If a

Question

If a < b < c , which of the following must be true?

(I) a < b^2
(II) b − a < c
(III) a^2 < b^2 < c^2

A. None
B. I only
C. II only
D. III only
E. II and III

Plug in a = − 5, b = 1/3, c = 4 and find none of them are true.

Hi, I want to know good pick number approach to this question, please.

Bunuel · Answer

(I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2.

(II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1.

(III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1.

None of the options must be true.

Answer: A.

Bunuel · Answer

Similar questions to practice: if-a-b-and-c-are-consecutive-positive-integers-and-a-b-144907.html if-a-b-and-c-are-consecutive-odd-positive-integers-and-a-154318.html All Must or Could be True Questions to practice: search.php?search_id=tag&tag_id=193 Hope this helps.

Crytiocanalyst · Answer

The key to solving is substituting the right values 
for 1) a=1/4 ,b=1/2 then the first inequality fall apart therefore out 
for 2) a=-1/2 ,b=1/2 and c=1 we get the value as equal which again disproves the inequality 
for 3) a=-1/4 b=-1/16 and c=-1/64 and eventually the disapprove the inequality

Therefore IMO A

kusum_ad · Answer

I’m a bit confused about how to approach these types of questions. Sometimes it seems like I need to try every possible value, like using fractions, to see if the answer makes sense. Other times, I’m just plugging in simple values like a=1, b=2, and c=3. How can I tell when to test every possibility versus when to stick with basic values?

sarthak1701 · Answer

In such questions use a variety of numbers, it will take slightly longer but considering this is a tough question, it is all right. I took these numbers:

3, 5, 7

-7, -5, -3

1/10, 1/5, 1/2

-1/2, -1/5, -1/10

None of the 3 options satisfy all these number sets. You only need ONE instance where it does not work out to eliminate that option.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If a < b < c , which of the following must be true?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If a < b < c , which of the following must be true?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards