If a

Question

If a < b and c < 0, which of the following are true? I. ac > bc II. a + c < b + c III. a - c > b - c A. I only B. II only C. III only D. I and II only E. Neither

Bunuel · Accepted Answer

Multiply a < b by c and don't forget to flip the sign of the inequality since we are multiplying by negative value: ac > bc. So, I must be true. As for II. Cancel c on both sides: a < b. II is true. The same for III. Cancel -c on both sides: a > b. So, III is not true. Answer: D.

run4run · Answer

no idea if can be graphed but I say the answer is B

gurpreetsingh · Answer

IMO its D.. OA please 1. AC > BC => AC-BC >0 (A-B) C > 0 true as C< 0 and A-B < 0...thus true. 2. Its also true Thus I and II only

Hussain15 · Answer

Nice explanation!! Kudos!!

OA is "D".

BDSunDevil · Answer

if a<b and c<0
then: a+c<b+0
can someone explain, how ii is true?

aish1232 · Answer

since c<0 and a<b so if we multiply a negative quantity to a smaller quantity then it turns out to be bigger in value(in both cases when a,b are negative or positive).so a is correct..simmilarly for b

siddharthmuzumdar · Answer

Nice question. Its easy to miss that even statement 1 is be true. Thanks gurpreetsingh.
 Answer: D

prabhakarsharma · Answer

Answer should be A.

Try with values. 2nd statement fails for a=-1, b=1, c=-1

pqhai · Answer

Please try again.

a + c = -1 -1 = -2
b + c = 1 -1 = 0

=> a + c < b + c 
(II) is correct.

Hope it helps

anceer · Answer

D is correct. as it works for both +ve and -ve numbers

e3thekid · Answer

I. ac > bc - we can divide both sides of inequality by c. We are given that c<0. Dividing by a negative number flips the inequality sign; after dividing by c, the inequality becomes a < b. We are told in the stem that a < b. TRUE II. a + c < b + c - since we are told that c is negative, the inequality can be re-written as: a - c < a -c. Adding c to both sides cancels the variable out. This then comes a < b, which we see is true given the stem. TRUE III. a - c > b - c - since c < 0, we can re-write this inequality as a -(-c) > b - (-c). This turns into a + c > b + c, where when we cancel out the c variable, the inequality becomes a > b. This goes against the given information of a < b in the stem. NOT TRUE I and II only Option D

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If a < b and c < 0, which of the following are true?

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