. On the other hand, if x = 1 and y = -2, then x > y and the answer to the question is no. Since we have more than one possible answer to the question, statement one alone is not sufficient. Eliminate answer choices A and D. Statement Two Alone: \Rightarrow -x - y < 0 We can rewrite the inequality as x + y > 0. This is not sufficient to determine whether x < y. If x = 1 and y = 2, then x < y and the answer to the question is yes. If x = 2 and y = 1, then x > y and the answer to the question is no. Since we have more than one possible answer to the question, statement two alone is not sufficient. Eliminate answer choice B. Statements One and Two Together: Since the expression in the first inequality is a difference of two squares, we can rewrite it as follows: \Rightarrow x^2 - y^2 < 0 \Rightarrow (x - y)(x + y) < 0 The second inequality tells us that x + y > 0, so we can divide each side of the above inequality by x + y without changing the direction of the inequality: \Rightarrow (x - y)(x + y)/(x + y) < 0/(x + y) \Rightarrow x - y < 0 \Rightarrow x < y This answers the question. Statements one and two together are sufficient. Answer: C

bumpbot · Answer

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Is x < y?

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