Which of the following must be true if x/y and x/z y/z?

Question

Competition Mode Question Which of the following must be true if x < y and \frac{x}{z} > \frac{y}{z} ? A. z < 0 B. z > 0 C. \frac{x}{y} > 0 D. x > 0 E. y > 0

CareerGeek · Answer

\frac{x}{z} > \frac{y}{z} --> \frac{(x - y)}{z} > 0 Since, x < y , --> x - y < 0 --> z < 0 ALWAYS (Since for \frac{(x - y)}{z} > 0 , ONLY negative/negative > 0) IMO Option A

vg18 · Answer

Which of the following must be true if xy/z? The eqs. xy/z will only be valid when z<0.

madgmat2019 · Answer

x y/z i.e x/z - y/z > 0 x-y/z > 0 Since x-y <0, so z has to be < 0 to make the equation > 0 So z must be < 0 OA:A

sampriya · Answer

z(x-y)>0

given x-y<0 therefore Z<0

option A

unraveled · Answer

Which of the following must be true if x < y and \(\frac{x}{z} > \frac{y}{z}\) ?

A. z < 0

B. z > 0

C. \(\frac{x}{y}\) > 0

D. x > 0

E. y > 0

Since x < y and inequality \(\frac{x}{z} > \frac{y}{z}\) is with opposite sign, z must be an entity that must be causing the change of sign.

Among the choices D and E are straightforward out since both can have both + and - signs.
C is also ruled out since x and y can have opposite signs.

Only possibility left is A because z > 0 would not lead to change in sign from < to >.

Answer A.

exc4libur · Answer

xy/z…x/z-y/z>0…x-y/z>0 x-y<0 so z<0 Ans. (A)

eakabuah · Answer

Given x y/z, this can only be true if x>0 and y>0 and z<0 or x<0 and y<0 and z<0. In both cases, z<0 must be true. To illustrate, lets consider the case where x>0 and y>0 and z<0 Let x=2 and y=3, we know x=2 < y=3. if z=-1, then x/z=-2 and y/z=-3. Since -2(x/z) > -3(y/z), then the given condition is satisfied. In the other case where x<0 and y<0, let x=-3 and y=-2. -3(x) < -2(y). x/z can only be greater than y/z if z<0, so let z=-1. Then x/z=3 and y/z=2. Since 3(x/z) > 2(y/z), then the given condition is satisfied. In both instances, z<0. Hence the answer is option A

Kalubalu · Answer

I cross multiplied, to get zx > zy which would indicate that a sign change has occurred so z < 0

A IMO

Archit3110 · Answer

the given condition xy/z can be true if x & z are -ve and y is +ve so IMO A ; z<0 should be correct Which of the following must be true if xy/z? A. z<0 B. z>0 C. xy>0 D. x>0 E. y>0

suchithra · Answer

Given x<y but \frac{x}{z}>\frac{y}{z}. Note that the sign is changed when divided by Z.

Theory : Multiplication/division with a negative number can change the inequality sign. Thefore Z has to be negative for this to hold true.

Answer is A.

lacktutor · Answer

Which of the following must be true if x < y and \((\frac{x}{z}) > (\frac{y}{z})\)?

\(\frac{(x —y)}{z} > 0\)
x—y < 0.

—> in order \(\frac{(x —y)}{z}\) to be positive, z must be less than zero. (z < 0)

The answer is A

Posted from my mobile device

hmdrza · Answer

Z should be negative. For example: x=2 and y=3 and z=-3 then we have 2<3 so x -3/3 so x/z > y/z.

BelalHossain046 · Answer

A is my answer Given, (X/z)>(y/z) Here, z can not be zero. So, z must be positive or negative. If z is positive, x>y. If z is negative, x

Raxit85 · Answer

Imo. A

Which of the following must be true if x<y and x/z >y/z?

Let's try from options.

A. z<0, Z is negative, x/z >y/z, If z = -1, -x>-y, y>x and the same condition x<y is mentioned. Hence, Z must be true to suffice the condition.

B. z>0, Z is positive, x/z >y/z, If z = 1, x>y, which contradicts the give condition x<y. incorrect

C. x/y>0, We don't know the signs of any variables, so there can be multiple options, which could be true, are available.

D. x>0, If x is positive, Y is also positive. But no more information about Z. So multiple values for inequality can be obtained

E. y>0. It implies that y = +ve and x can be +ve/-ve. So, again multiple values for inequality can be obtained

ScottTargetTestPrep · Answer

We see that the inequality sign flips when both x and y are divided by z. This happens when z is negative, i.e., z < 0. Alternate Solution: Using the second inequality, we have: x/z - y/z > 0 (x - y)/z > 0 Since (x - y)/z is positive, (x - y) and z are either both positive or both negative. On the other hand, from the first inequality, we have: x - y < 0 Since (x - y) is negative, it follows that z must also be negative; i.e. z < 0. Answer: A

bumpbot · Answer

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Which of the following must be true if x/y and x/z > y/z?

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