x is an even integer between 20 and 80, is the units' digit of x equal to 2?
x=Even, has to end with 2,4,6,8
(1) The tens' digit and units' digit both are prime number. => xy
=>x and y are single digit Prime Numbers = 2,3,5,7
Possible combinations are 22,32,52,72
as it has to be even and each digit has to be prime
Sufficient, as all possible combination ends with a 2
(2) The sum of two digits is a prime number.
32=> 3+2=5 -> Yes
34=> 3+4=7 -> Not
Not sufficient, two possibilities
Answer
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x=Even, has to end with 2,4,6,8
(1) The tens' digit and units' digit both are prime number. => xy
=>x and y are single digit Prime Numbers = 2,3,5,7
Possible combinations are 22,32,52,72
as it has to be even and each digit has to be prime
Sufficient, as all possible combination ends with a 2
(2) The sum of two digits is a prime number.
32=> 3+2=5 -> Yes
34=> 3+4=7 -> Not
Not sufficient, two possibilities
Answer
...
