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Is a^3 + b^5 > c^4?

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Is a^3 + b^5 > c^4?  [#permalink]

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New post 29 Apr 2016, 04:02
1
2
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

51% (01:08) correct 49% (01:32) wrong based on 82 sessions

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Re: Is a^3 + b^5 > c^4?  [#permalink]

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New post 29 Apr 2016, 05:52
1
Is a^3 + b^5 > c^4?

(1) a < b < c
Scenario 1: let a=1/2, b=1 and c=2
-----------> (1/2)^3 + (1^5 > 2^4
-----------> 1/8 + 1 > 16 FALSE
Scenario 2: let a=2, b=3 and c=4
-----------> 2^3 + 3^5 > 4^4
-----------> 1944 > 256 TRUE
Statement 1 alone is not sufficient (cross out A and D)

(2) b < 0
The only thin we can conclude from this statement is that b^5 is negative since the -ve number b is raised to an odd exponent 5.
No info about a or c
Statement 2 alone is not sufficient (cross out B as well A and D)

Both statements together:
-----------> b<0 => a<0 and c>0
-----------> for any values of a and b, the a^3 + b^5 is -ve becuase both a and b are -ve numbers raised to odd exponents
-----------> c>0 so c^4 is positive
The final answer a^3 + b^5 IS NOT LESS THAN c^4
====> the answer is "C"
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Re: Is a^3 + b^5 > c^4?  [#permalink]

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New post 29 Apr 2016, 12:13
deabas wrote:
Is a^3 + b^5 > c^4?

(1) a < b < c
Scenario 1: let a=1/2, b=1 and c=2
-----------> (1/2)^3 + (1^5 > 2^4
-----------> 1/8 + 1 > 16 FALSE
Scenario 2: let a=2, b=3 and c=4
-----------> 2^3 + 3^5 > 4^4
-----------> 1944 > 256 TRUE

Statement 1 alone is not sufficient (cross out A and D)

(2) b < 0
The only thin we can conclude from this statement is that b^5 is negative since the -ve number b is raised to an odd exponent 5.
No info about a or c
Statement 2 alone is not sufficient (cross out B as well A and D)

Both statements together:
-----------> b<0 => a<0 and c>0
-----------> for any values of a and b, the a^3 + b^5 is -ve becuase both a and b are -ve numbers raised to odd exponents
-----------> c>0 so c^4 is positive
The final answer a^3 + b^5 IS NOT LESS THAN c^4
====> the answer is "C"


2^3 + 3^5 > 4^4 = 8+243>256 = > 251>256 False
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Re: Is a^3 + b^5 > c^4?  [#permalink]

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New post 13 Jul 2017, 20:06
Is a^3 + b^5 > c^4?

(1) a < b < c
(2) b < 0

(1) if a=1;b=2;c=3 then YES but if A=1.8;b=1.99;c=2 then NO - insufficient

(2) even though b is less than 0, we still don't know what is a. a could be 10, while c could be 1 so the answer would be YES, and vise versa a could be 1, while c could be 10 and the answer is NO - insufficient

(1) + (2) combining the two we know that a and b are negative - regardless of what numbers we pick, the answer will be NO - SUFFICIENT.

Answer C
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Re: Is a^3 + b^5 > c^4?  [#permalink]

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New post 14 Aug 2017, 03:25
Milano2017 wrote:
Is a^3 + b^5 > c^4?

(1) a < b < c
(2) b < 0

(1) if a=1;b=2;c=3 then YES but if A=1.8;b=1.99;c=2 then NO - insufficient

(2) even though b is less than 0, we still don't know what is a. a could be 10, while c could be 1 so the answer would be YES, and vise versa a could be 1, while c could be 10 and the answer is NO - insufficient

(1) + (2) combining the two we know that a and b are negative - regardless of what numbers we pick, the answer will be NO - SUFFICIENT.

Answer C


I dont understand how a=1;b=2;c=3 gives YES. LHS : 1^3 + 2^5 = 1 + 32 = 33. RHS: 3^4 = 81. LHS < RHS. It is still No.
Am I missing something?
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Re: Is a^3 + b^5 > c^4?  [#permalink]

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New post 14 Aug 2017, 03:45
1
Bang2919 wrote:
Milano2017 wrote:
Is a^3 + b^5 > c^4?

(1) a < b < c
(2) b < 0

(1) if a=1;b=2;c=3 then YES but if A=1.8;b=1.99;c=2 then NO - insufficient

(2) even though b is less than 0, we still don't know what is a. a could be 10, while c could be 1 so the answer would be YES, and vise versa a could be 1, while c could be 10 and the answer is NO - insufficient

(1) + (2) combining the two we know that a and b are negative - regardless of what numbers we pick, the answer will be NO - SUFFICIENT.

Answer C


I dont understand how a=1;b=2;c=3 gives YES. LHS : 1^3 + 2^5 = 1 + 32 = 33. RHS: 3^4 = 81. LHS < RHS. It is still No.
Am I missing something?


You are right. It's a typo: the first case gives a No answer while the second case gives an Yes answer.
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Re: Is a^3 + b^5 > c^4? &nbs [#permalink] 14 Aug 2017, 03:45
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