GMAT Club Around The World!!! If a b^2 c^3, which of the following

Question

If  a > b^2 > c^3 , 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

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Bunuel · Accepted Answer

Experts' Global Official Video Explanation

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ElninoEffect · Answer

a > b^2 > c^3 . Given

I.  a > b > c 
a =100; b = 5 ; c = 1 So, this can be true.
II.  c > b > a 
c=0.7; b=0.6; a=0.4 This is also possible.
III.  a > c > b 
a=100; b =0.6; c=0.7 This is also possible.

All three cases are possible.
  E

apretty · Answer

First, note that a is always positive I. Pick a positive a , assign b=0 , and pick a negative c , we get a>b>c . You can choose another case, but overall (I) is possible. II. Since we know a is positive -> b and c are positive, too. And that 0 < c^3 < a < c -> c <1 . The first way to think, if you choose a random number 0 c^2*c = c^3 . The same thinking way for a and b that you can find a to satisfy a > b^2 . (II) is possible. Another way for those who still struggle with the aforementioned lines: let pick a=0.5 for example -> 0.5^3 = 0.125 . We see that 0.125 < 0.16 = 0.4^2 (or you can just try the square of a number smaller than 0.5 ), so we take 0.4 as b , then we easily pick c , ( 0.2 for instance). (II) is possible III. This case is easier. Take the same b,c that we chose in (II), together with a very large a (1,10,100, ...), we get a>c>b So (E) is the answer.

gmatophobia · Answer

We know that

a >  b ^ 2  >  c ^ 3

Because  b ^ 2  is positive, b can be +ve  or  -ve

I. a>b>c

a = 0.2
b = 0.35 |  b ^ 2  = 0.1425
c = 0.4 |  c ^ 3  = 0.096

Valid

II. c>b>a

a = 0.3
b = 0.5 |  b ^ 2  = 0.25
c = 0.6 |  c ^ 3  = 0.216

Valid

III. a>c>b

a = 0.3
b = -0.5 |  b ^ 2  = 0.25
c = -0.3 |  c ^ 3  = -0.027

Valid

IMO E

100mitra · Answer

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

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

Consider
a = 3, b = 4, c = 5
3<16<25
a<b<c - II. c>b>a

a = 0.3, b = 0.4, c = 0.5
0.3>0.16>0.125
a>b>c - I a>b>c

a = -3, b = -4, c = -5
-125<-3 < 16 - c<a<b

Correct Option C

ChakAvi · Answer

If  a > b^2 > c^3 , 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

Let, a =8, b=2, c=1... a>b^2>c^3 satisfies...
Then, a>b>c.. I. correct.
Let, a=1.5, b =-1, c=0.5..a>b^2>c^3 satisfies
The, a>c>b....III Correct

But to satisfy the given condition, a cannot be the lowest.

IMO Answer D

bumpbot · Answer

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GMAT Club Around The World!!! If a > b^2 > c^3, which of the following

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GMAT Club Around The World!!! If a > b^2 > c^3, which of the following

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