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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If a and b are positive integers less than 10, what is the mode of the

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Math Expert V
Joined: 02 Sep 2009
Posts: 55631
If a and b are positive integers less than 10, what is the mode of the  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 46% (02:26) correct 54% (02:08) wrong based on 246 sessions

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GMAT CLUB TESTS' FRESH QUESTION:

{a, b, 1, 2}
If a and b are positive integers less than 10, what is the mode of the list above?

(1) The number of different permutations of the numbers in the list is 12.
(2) A four-digit number 21ab is divisible by 9

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Math Expert V
Joined: 02 Aug 2009
Posts: 7752
Re: If a and b are positive integers less than 10, what is the mode of the  [#permalink]

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2
1
Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION:

{a, b, 1, 2}
If a and b are positive integers less than 10, what is the mode of the list above?

(1) The number of different permutations of the numbers in the list is 12.
(2) A four-digit number 21ab is divisible by 9

Mode means the integer repeated max time

(1) The number of different permutations of the numbers in the list is 12.
All four cannot be different, otherwise permutations would be 4!=4*3*2=24
Since there are 12 permutations, and 12=24/2=4!/2=4!/2!
So there is one pair same and other two distinct..
But mode could be any 1, or 2 or a variable
Insufficient

(2) A four-digit number 21ab is divisible by 9
Since divisibility depends on sum of the number, so a+b+2+1=3+a+b is div by 9
Since a be B are interchangeable, we cannot find the value of variable
Number could 2115,2151,2124,2142,2133,2169,2196,2178,2187
So insufficient

Combined
One pair and other two distinct, so possibilities 2115,2124,2133
So mode can be 1,2 or 3
Insufficient

E
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Math Expert V
Joined: 02 Sep 2009
Posts: 55631
Re: If a and b are positive integers less than 10, what is the mode of the  [#permalink]

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Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION:

{a, b, 1, 2}
If a and b are positive integers less than 10, what is the mode of the list above?

(1) The number of different permutations of the numbers in the list is 12.
(2) A four-digit number 21ab is divisible by 9

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Re: If a and b are positive integers less than 10, what is the mode of the  [#permalink]

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Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION:

{a, b, 1, 2}
If a and b are positive integers less than 10, what is the mode of the list above?

(1) The number of different permutations of the numbers in the list is 12.
(2) A four-digit number 21ab is divisible by 9

# 1:
4!= 24 but given permutation is 12 so 4!/2!= 12 but 2 numbers can be any between (0-10) in sufficient

#2: 21ab is divisible by 9 , so number sum 2+1+a+b= 9 , for which we have many values so in sufficeint

from 1&2 : we wont get any 1 single value to determine the mode... IMO E
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Intern  B
Joined: 12 Dec 2018
Posts: 1
Re: If a and b are positive integers less than 10, what is the mode of the  [#permalink]

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chetan2u wrote:
Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION:

{a, b, 1, 2}
If a and b are positive integers less than 10, what is the mode of the list above?

(1) The number of different permutations of the numbers in the list is 12.
(2) A four-digit number 21ab is divisible by 9

Mode means the integer repeated max time

(1) The number of different permutations of the numbers in the list is 12.
All four cannot be different, otherwise permutations would be 4!=4*3*2=24
Since there are 12 permutations, and 12=24/2=4!/2=4!/2!
So there is one pair same and other two distinct..
But mode could be any 1, or 2 or a variable
Insufficient

(2) A four-digit number 21ab is divisible by 9
Since divisibility depends on sum of the number, so a+b+2+1=3+a+b is div by 9
Since a be B are interchangeable, we cannot find the value of variable
Number could 2115,2151,2124,2142,2133,2169,2196,2178,2187
So insufficient

Combined
One pair and other two distinct, so possibilities 2115,2124,2133
So mode can be 1,2 or 3
Insufficient

E

Please correct me if I'm wrong

Number of permutations of 4 different terms is 4! which is 24
If 2 are different and 2 similar then number of permutations is 4!/2! which is 12

Statement A says - number of permutations is 12 => 2 elements are similar and 2 are unique => Mode 2 => A is sufficient
Intern  B
Joined: 26 Oct 2010
Posts: 12
Re: If a and b are positive integers less than 10, what is the mode of the  [#permalink]

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SRK780 wrote:
chetan2u wrote:
Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION:

{a, b, 1, 2}
If a and b are positive integers less than 10, what is the mode of the list above?

(1) The number of different permutations of the numbers in the list is 12.
(2) A four-digit number 21ab is divisible by 9

Mode means the integer repeated max time

(1) The number of different permutations of the numbers in the list is 12.
All four cannot be different, otherwise permutations would be 4!=4*3*2=24
Since there are 12 permutations, and 12=24/2=4!/2=4!/2!
So there is one pair same and other two distinct..
But mode could be any 1, or 2 or a variable
Insufficient

(2) A four-digit number 21ab is divisible by 9
Since divisibility depends on sum of the number, so a+b+2+1=3+a+b is div by 9
Since a be B are interchangeable, we cannot find the value of variable
Number could 2115,2151,2124,2142,2133,2169,2196,2178,2187
So insufficient

Combined
One pair and other two distinct, so possibilities 2115,2124,2133
So mode can be 1,2 or 3
Insufficient

E

Please correct me if I'm wrong

Number of permutations of 4 different terms is 4! which is 24
If 2 are different and 2 similar then number of permutations is 4!/2! which is 12

Statement A says - number of permutations is 12 => 2 elements are similar and 2 are unique => Mode 2 => A is sufficient

Finding the Mode means finding the value that is most repeated. Not, how many times the value is repeated.

For e.g. in a sample set of ( 1, 1, 1, 2, 3, 3), the mode is 1. not 3. Hope it helps. Re: If a and b are positive integers less than 10, what is the mode of the   [#permalink] 05 Jan 2019, 02:49
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