Is ab a prime number? (1) a is a prime number. (2) b is not

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

Is ab a prime number? (1) a is a prime number. (2) b is not

by GMATinsight » Thu Oct 08, 2015 1:59 am

Is ab a prime number?

(1) a is a prime number.
(2) b is not a prime number.

Answer: option E

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Source: Beat The GMAT — Data Sufficiency | Thu Oct 08, 2015 1:59 am

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

by GMATinsight » Thu Oct 08, 2015 2:00 am

GMATinsight wrote:Is ab a prime number?

(1) a is a prime number.
(2) b is not a prime number.

Answer: option E

Question : Is ab a prime number?

Statement 1: a is a prime number.
if b is 1 then ab will be a prime number. But
If b is not equal to 1 then ab will not be a Prime Number. Hence,
NOT SUFFICIENT

Statement 2: b is not a prime number.
if b is 1 and a is prime then ab will be a prime number. But
If b is equal to 4 and a is any Integer then ab will not be a Prime Number. Hence,
NOT SUFFICIENT

Combining the two statements
Case 1: a = 2, b=1, ab=2 i.e. PRIME NUMBER
Case 2: a = 2, b=4, ab=8 i.e. NOT A PRIME NUMBER. Hence,
NOT SUFFICIENT

Answer: option E

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Thu Oct 08, 2015 6:37 am

GMATinsight wrote:Is ab a prime number?

(1) a is a prime number.
(2) b is not a prime number.

Target question: Is ab a prime number?

Statement 1: a is a prime number
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several scenarios that satisfy statement 1. Here are two:
Case a: a = 2 and b = 1 , in which case ab = 2, and 2 IS prime
Case b: a = 2 and b = 6 , in which case ab = 12, and 12 in NOT prime
Since 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: b is not a prime number
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several scenarios that satisfy statement 2. Here are two:
Case a: a = 2 and b = 1 , in which case ab = 2, and 2 IS prime
Case b: a = 2 and b = 6 , in which case ab = 12, and 12 in NOT prime
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are still several possible scenarios that meet both statements. Here are two:
Case a: a = 2 and b = 1 , in which case ab = 2, and 2 IS prime
Case b: a = 2 and b = 6 , in which case ab = 12, and 12 in NOT prime

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com