Is x

Question

Is x < y?

(1) y/x < 1
(2) y < 0

Bunuel · Answer

Is x < y?

(1) y/x < 1. If x is positive, then when cross-multiplying we get y < x and answer NO but if x is negative, then when cross-multiplying we get y > x and answer YES. Not sufficient.

(2) y < 0. Not sufficient.

(1)+(2) We still don't know whether x is positive or not, hence don't know whether y < x or y > x. Not sufficient.

Answer: E.

Hope it's clear.

ENGRTOMBA2018 · Answer

The question asks is x Case 1: y=-5, x =6 , answer = NO Case 2: y= -5, x=-6, answer = YES Thus, not sufficient. Per statement 2, y<0, clearly not sufficient. Combining, you get y/x<1 and y<0. The 2 cases mentioned in statement 1 are still applicable, giving us 2 different answers ---> E is thus the correct answer. Hope this helps.

rohit8865 · Answer

(1)(y/x)-1<0------>(y-x)/x<0

means num. and den. have opposite signs.
But we dont know the value X
so insuff....

(2)y<0
same here we don't know the value of X ..it can be positive for a NO and can be more lesser than y for YES..insuff

combining we again don't know about X

so Ans E

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is x < y?

(1) y/x < 1
(2) y < 0

In the original condition, there are 2 variables(x,y), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), multiply x^2 to the both equations, y/x<1, which becomes yx<x^2 -> x(x-y)>0. However, you cannot figure out the sign of x, which is not sufficient.
Thus, E is the answer.

 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

bumpbot · Answer

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Is x < y? (1) y/x < 1 (2) y < 0

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