If √k is not an integer, then is k a prime number?
(1) k < 10
(2) k < 5
OA E
Source: Magoosh
If √k is not an integer, then is k a prime number?
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Let's take each statement one by one.BTGmoderatorDC wrote:If √k is not an integer, then is k a prime number?
(1) k < 10
(2) k < 5
OA E
Source: Magoosh
(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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Given: √k is not an integerBTGmoderatorDC wrote:If √k is not an integer, then is k a prime number?
(1) k < 10
(2) k < 5
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
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Using both statements, k can be 2, and thus prime, or -1, and not prime, so the answer is E.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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