EricKryk wrote:If S is the infinite sequence 9, 99, 999, ..., 10^k-1, is every term in S divisible by prime number p?
1) p is greater than 2
2) At least one term in sequence S is divisible by p
This is a great candidate for rephrasing the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Target question: Is every term in S divisible by prime number p?
Given: S is the infinite sequence 9, 99, 999, ..., 10^k-1
IMPORTANT: Let's examine a few terms in this sequence.
9 = (3)(3)
99 = (3)(3)(11)
999 = (3)(3)(3)(37)
Notice that 3 is the only prime number that divides into the first 3 terms, and the question is looking for a prime number that divides into ALL of the terms in an INFINITE sequence.
Since 3 is the only such prime number that will divide into all of the terms, we can rephrase the target question...
REPHRASED target question: Does p = 3?
Statement 1: p is greater than 2
This doesn't really narrow things down too much.
There are several values of p that satisfy this condition. Here are two:
Case a: p = 3, in which case
p DOES equal 3
Case b: p = 5, in which case
p does NOT equal 3
Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: At least one term in sequence S is divisible by p
This doesn't help us much either.
In fact, there are several values of p that satisfy this condition. Here are two:
Case a: p = 3, in which case
p DOES equal 3
Case b: p = 11, in which case
p does NOT equal 3
Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
There are still several values of p that satisfy BOTH statements. Here are two:
Case a: p = 3, in which case
p DOES equal 3
Case b: p = 11, in which case
p does NOT equal 3
Since we cannot answer the
REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT
Answer =
E
Cheers,
Brent
