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

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Set A and Set B each contain three whole numbers ranging from 1 to 10. [#permalink]

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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.

Kudos for a correct solution.

Source: Chili Hot GMAT
[Reveal] Spoiler: OA

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Re: Set A and Set B each contain three whole numbers ranging from 1 to 10. [#permalink]

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New post 27 Nov 2014, 07:26
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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]

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New post 27 Nov 2014, 09:22
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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]

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New post 27 Nov 2014, 19:31
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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]

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New post 28 Nov 2014, 07:49
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: Set A and Set B each contain three whole numbers ranging from 1 to 10. [#permalink]

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New post 29 Nov 2014, 00:59
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]

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Re: Set A and Set B each contain three whole numbers ranging from 1 to 10. [#permalink]

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New post 22 May 2017, 07:39
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Re: Set A and Set B each contain three whole numbers ranging from 1 to 10.   [#permalink] 22 May 2017, 07:39
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