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19 May 2019, 07:08
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This is a moderately difficult question on Inequalities, with the second statement being slightly tricky to analyse. So you will have to be slightly careful in interpreting it. Option B is one of the trap answers here.
We know that x and y are integers, but we do not know their signs. We are trying to ascertain if x>y. In other words, we are trying to ascertain if (x-y)>0.
From statement I alone, we only know that (x+y) > 0. This is hardly sufficient to uniquely answer whether (x-y)>0.
If x = 3 and y = 2, (x+y) = (3+2) = 5 which is definitely greater than 0; also, for these values of x and y, x>y and the answer to the main question will be a YES.
If x = -1 and y = 2, (x+y) = (-1+2) = 1 which is definitely greater than 0; but, for these values of x and y, x<y and the answer to the main question will be a NO.
Therefore, statement I alone is insufficient. So, answer options A and D can be ruled out. The possible answer options are B, C or E.
From statement II alone, we know that \(y^x\) < 0 which means \(y^x\) is negative. So, we can surely say that y has to be negative i.e. y<0. But we cannot say anything about the sign of x.
If y = -3 and x = 1, \((-3)^1\) <0. Here, x>y; if y = -3 and x = -5, \((-3)^-5\)<0, here x<y.
Therefore, statement II alone is insufficient. So, answer option B can be ruled out. The possible answer options are C or E.
Using the data from statements I and II, from the second statement, we know that y is negative, but x can be positive or negative. But, both x and y cannot be negative since x+y>0. Hence, x has to be positive and y has to be negative.
Therefore, we can surely say that x>y. So, the correct answer option is C.
As mentioned earlier, you have to exercise a fair degree of caution while interpreting statement II, because it can trick you into assuming that x has to be positive. Also, trying out simple values while evaluating the inequalities will help analyse them better..
Hope this helps!
We know that x and y are integers, but we do not know their signs. We are trying to ascertain if x>y. In other words, we are trying to ascertain if (x-y)>0.
From statement I alone, we only know that (x+y) > 0. This is hardly sufficient to uniquely answer whether (x-y)>0.
If x = 3 and y = 2, (x+y) = (3+2) = 5 which is definitely greater than 0; also, for these values of x and y, x>y and the answer to the main question will be a YES.
If x = -1 and y = 2, (x+y) = (-1+2) = 1 which is definitely greater than 0; but, for these values of x and y, x<y and the answer to the main question will be a NO.
Therefore, statement I alone is insufficient. So, answer options A and D can be ruled out. The possible answer options are B, C or E.
From statement II alone, we know that \(y^x\) < 0 which means \(y^x\) is negative. So, we can surely say that y has to be negative i.e. y<0. But we cannot say anything about the sign of x.
If y = -3 and x = 1, \((-3)^1\) <0. Here, x>y; if y = -3 and x = -5, \((-3)^-5\)<0, here x<y.
Therefore, statement II alone is insufficient. So, answer option B can be ruled out. The possible answer options are C or E.
Using the data from statements I and II, from the second statement, we know that y is negative, but x can be positive or negative. But, both x and y cannot be negative since x+y>0. Hence, x has to be positive and y has to be negative.
Therefore, we can surely say that x>y. So, the correct answer option is C.
As mentioned earlier, you have to exercise a fair degree of caution while interpreting statement II, because it can trick you into assuming that x has to be positive. Also, trying out simple values while evaluating the inequalities will help analyse them better..
Hope this helps!
16 Mar 2021, 07:35
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Walkabout
Given: x and y are integers
Target question: If x and y are integers, is x > y?
Statement 1: x + y > 0
This statement is clearly not sufficient.
There are many possible values of x and y that satisfy statement 1. Consider these two possible cases:
Case a: x = 2 and y = -1. In this case, the answer to the target question is YES, x is greater than y
Case b: x = -1 and y = 2. In this case, the answer to the target question is NO, x is not greater than y
Statement 2: y^x < 0
If x and y are integers, and y^x < 0, then we can be certain of two things:
1) y is negative
2) x is odd
There are several values of x and y that satisfy these conditions. Here are two:
Case a: x = 3 and y = -1. In this case, the answer to the target question is YES, x is greater than y
Case b: x = -3 and y = -1. In this case, the answer to the target question is NO, x is not greater than y
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 2 tells us that y is negative
Statement 1 tells us that x + y > 0
If y is negative, and x + y > 0, then it must be the case that x is positive
If x is positive and y is negative, it must be the case that the answer to the target question is YES, x is greater than y
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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Expert reply
14 Apr 2021, 15:23
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Video solution from Quant Reasoning:
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