If x, y, and z are integers, is xz 0 (2) yz

Question

If x, y, and z are integers, is xz < 0?

(1) xy > 0
(2) yz < 0

Bunuel · Answer

9. Inequalities 
     Theory   
 Inequalities Made Easy! 
 Inequalities: Tips and hints 
 Arithmetic with Inequalities 
 Wavy Line Method Application - Complex Algebraic Inequalities 
 Solving Quadratic Inequalities: Graphic Approach 
 Inequalities - Quadratic Inequalities 
 Graphic approach to problems with inequalities 
 Inequalities trick 
 INEQUATIONS(Inequalities) Part 1 
 INEQUATIONS(Inequalities) Part 2 
     Questions   
 Inequality and absolute value questions from my collection 
 DS Questions 
 PS Questions

For more check  Ultimate GMAT Quantitative Megathread

KSBGC · Answer

we are looking for whether xz is less the 0 or not.

statement 1: xy> 0
 in this case both x and y can be negative or positive. on the other hand no information pertinent to z is given. insufficient.

statement 2: yz< 0

here we are clear that either y or z is negative but we don't know which of this 2 is negative.

combining 2 statements: 
from statement 1 we know x an y both can be positive or negative.

phase 1: lets assume both x and y are positive. in that case in statement 2 z will be negative. in that case xz<0
phase 2: lets assume both x and y are negative. in that case in statement 2 z will be positive. in that case xz< 0

therefore correct answer will be C.

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (x,y and z) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Since xy > 0 and yz < 0, we have (xz)y^2 < 0 or xz<0.
Both conditions together are sufficient.

Since this question is an inequality question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
Since we don't have information about z, condition 1) is not sufficient.

Condition 2)
Since we don't have information about x, condition 2) is not sufficient.

Therefore, C is the answer.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.

Kinshook · Answer

Asked: If x, y, and z are integers, is xz < 0? (1) xy > 0 Since z is unknown NOT SUFFICIENT (2) yz < 0 Since x is unknown NOT SUFFICIENT (1) + (2) (1) xy > 0 (2) yz < 0 xy^2z <0 xz<0 SUFFICIENT IMO C

MHIKER · Answer

(1) x and y both are either positive or negative but no information about z. INSUFFICIENT.

(2) Either y or z is negative but no information about x. INSUFFICIENT.

Considering both the information (1) and (2):
If x and y are positive then z must be negative. So xz<0
If x and y are negative then z must be positive, so xz<0 
Sufficient.

The Answer is C.

bumpbot · Answer

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If x, y, and z are integers, is xz < 0? (1) xy > 0 (2) yz < 0

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