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Is x + y > 0 ?

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by Vincen » Wed Jan 24, 2018 8:45 am
Is x + y > 0?

(1) x^2 - y^2 > 1
(2) x/y + 1 > 0

The OA is the option E.

Using both statements together is not sufficient to solve this DS question?

Experts, may you give me some help? Thanks.
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Source: — Data Sufficiency |
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by DrMaths » Thu Jan 25, 2018 7:27 am
Vincen wrote:Is x + y > 0?

(1) x^2 - y^2 > 1
(2) x/y + 1 > 0

The OA is the option E.

Using both statements together is not sufficient to solve this DS question?

Experts, may you give me some help? Thanks.
(1) x and/or y could be negative, so we don't have info to compare them INSUFFICIENT
(2) We don't know if y is negative, so again it is INSUFFICIENT

STATEMENT (1) is the difference of 2 squares:
x^2 - y^2 = (x + y)(x - y) > 1
If x + y > 0, then (x - y) is positive, therefore x > y

STATEMENT (2) - if x and y are both positive, x>y (from (2)) then yes...
However, if say, x = 2 and y = 1, -1, ,-2 then x/y = 2, -2, -1... INSUFFICIENT
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by [email protected] » Thu Jan 25, 2018 12:01 pm
Hi Vincen,

We're asked if X + Y is greater than 0. This is a YES/NO question and we can solve it by TESTing VALUES.

1) X^2 - Y^2 > 1

IF.... X = 2, Y = 1, then 2+1 IS greater than 0 and the answer to the question is YES.
IF.... X = -2, Y = -1, then -2 + (-1) is NOT greater than 0 and the answer to the question is NO.
Fact 1 is INSUFFICIENT.

2) (X/Y) + 1 > 0

The same TESTs we used in Fact 1 also 'fit' Fact 2:
IF.... X = 2, Y = 1, then 2+1 IS greater than 0 and the answer to the question is YES.
IF.... X = -2, Y = -1, then -2 + (-1) is NOT greater than 0 and the answer to the question is NO.
Fact 2 is INSUFFICIENT.

Combined, we don't have to do any additional work; the TESTs that we have already fit BOTH Facts and lead to 2 different answers (one "YES" and one "NO").
Combined, INSUFFICIENT

Final Answer: E

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