Is z x, if y x and x is a negative integer?

Question

If y > x and x is a negative integer, is z>x?

(1) zy > 0

(2)  \frac{y}{x}>\frac{z}{x}

gvij2017 · Answer

if y > x and x is a negative integer. Is z > x?

(1) zy > 0
If y is negative, z is negative. but z can be less or more than x. 0>y>z>x or 0>y>x>z 
Insufficient.

(2) y/x>z/x
As x is negative integer, by removing x, the inequality becomes y<z. 
Now it is already given that y>x
so we can say z>y>x means z>x
Sufficient.

B is answer.

sahilvermani · Answer

I am not understanding how (2) alone is sufficient.

It says y/x > z/x

This means xy > xz (by multiplying both side of the inequality by x^2)

So, we can have the values of (x,y,z) as (1,3,2) in which case x is positive or we can have the values of (x,y,z) as (-1,2,3) in which case x is negative.

Can you please explain where I am going wrong.

gvij2017 · Answer

Pleasure to explain. Given y/x>z/x y/x - z/x >0 (y-z)/x >0 We already know that x is negative, therefore, y-z<0 means yx. Furthermore, when we divide x^2 by x then we can get x or -x depends whether x is negative or positive. In last, in case of inequalities, first shift all expression at one side then do mathematical operations. This is what I have learned. Welcome for your next query!

sahilvermani · Answer

Thanks. I actually mis-read the question:(.

I thought we had to find out if x is negative....

MathRevolution · Answer

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

Remember the relation between the Variable Approach, and Common Mistake Types 3 and 4 (A and B)[Watch lessons on our website to master these approaches and tips]

Step 1: Apply Variable Approach(VA)

Step II: After applying VA, if C is the answer, check whether the question is key questions.

StepIII: If the question is not a key question, choose C as the probable answer, but if the question is a key question, apply CMT 3 and 4 (A or B).

Step IV: If CMT3 or 4 (A or B) is applied, choose either A, B, or D.

Let's apply CMT (2), which says there should be only one answer for the condition to be sufficient. Also, this is an integer question and, therefore, we will have to apply CMT 3 and 4 (A or B).

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find Is 'z > x' ? where 'x' is a negative integer and y > x.

Second and the third step of Variable Approach: From the original condition, we have 3 variables (x, y, and z) + 1 Equation( y > x). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 2 equations, C would most likely be the answer.

But we know that this is a key question [Integer question] and if we get an easy C as an answer, we will choose A or B.

Let’s take a look at each condition.

Condition(1) tells us that zy > 0.

=> Product of two numbers will be greater than zero when they both have the same sign.

=> if y is negative, then z is negative But if y is positive then z is positive.

=> If z is positive then z > x - YES but if z is negative it may be greater or less than x

Since the answer is not a unique YES or NO, the condition is not sufficient by CMT 1.

Condition(2) tells us that \(\frac{y}{x}\) > \(\frac{z}{x}\) .

=> x = negative integer and by removing negative number inequality changes from y > z to y < z { z > y)

=> y > x and z > y and hence, z > x - YES

Since the answer is a unique YES, the condition(2) alone is sufficient by CMT 1.

Condition (2) alone is sufficient.

So, B is the correct answer.

Answer: B

Basshead · Answer

Is z > x, if y > x and x is a negative integer?

(1) zy > 0

z and y can both be negative or positive. INSUFFICIENT.

(2) \(\frac{y}{x}>\frac{z}{x}\)

Cross multiply to get yz > zx
yx - zx > 0
x(y-z) > 0
Both x and (y-z) have to be negative or positive. Since we're told in the question stem that x is negative, then (y-z) must be negative.

y - z < 0
y < z
x < y < z

SUFFICIENT.

Answer is B.

Is z > x, if y > x and x is a negative integer?

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