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If xyz < 0, is x < 0 ? [#permalink]
27 Jun 2014, 09:22

Expert's post

2

This post was BOOKMARKED

SOLUTION

If xyz < 0, is x < 0?

xyz < 0 implies that either all three unknowns are negative or one is negative and the remaining two are positive.

(1) x - y < 0. This means that x < y. Could x be negative? Yes, if x, y, and z are negative. Could x be positive? Yes, if x and y are positive and z is negative. Not sufficient.

(2) x - z < 0. Basically the same here. We have that x < z. Could x be negative? Yes, if x, y, and z are negative. Could x be positive? Yes, if x and z are positive and y is negative. Not sufficient.

(1)+(2) We have that x < y and x < z. Could x be positive? No, because if x is positive then from x < y and x < z, both y and z must be positive but in this case xyz will be positive not negative as given in the stem. Therefore x must be negative. Sufficient.

Answer: C.

Try NEW inequalities PS question. _________________

Here x can take value of a positive or a negative number. x can be a negative number and y and z can be positive number or x and y can be positive numbers and z can take a negative value. Statement is insufficient.

Statement two: x-z<0 x<z

This statement is insufficient to determine sign of x. x,y and z all can be negative or x and z can take positive values and y can be a negative number.

Both statements combined together, x is the smallest number and product of x,y and z is a negative value. so x has to be a negative number. Either x is a negative number and y and z are positive or all the three numbers are negative. In both the cases, x is a negative number. Hence Ans=C

Re: If xyz < 0, is x < 0 ? [#permalink]
29 Jun 2014, 11:30

Expert's post

SOLUTION

If xyz < 0, is x < 0?

xyz < 0 implies that either all three unknowns are negative or one is negative and the remaining two are positive.

(1) x - y < 0. This means that x < y. Could x be negative? Yes, if x, y, and z are negative. Could x be positive? Yes, if x and y are positive and z is negative. Not sufficient.

(2) x - z < 0. Basically the same here. We have that x < z. Could x be negative? Yes, if x, y, and z are negative. Could x be positive? Yes, if x and z are positive and y is negative. Not sufficient.

(1)+(2) We have that x < y and x < z. Could x be positive? No, because if x is positive then from x < y and x < z, both y and z must be positive but in this case xyz will be positive not negative as given in the stem. Therefore x must be negative. Sufficient.

Answer: C.

Kudos points given to correct solutions above.

Try NEW inequalities PS question. _________________