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Math Expert V
Joined: 02 Sep 2009
Posts: 58453
Is ab a prime number?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 57% (01:02) correct 43% (00:59) wrong based on 324 sessions

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Is ab a prime number?

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

Kudos for a correct solution.

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Re: Is ab a prime number?  [#permalink]

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Bunuel wrote:
Is ab a prime number?

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

Kudos for a correct solution.

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

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Re: Is ab a prime number?  [#permalink]

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1
Bunuel wrote:
Is ab a prime number?

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

Kudos for a correct solution.

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: http://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

Cheers,
Brent
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Re: Is ab a prime number?  [#permalink]

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From Option A:
if b=1 then ab is a prime number else ab is not a prime number .Not sufficient
From Option B:
if b=1 and a is a prime number then ab is a prime number .For other values of a ,ab is not a prime number.
else if b=2,3,4... ab is not a prime number .Not sufficient.

Correct answer is E.
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Manish Khare
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Math Expert V
Joined: 02 Sep 2009
Posts: 58453
Re: Is ab a prime number?  [#permalink]

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Bunuel wrote:
Is ab a prime number?

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

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No. This question stem asks: “Is ab a prime number?”

Given information in the question stem or diagram: There is no important information given in the question stem.

Statement 1: a is a prime number. This statement is not sufficient but it is tricky. Using conceptual knowledge, many people will assume that the product ab could never be prime. When you multiply any prime number with another positive integer, it could never be prime unless that integer is 1. However, since b could be 1 or any fraction, this statement is not sufficient, and you can eliminate choices A and D. For instance, if a is 7 and b is 1 or 2 7 then the answer is “yes.” However if b is any positive integer other than 1, then the answer is “no.” Note: This question is about avoiding assumptions! Do not assume that b is a whole number, and don’t forget about the very important number 1.

Statement 2: b is not a prime number. If b is not prime then b could easily be a fraction or equal to 1. In either case it is very possible for ab to be a prime number and it is very easy to show that it might not be. Not sufficient. Eliminate answer B.

Together: Taken together you know that a is prime and b is not. But this leaves you in the same dilemma as with Statement 1 alone. Certainly a and b can multiply to equal a non-prime number such as “a = 2 and b = 6.” 12 is not a prime number. However, if b =1 then whatever prime number a equals will remain and ab will be that prime number. As in the first statement, the key in this problem is to avoid assumptions and remember that nothing limits b to an integer and nothing excludes the value of 1. Answer is E.
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Re: Is ab a prime number?  [#permalink]

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Statement 1. A is a prime number.
Case 1. If ‘b’ = 1; ab is a prime number.
Case 2. If ‘b’ not equal to 1; ab is not a prime number. Hence, Insufficient.
Statement 2. ‘b’ is not a prime number.
Case 1. Let b = 4(non-prime) and a = 1/2. Then, ab = 2 i.e. a prime number.
Case 2. Let b = 4(non-prime) and a = 1. Then ab = 4 i.e. a composite number.Hence, Insufficient.
Statement 1 & 2 together. ‘a’ is a prime and ‘b’ is a non- prime number.
Case 1. Let a = 2(Prime number) and b = 1 (non-prime number). Then, ab = 2 i.e. a prime number.
Case 2. Let a = 2(Prime number) and b = 4 (non- prime number). Then, ab= 8 i.e. non-prime number. Hence, Insufficient.
Hence, e is the answer. Re: Is ab a prime number?   [#permalink] 20 Dec 2018, 03:37
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