12 Days of Christmas GMAT Competition - Day 6: If a^3 b^2 c, which

Question

12 Days of Christmas GMAT Competition with Lots of Fun

If a^3 > b^2 > c, which of the following may be true?
 
I. a > b > c
II. c > b > a
III. a > c > b

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

rvgmat12 · Answer

If a^3 > b^2 > c, which of the following may be true?

I. a > b > c
II. c > b > a
III. a > c > b

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

All three may be true
I. a > b > c

a = 100 , b = 20, c=1

II. c > b > a

a = 4, b = 5, c = 10

III. a > c > b

a= 100, c= 1, b = -2

E is the answer

kguduri · Answer

Given ,  a^{3} > b^{2} > c 
The questions asks which of the following  may be  true. So just one instance that satisfies the conditions would be enough.

I. a > b > c
Most easiest to satisfy.
 4>2>1  (Taking a= 4 , b=2 , c =1)

4^{3} > 2^{2} > 1 => 64>4>1 
Option 1 is true.

II. c > b > a
 10>5>4  (Taking a= 4 , b=5 , c =10)

4^{3} > 5^{2} > 10 => 64>25>10 
Option 2 is true.

III. a > c > b
 10>8>3  (Taking a= 10 , b=3 , c =8)

10^{3} > 3^{2} > 8 => 1000>9>8 
Option 3 is true.

Answer - E. I, II, and III

Lizaza · Answer

Well, for the original task, any integers above 1 will do even when  a=b=c,  not to mention the situation when   a>b>c , so obviously   the Option I is possible. 
 
Now, option III is also quite straightforward, because  a  is very easy to select to be the highest - like a 100, easily.
However, what should be  b  and  с  so that  b^2 > c  but  c>b ? This is again not complicated, when с is, for instance, 4, and b is 3:
  100^3>3^2>4 , and   100>4>3 
So,   the Option III is also possible.

Finally, let's look at Option II. For a number to become substantially higher as a cube, this number has to be a positive integer.
Therefore,  c > b > a  can easily be   7 > 6 > 5 .
And in this case,  5^3 > 6^2 > 7  - so,   the Option II is also possible.

Therefore,   the correct answer is E  , where all situations are possible.

AKukreja · Answer

Bunuel  Hey, Bunuel! Is there any collection of such questions where we have to see whether a>b>c if a^3>b^3>c^3 etc etc?

Bunuel · Answer

9. Inequalities 
     Theory   
 Inequalities Made Easy! 
 Inequalities: Tips and hints 
 Arithmetic with Inequalities 
 Wavy Line Method Application - Complex Algebraic Inequalities 
 Solving Quadratic Inequalities: Graphic Approach 
 Inequalities - Quadratic Inequalities 
 Graphic approach to problems with inequalities 
 Inequalities trick 
 INEQUATIONS(Inequalities) Part 1 
 INEQUATIONS(Inequalities) Part 2 
     Questions   
 Inequality and absolute value questions from my collection 
 DS Questions 
 PS Questions

For more check  Ultimate GMAT Quantitative Megathread

Hope it helps.

Adarsh_24 · Answer

a^3>b^2>c

1. a>b>c
Both same direction. So just make sure sufficiently large difference between them.
 a^3>b2>c : 1000,100,1
Hmm. Thats not going to work as a=b=10
Need to make outer one even bigger.
 a^3>b^2>c:1000000,100,1
a>b>c: 100>10>1

2. c>b>a
So essentially a^3>b^2>c>b>a
Looks like the higher powers are infact bigger. This is true for x>1.
So 27,16,5,4,3

3. a > c > b
almost same as first. just need c and b swapped.
So take first example. the one you want to make smaller, take negative root.
 a^3>b^2>c:1000000,100,1
a>c>b: 100>1>-10

EnglishAgast · Answer

Hello  Bunuel  , I have seen multiple similar questions like this (a^3 > b^2 > c)

For a general case, i.e. any number (not necessarily an +/-/integer and with a tag of  MAY BE TRUE  stem, i have come to a conclusion that in all, there are 6 combinations that can be played around with and all 6 of them satisfies a  MAY BE TRUE  stem.

If it were to be  MUST BE TRUE  case, then none (out-of-6) of them should satisfy.

Pls could you advise on this interpretation? Thanks!

12 Days of Christmas GMAT Competition - Day 6: If a^3 > b^2 > c, which

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