sanju09 wrote:If x is an integer such that 9 < x < 100, is x prime?
(1) Both the tens digit and the units digit of x are prime.
(2) x + 6 is prime.
Statement 1: Both the tens digit and the units digit of x are prime.
Prime digits are 2, 3, 5, and 7.
If x=23, then x is prime.
If x=25, then x is not prime.
INSUFFICIENT.
Statement 2: x + 6 is prime
Before testing NEW values, try to RECYCLE the values used to satisfy statement 1.
If x=23, then x+6=29, satisfying statement 2.
In this case, x is prime.
If x=25, then x+6=31, satisfying statement 2.
In this case, x is not prime.
INSUFFICIENT.
Statements combined:
Both statements are satisfied by x=23 (which is prime) and by x=25 (which is not prime).
INSUFFICIENT.
The correct answer is
E.
In the solution above, the values used to satisfy statement 1 happen also to satisfy statement 2.
If statement 1 had not provided these values, here would be an efficient way to find them when we evaluate statement 2.
Make a list of possible values for x+6:
x + 6 = 17, 23, 29, 31...
Then subtract 6 to get a list of possible values for x:
x = 11, 17, 23, 25...
Since the resulting list includes x=23 (which is prime) and x=25 (which is not prime), statement 2 is INSUFFICIENT.
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