If xy 0 and yz

Question

If  xy > 0  and  yz < 0 , then which of the following must be negative?

A  xyz

B  xy^2z

C  x^2y^2z

D  x^2y^2z^2

E  \frac{xy}{z}

KanishkM · Answer

IMO B

If  xy > 0  and  yz < 0

there can be 2 cases

x can be +ive, y can be +ive  &  y can be +ive, z can be -ive

x can be -ive, y can be -ive  &  y can be -ive, z can be +ive

Now just go through the options one by one

A  xyz , -ive or +ive, depending on the mentioned cases

B  xy^2z , always -ive

KSBGC · Answer

xy>0 and yz<0. multiply these 2 . xy^2z<0. xy*yz <0 xy>0 yz<0 one is positive and another one is negative. ultimate result must be negative. B is the correct answer.

Archit3110 · Answer

test the cases
xy >0
when both x & y are either + or -
so in that case yz<0 when either of values are of opposite sign

we can say that
option B stands out

IMO B

ScottTargetTestPrep · Answer

Looking at the first inequality we see that either x and y are both positive or they are both negative.

Combine that with the second inequality. If y is positive, z is negative, and when y is negative, z is positive.

Thus, our scenarios are:

x = pos, y = pos, z = neg

Or

x = neg, y = neg, z = pos

We see that x and z always have opposite signs, and thus, (x)(y^2)(z) is always negative.

Alternate solution:

We can use the following fact: If a > 0 and b < 0, then ab < 0. Therefore, we can multiply the two inequalities to obtain:

x(y^2)z < 0

Answer: B

bumpbot · Answer

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If xy > 0 and yz < 0, then which of the following must be negative?

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