If a < b and c < b, is abc < a ? (1) ab < 0 (2) ac > 0

Dillesh4096
Highlighted part doesn't satisfy the Second statement (ac >0) hence it is incorrect

Hi GMATinsight,

I mistook b < c for b > c at the start (Highlighted Part). Editing the same.

Thanks.

abc-a<0
a(bc-1)<0
if a>0 and bc<1 then ans yes
if a<0 and bc>1 then ans yes

(1) insufic
ab<0, then a and b have dif signs
since a<b, then a=neg and b=pos
nothing about c

(2) insufic
ac>0, then a and c have same signs
a,c=++ or a,c=--
nothing about b

(1/2) sufic
if a<0, b>0, c<0
then a<0 and bc<0
thus, a(bc-1)<0 = neg(neg-neg) > 0
answer to the question is no

Ans (C)

Rather than rephrase the question stem, it may be easier to jump immediately to the statements. Since the variable A lies on both sides of the inequality sign, if we can determine the sign of A, we can divide by A and simplify the Question Stem.

Is ABC < A?

s1: AB < 0

s1 tells us that A and B must have opposite signs

case 1: A = +positive ; B = -negative

however, we are Given: A < B
this case is impossible since a (positive) value can never be less than a (negative) value.

thus, statement 1, in conjunction with the given info., tells us that case 2 must be true:

Case 2:
A = (-)neg
B = +pos

since we know the sign of the Variable A, we can divide both sides of the question stem by A. The question becomes:

Is: (BC) < 1

we do NOT know the sign of C however.
we are given: C < B

(I) A = -1 , B = +2 , C = +1
satisfies the given constraint and statement 1. BC = (+2) (+1) = +2 ---- a value that is NOT less than 1.
NO

(II) A = -1 , B = +2 , C = -3
satisfies the given constraint and statement 1. BC = (+2) (-3) = -5 ----- a value < 1
YES

since we get two different answers (YES and NO) statement 1 is NOT sufficient

statement 2: AC > 0

s2 tells us that A and C must have the SAME Sign.

case 1: A = +pos ; C = +pos

we can then divide both sides of the question stem by A under this assumption and the inequality sign does not reverse.
Q becomes: Is BC < 1?

further, since we are given that C < B
B must be greater than the +pos value of C
B = +positive also

but we do not know whether A, B, and C are Integers, Decimals, Rational or Irrational numbers, etc.

(I) A = +1/4 ; B = +1/2 ; C = +1/4

IS: BC < 1 ?
YES

(II) A = +1 ; B = +2 ; C = +1

IS: BC < 1?
NO

again, since we get two different answers (YES and NO) statement 2 is NOT sufficient alone

(S1 & S2) together:

from statement 1, we were able to infer that:

A = (-)neg
B = +pos

further, statement 2 tells us that:
AC > 0

or, the variables A and C must have the SAME SIGN

therefore, we can infer:

C = (-)negative

Summary:
A = (-)negative ; B = +positive ; C = (-)negative

*Is: ABC < A ?

divide both sides by A, a negative value, reversing the inequality sign in the process.

*Is: BC > 0 ?

since we know that B is positive and C is negative, they must have opposite signs, and we can answer the question with a DEFINITE NO: BC < 0

*C* Statements together are sufficient