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The following sets are given

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Carcass
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The following sets are given [#permalink] New post   23 Apr 2021, 09:53
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The following sets are given, where \(x\) is an integer \(>1\):

\(A=[(-1+x+x^2),(1-x+x^2),(1+x+x^2)]\)

\(B=[(-1+x^2+x^3),(1-x^2+x^3),(1+x^2+x^3)]\)

Which statements are true?

Select all that apply

A. The greatest of A is less than the least element of B.

B. The greatest element of A is greater than the least element of B.

C. The greatest element of A is less than the greatest element of B.

D. The average of elements of A is greater than the average of elements of B.

E. The average of the elements of A is smaller than the average of the elements of B

F. the average of the elements of A is equal to the average of the elements of B.

G. The average of the elements of A is twice the average of the elements of B

Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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C,E
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tapas3016
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Re: The following sets are given [#permalink] New post   24 Apr 2021, 20:37
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Carcass wrote:
The following sets are given, where \(x\) is an integer \(>1\):

\(A=[(-1+x+x^2),(1-x+x^2),(1+x+x^2)]\)

\(B=[(-1+x^2+x^3),(1-x^2+x^3),(1+x^2+x^3)]\)

Which statements are true?

Select all that apply

A. The greatest of A is less than the least element of B.

B. The greatest element of A is greater than the least element of B.

C. The greatest element of A is less than the greatest element of B.

D. The average of elements of A is greater than the average of elements of B.

E. The average of the elements of A is smaller than the average of the elements of B

F. the average of the elements of A is equal to the average of the elements of B.

G. The average of the elements of A is twice the average of the elements of B


A very lengthy question :shock:

Considering x as 2, following are the sets.
A - 5,3,7
B - 11,5,13

A. 7<5 No
B. 7>5 Yes
C. 7>5 Yes
D. 5>9.6 No
E. 5<9.6 Yes
F. 5=9.6 No
G.5=2*9.6 No

Hence, BCE
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KC15
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Re: The following sets are given [#permalink] New post   05 Sep 2022, 11:01
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tapas3016 wrote:
Carcass wrote:
The following sets are given, where \(x\) is an integer \(>1\):

\(A=[(-1+x+x^2),(1-x+x^2),(1+x+x^2)]\)

\(B=[(-1+x^2+x^3),(1-x^2+x^3),(1+x^2+x^3)]\)

Which statements are true?

Select all that apply

A. The greatest of A is less than the least element of B.

B. The greatest element of A is greater than the least element of B.

C. The greatest element of A is less than the greatest element of B.

D. The average of elements of A is greater than the average of elements of B.

E. The average of the elements of A is smaller than the average of the elements of B

F. the average of the elements of A is equal to the average of the elements of B.

G. The average of the elements of A is twice the average of the elements of B


A very lengthy question :shock:

Considering x as 2, following are the sets.
A - 5,3,7
B - 11,5,13

A. 7<5 No
B. 7>5 Yes
C. 7>5 Yes
D. 5>9.6 No
E. 5<9.6 Yes
F. 5=9.6 No
G.5=2*9.6 No

Hence, BCE



I don't agree that B is always true. As x gets larger, this will no longer apply.
Consider x=3
Set A = (11,7,13) and Set B = (35,19,37).
In this case, 13 is NOT greater than 19.
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rainer85
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Re: The following sets are given [#permalink] New post   12 Sep 2022, 17:50
Can someone please explain how B is correct? Since X can be any positive integer greater than 1 could you not plug in some gigantic number and get a result that proves B to be false?
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Re: The following sets are given [#permalink] New post   13 Sep 2022, 06:10
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Thanks. Edited the answer.

rainer85 wrote:
Can someone please explain how B is correct? Since X can be any positive integer greater than 1 could you not plug in some gigantic number and get a result that proves B to be false?
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Re: The following sets are given [#permalink]
13 Sep 2022, 06:10
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