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Could be x positive, y negative and z negative then xz = negative (E.g x = 10, y = -1, z = -10)
Or x negative, y negative and z negative then xz = positive (E.g x = -1, y = -2, z = -3)

Insufficient.

2) yz > 0.

Could be y positive, z positive, then xz would be positive (E.g. y = 10, z = 5 and x > 10)
Or y negative, z negative, then xz would be negative/positive. (E.g. y = -3, z = -5 and x > -3)

Insufficient.

Using 1) and 2)

Could be y negative, z negative, then x must be positive and xz = negative
or
Could be y positive, z positive, then x must be negative (Does not hold since x > y)

Could be x positive, y negative and z negative then xz = negative (E.g x = 10, y = -1, z = -10) Or x negative, y negative and z negative then xz = positive (E.g x = -1, y = -2, z = -3)

Insufficient.

2) yz > 0.

Could be y positive, z positive, then xz would be positive (E.g. y = 10, z = 5 and x > 10) Or y negative, z negative, then xz would be negative/positive. (E.g. y = -3, z = -5 and x > -3)

Insufficient.

Using 1) and 2)

Could be y negative, z negative, then x must be positive and xz = negative or Could be y positive, z positive, then x must be negative (Does not hold since x > y)

Ans C

This can't be if xy < 0. either one could be negative, but not both. (but from given information, we know that x>y, so x is positive and y is negative)

Could be x positive, y negative and z negative then xz = negative (E.g x = 10, y = -1, z = -10) Or x negative, y negative and z negative then xz = positive (E.g x = -1, y = -2, z = -3)

Insufficient.

"Or x negative, y negative" negative * negative = positive // flaw.

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