BTGmoderatorDC wrote:If √k is not an integer, then is k a prime number?


(1) k < 10

(2) k < 5

OA E

Source: Magoosh

Let's take each statement one by one.

(1) k < 10

Case 1: Say k = 8, not prime

We have √k = √8 = not an integer

Case 2: Say k = 7, prime

We have √k = √7 = not an integer

No unique answer. Insufficient.

(2) k < 5

Case 1: Say k = 4,5, not prime
(note that it is not given that k is an integer)

We have √k = √4.5 = not an integer

Case 2: Say k = 3, prime

We have √k = √3 = not an integer

No unique answer. Insufficient.

(1) and (2) together

Cases discussed in Statement 2 are applicable here too. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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BTGmoderatorDC wrote:If √k is not an integer, then is k a prime number?
(1) k < 10
(2) k < 5

Given: √k is not an integer

Target question: Is k a prime number?

Statement 1: k < 10
Let's TEST some values.
There are several values of k that satisfy statement 1. Here are two:
Case a: k = 1.3 (√1.3 is not an integer). In this case, the answer to the target question is NO, k is NOT a prime number
Case b: k = 3 (√3 is not an integer). In this case, the answer to the target question is YES, k IS a prime number
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: k < 5
Let's TEST some values.
There are several values of k that satisfy statement 2. Here are two:
Case a: k = 1.3 (√1.3 is not an integer). In this case, the answer to the target question is NO, k is NOT a prime number
Case b: k = 3 (√3 is not an integer). In this case, the answer to the target question is YES, k IS a prime number
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: k = 1.3 (√1.3 is not an integer). In this case, the answer to the target question is NO, k is NOT a prime number
Case b: k = 3 (√3 is not an integer). In this case, the answer to the target question is YES, k IS a prime number
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

Using both statements, k can be 2, and thus prime, or -1, and not prime, so the answer is E.