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Set A and Set B each contain three whole numbers ranging from 1 to 10.

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Bunuel
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Set A and Set B each contain three whole numbers ranging from 1 to 10. [#permalink] New post   27 Nov 2014, 07:51
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64% (02:06) correct 36% (01:59) wrong based on 257 sessions
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Tough and Tricky questions: Statistics.



Set A and Set B each contain three whole numbers ranging from 1 to 10. With regard to the data contained in each set, is the arithmetic mean of Set A greater than the arithmetic mean of Set B?

(1) The median of Set A is greater than the median of set Set B.
(2) The mode of Set A is greater than the mode of Set B.

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Source: Chili Hot GMAT
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E
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desaichinmay22
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Re: Set A and Set B each contain three whole numbers ranging from 1 to 10. [#permalink] New post   27 Nov 2014, 08:26
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Statement 1 : The median of Set A is greater than the median of set Set B.

set A = (3,3,4) , set B = (1,1,9) ..... mean of set A is less than mean of set B
set A = (4,4,6), set B= (2,2,8) ....... mean of set A is greater than mean of set B

statement is insufficient.

statement 2 : The mode of Set A is greater than the mode of Set B.

set A = (3,3,4) , set B = (1,1,9) ..... mean of set A is less than mean of set B
set A = (4,4,6), set B= (2,2,8) ....... mean of set A is greater than mean of set B

statement in insufficient.

1+2 combined, statements are insufficient.

Ans - E
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Re: Set A and Set B each contain three whole numbers ranging from 1 to 10. [#permalink] New post   27 Nov 2014, 10:22
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From statement 1, we could get two sets: A-7, 7, 7 and B-6, 6, 10--A has a higher median and B has a higher mean. A-5, 5, 5 and B-1, 1, 10--A has a higher median and mean. Insufficient

From statement 2, we can use the same two sets. Also insufficient.

Choice E
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Re: Set A and Set B each contain three whole numbers ranging from 1 to 10. [#permalink] New post   27 Nov 2014, 20:31
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By plugging in different value we can see we can not conclude anything.

Hence answer is E.

Lets say first set is A{a,b,c} and second set is B{x,y,z}

so is a+b+c > x+y+z ?

Statement 1: The median of Set A is greater than the median of set Set B.
A{1,5,6} and B{4,4,10} ---No
A{4,5,10} and B{1,4,10} ---Yes
Insufficient

Statement2: The mode of Set A is greater than the mode of Set B.
A{2,2,3} and B{1,1,10} ---No
A{8,8,9} and B{1,1,2} ---Yes

Statement 1 and 2: We again get answer as Yes and No.

So answer is E.
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Re: Set A and Set B each contain three whole numbers ranging from 1 to 10. [#permalink] New post   28 Nov 2014, 08:49
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Bunuel wrote:

Tough and Tricky questions: Statistics.



Set A and Set B each contain three whole numbers ranging from 1 to 10. With regard to the data contained in each set, is the arithmetic mean of Set A greater than the arithmetic mean of Set B?

(1) The median of Set A is greater than the median of set Set B.
(2) The mode of Set A is greater than the mode of Set B.

Kudos for a correct solution.

Source: Chili Hot GMAT


The correct answer is E.
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Re: Set A and Set B each contain three whole numbers ranging from 1 to 10. [#permalink] New post   29 Nov 2014, 01:59
Bunuel wrote:

Tough and Tricky questions: Statistics.



Set A and Set B each contain three whole numbers ranging from 1 to 10. With regard to the data contained in each set, is the arithmetic mean of Set A greater than the arithmetic mean of Set B?

(1) The median of Set A is greater than the median of set Set B.
(2) The mode of Set A is greater than the mode of Set B.

Kudos for a correct solution.

Source: Chili Hot GMAT


A =(x,y,z)
B =(k,l,m)
(1) assume y is median of A, and l is median of B. cant conclude (x+y+z)/3 > (k+l+m)/3 => not sufficient
(2) x,y,...m are different. can't conclude => not sufficient
(1)+ (2) not sufficient =>E
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Re: Set A and Set B each contain three whole numbers ranging from 1 to 10. [#permalink] New post   09 Mar 2019, 14:13
This is a very good question. I understand how statements A and B are insufficient. However, in everyone's explanations, I don't understand how you tested the statements COMBINED. Anyone care to explain?
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Re: Set A and Set B each contain three whole numbers ranging from 1 to 10. [#permalink] New post   10 May 2024, 03:39
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Re: Set A and Set B each contain three whole numbers ranging from 1 to 10. [#permalink]
10 May 2024, 03:39
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