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
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