LogicGuru1
Bunuel
If S is a series of numbers of the form X, XX, XXX, XXXX, XXXXX, …, where X is a non-zero digit, is every number in this series a multiple of the same prime number P?
(1) P is an odd number such that P < X
(2) X is a multiple of P
If S is a series of numbers of the form X, XX, XXX, XXXX, XXXXX, …, where X is a non-zero digit, is every number in this series a multiple of the same prime number P?
(1) P is an odd number such that P < X
Since X is a one digit number it can take any value from 1-9
P is prime and P is odd and since P is less than one digit number X, we know that our prime is an odd prime less than the highest one digit number 9
therefore P=3,5,7
So many possible cases
P can be 3 but the elements in the set can be {4,44,444,444} NOT a multiple of P(3)
P can be 5 and the element in the set can be {5,55,555,,,} YES it is a Multiple of P(5)
Insufficient
Note that P < X.
So P = 5 and X = 5 is not valid. But P = 3 and X = 6 is a valid example for YES.
(2) X is a multiple of P
P is a prime, so our our range of primes is single digit prime=> 2,3,5,7 (because the lowest element X in the set is single digit)
The set can look like
When P= 2 then S={2,22,222,2222...}
When P= 3 then S= {3,33,333,3333,33333,..}
When P= 5 then S={5,55,555,5555,...} or
When P= 7 then S={7,77,777.....}
NOTICE HOW THE CONDITION STATED IN THE FIRST STATEMENT THAT P<X BECOMES REDUNTANT ; BECAUSE EVEN IF WE REMOVE THE FIRST ELEMENT (SINCE IN CASE OF FIRST ELEMENT P=X) , STILL THE REST OF THE ELEMENT OF THE SET WILL BE MULTIPLES OF P
Sufficient
All element {X,XX,XXX...} in the set {S} are multiple of the prime {P}
ANSWER IS B[/quote]
Note that P < X (the digit) in statement 1. It means that if P = 2, X = 4 or 6 or 8. It means X cannot be 2. The comparison is not between P and the first number. It is between P and the digit X.
According to statement 2:
If P = 2, we have {2, 22, 222, 2222 ...} or {4, 44, 444, 4444...} or {6, 66, 666...}
etc
If P = 3, we have {3, 33, 333...} or {6, 66, 666...} etc