If a, b and c are integers, and ac/b

Question

If a, b and c are integers, and \frac{ac}{b} < 0 , then which of the following must be false? A) ab + ac + bc < 0 B) ca + b > 0 C) bc – a < 0 D) (b-c)(c-a) > 0 E) ca - abc < 0

kolodits · Answer

According to the question prompt, either one out of a,b,c or all of them are negative. In addition a,b,c are non zero, and are all integer.
Trying to eliminate the options:
A) Since all could be negative (e.g. a=b=c=-1), then this statement could be true.
B) in case a=-1, b=2, c=1, then ac+b =-1+2=1>0. Could be true.
C) In case a=1,b=1,c=-1, then bc-a = -1 -1=-2<0. Could be true.
D) In case a=1,b=-1,c=2, then (b-c)(c-a)=(-1-2)(2-1)=(-3)(1)=-3<0. Could be true.
E) According to this option ac<abc and from the question prompt we know that abc<0, thus ac<0. Therefore, b must be positive integer. In case b=1 then ac=abc, which is false . In case b>1 then it should be abc<ac, which could not be correct. Therefore, this statement is always false.
The answer is E.

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rohit8865 · Answer

assume any 3 negative numbers easily we can rule out top 3 options D) b>c>a if all are positive.....not possible if all are negative ....possible E)checking option E ac(1-b)<0 thus case 1:- if ac< 0 then 1-b>0 or b<1 since b cannot be 0 thus b <0 since b is integer but ac<0 and b<0 is not possible as ac/b<0 case2:- if ac>0 then (1-b)<0 or b>1 again ac and b >0 is not possible as ac/b<0 thus option E is correct i first assumed all negative nos. and got the ans correct

Ans E

HKD1710 · Answer

ac/b < 0 , following are the possibilities of signs integers a,b or c can take.

Case (1) either 2 +ve and 1 -ve

Case (2) all -ve

A) ab + ac + bc < 0
if a & b +ve and c -ve then +ve + -ve + -ve can be < 0
Hence it cannot be MUST BE FALSE.

B) ca + b > 0
If all a,b & c are negative then +ve + -ve could be > 0
Hence it cannot be MUST BE FALSE.

C) bc - a < 0
if a & b +ve and c is -ve then -ve + +ve could be < 0
Hence it cannot be MUST BE FALSE.

D) (b-c) (c-a) > 0
(b-c) (a-c) < 0
either b > c or a > c
say b and c are +ve and b > c and a is -ve then (+ve) * (-ve) will be -ve.
Hence it cannot be MUST BE FALSE.

E) ca - abc < 0
ca (1 - b) < 0
ca (b - 1) > 0 for this to be true:
either ac > 0 or b > 1 i.e. all a,b & c +ve - this cannot be a case as opposed to case 1&2
OR ac < 0 AND b < 1 i.e. a & c both has to be -ve. this cannot be a case as opposed to case 1&2

hence ca - abc < 0 MUST BE FALSE

bumpbot · Answer

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If a, b and c are integers, and ac/b < 0, then which of the following

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