Bunuel wrote:
Is the positive integer y a prime number?
(1) 80 < y < 95
(2) y = 3x + 1, where x is a positive integer
Target question: Is y a prime number? Given: y is a positive integer Statement 1: 80 < y < 95 This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of y that satisfy statement 1. Here are two:
Case a: y = 81, in which case
y is NOT primeCase b: y = 83, in which case
y IS primeSince 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: http://www.gmatprepnow.com/articles/dat ... lug-values Statement 2: y = 3x + 1, where x is a positive integer There are several values of y that satisfy statement 2. Here are two:
Case a: y = (3)(1) + 1 = 4, in which case
y is NOT primeCase b: y = (3)(2) + 1 = 7, in which case
y IS primeSince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Let's list ALL possible values of y.
y = (3)(27) + 1 = 82 (
82 is NOT prime)
y = (3)(28) + 1 = 85 (
85 is NOT prime)
y = (3)(29) + 1 = 88 (
88 is NOT prime)
y = (3)(30) + 1 = 91 (
91 is NOT prime)(91 = 13 times 7)
y = (3)(31) + 1 = 94 (
94 is NOT prime)
So, we can conclude that
y is NOT primeSince we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
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