EMPOWERgmatRichC wrote:
Z is a positive integer greater than 3. How many distinct prime factors does (Z + 1)(Z – 1) have?
1) Z is not even
2) Z is not a multiple of 5
Target question: How many distinct prime factors does (Z + 1)(Z – 1) have? Given: Z is a positive integer greater than 3 Statement 1: Z is not even This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of Z that satisfy statement 1. Here are two:
Case a: Z = 9, in which case (Z + 1)(Z - 1) = (10)(8) = 80 = (2)(2)(2)(2)(5).
In this case, we have TWO distinct prime factorsCase b: Z = 11, in which case (Z + 1)(Z - 1) = (12)(10) = 120 = (2)(2)(2)(3)(5).
In this case, we have THREE distinct prime factorsSince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values Statement 2: Z is not a multiple of 5 This statement doesn't FEEL sufficient either, so I'll TEST some values.
There are several values of Z that satisfy statement 2. Here are two:
Case a: Z = 9, in which case (Z + 1)(Z - 1) = (10)(8) = 80 = (2)(2)(2)(2)(5).
In this case, we have TWO distinct prime factorsCase b: Z = 11, in which case (Z + 1)(Z - 1) = (12)(10) = 120 = (2)(2)(2)(3)(5).
In this case, we have THREE distinct prime factorsSince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Notice that I used the same values of Z for the first 2 statements. This means that the same Z-values satisfy BOTH statements.
That is:
Case a: Z = 9, in which case (Z + 1)(Z - 1) = (10)(8) = 80 = (2)(2)(2)(2)(5).
In this case, we have TWO distinct prime factorsCase b: Z = 11, in which case (Z + 1)(Z - 1) = (12)(10) = 120 = (2)(2)(2)(3)(5).
In this case, we have THREE distinct prime factorsSince we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer = E
Cheers,
Brent