If a

Question

If a < b and c < b, is abc < a ?

(1) ab < 0
(2) ac > 0

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GMATinsight · Answer

Question : is abc < a ? Question : is abc-a < 0 ? Question : is a(bc-1) < 0 ? Given: b > a and c Statement 1 : ab < 0 i.e. a is negative and b is positive but sign of bc-1 is unknown hence NOT SUFFICIENT Statement 2 : ac > 0 i.e. a and c are both negative or both positive but sign of bc-1 is unknown hence NOT SUFFICIENT Combining statements ac > 0, ab < 0 i.e. a and c are negative while b is positive i.e. a and (bc-1) are both negative i.e. product is positive SUFFICIENT Answer: Option C

CareerGeek · Answer

a < b and c < b or b > c --> a < c < b Question: Is abc < a ? --> Is abc - a < 0 --> Is a(bc - 1) < 0 (1) ab < 0 For product to be negative, both should have opposite signs --> Since a < b a < 0 & b > 0. Nothing can be said about 'c' --> c can be >0 or <0 To Find: If a(bc - 1) < 0 or not Since a < 0, bc - 1 should be greater than 1 We do not know anything about the values of c. Eg: b = 1/2 & c = -1, bc = 1/2 (<1) --> a(bc - 1) < 0 If b = 2 & c = 1, bc = 2 (>1) --> a(bc - 1) > 0 No Definite answer --> Insufficient (2) ac > 0 --> a > 0 & c > 0 or a < 0 & c < 0 Case 1: a > 0 & c > 0: --> b > 0 To Find: If a(bc - 1) < 0 or not If a > 0, bc - 1 should be less than 0 We do not know anything about the values of b & c. Eg: b = 1/2 & c = 1, bc = 1/2 (<1); or if b = 2 & c = 3, bc = 6 (>1) --> Insufficient Case 2: a < 0 & c < 0: --> b <0 or >0 No Definite answer --> Insufficient Combining (1) & (2), a < 0 & b > 0; --> c < 0 Only To find: If a(bc - 1) < 0 or not Since a < 0 and bc < 0 (b > 0 & c < 0), bc - 1 < 0 --> a(bc - 1) > 0 ALWAYS A Definite value --> Sufficient Option C

GMATinsight · Answer

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

CareerGeek · Answer

Hi  GMATinsight ,

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

Thanks.

exc4libur · Answer

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 a0, 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)

Fdambro294 · Answer

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

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

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