If 0

Question

If 0 < ab < ac, then which of the following must be true? A. abc > 0 B. c^2 - b^2 >0 C. |b| > |c| D. abc < 0 E. |a|/a = 1

Bunuel · Accepted Answer

0 < ab < ac is possible when all three unknowns are negative as well as when all three unknowns are positive. Case 1: all three unknowns are negative. 0 < ab < ac; Reduce by a and flip the sign: 0 > b > c. A. abc > 0. NOT true (the product of three negative numbers is negative). B. c^2 - b^2 >0 --> c^2 > b^2 --> |c| > |b| --> c is further from 0 than b. TRUE. C. |b| > |c|. NOT true (check above). D. abc < 0. TRUE. E. |a|/a = 1. NOT true (if a < 0, then |a|/a = -a/a = -1 not 1). Case 2: all three unknowns are positive. 0 < ab < ac; Reduce by a: 0 < b < c. A. abc > 0. TRUE. B. c^2 - b^2 >0 --> c^2 > b^2 --> |c| > |b| --> c is further from 0 than b. TRUE. C. |b| > |c|. NOT true (check above). D. abc < 0. NOT true. E. |a|/a = 1. TRUE. As we can see only B is true in both cases. Answer: B.

Raja1406 · Answer

00 and ac>0 then are two cases 1st)a>0 then b>0 and c>0 And c>b 2nd) a<0 then b<0 and c<0 And b>c but |b|<|c| Option B is the Answer. Posted from my mobile device

lacktutor · Answer

00 If a<0, then b and c will be negative numbers in 0 | c | If a<0, this answer will be right all the time. But If a >0, we can get c>b in 0

pratik2018 · Answer

If 0 < ab < ac, then which of the following must be true?
A. abc > 0 a = -1 b = -2 c = -3 0< 2< 3 abc< 0 in this case
B. c^2 - b^2 >0 - correct answer
C. |b| > |c| a = 1 , b = 2 , c = - 1 0 < 2 < - 1 doesnt work for cases where a > 1
D. abc < 0 a = 1 b = 2 c = 3 0< 2< 3 abc> 0 in this case
E. |a|/a = 1 basically a is positive only but we have cases above where a can take negative value.

Correct answer B

rahulms94 · Answer

Can someone please explain how option B is correct.
Given b<c, if we assume b=-3 and c=-2, then
C^2 - b^2 would be 4 - 9 = - 5 which is <0

Posted from my mobile device

pratiksha1998 · Answer

can someone explain why option D is incorrect?

chetan2u · Answer

ac>ab>0 means a and c have same sign and also a and b have same sign. 
Thus all three a, b and c have same sign. 
Two cases
1) All negative : abc<0
2) All positive: abc>0
So, need not be true always.

Crytiocanalyst · Answer

HI rahulms94 ,
You have done simplification that lead to you simplfying the eqn to b<c

Given ab<ac => b<c only if a is positive in which case c^2 - b^2 >0

you chose b=-3 and c=-2 then the eqn will not be valid for a=-10 30 is not less than 20
you chose the values in a hurry if i am not wrong
Therefore youre answer was wrong

HOpe it helps

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If 0 < ab < ac, then which of the following must be true?

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