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# if a and b denote two prime numbers, is the product ab <10?

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Senior Manager
Joined: 17 Oct 2016
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if a and b denote two prime numbers, is the product ab <10?  [#permalink]

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08 Mar 2019, 21:53
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15% (low)

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84% (01:11) correct 16% (01:18) wrong based on 38 sessions

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If a and b denote two prime numbers, is the product ab <10?

A. a is the smallest prime number

B. b < 8 and b > a

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Chasing the dragon
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Joined: 19 Jan 2019
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if a and b denote two prime numbers, is the product ab <10?  [#permalink]

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08 Mar 2019, 23:20
Statement 1 - a is the smallest prime number.. a= 2... Nothing about b.. if b = 3
ab<10, if b= 7 , ab> 10
Not sufficient.

Statement 2 - b<8 and b>a
Same as statement 1, not sufficient...

Combining both statements won't help.. a= 2, and b > 2, if b= 3 answer is yes, if b= 13 , the answer is no... Therefore E is the right choice.

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Re: if a and b denote two prime numbers, is the product ab <10?  [#permalink]

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09 Mar 2019, 10:38
Top Contributor
fitzpratik wrote:
If a and b denote two prime numbers, is the product ab <10?

A. a is the smallest prime number

B. b < 8 and b > a

Given: a and b denote two prime numbers

Target question: Is the product ab <10?

Statement 1: a is the smallest prime number
Statement 1 is NOT SUFFICIENT

Statement 2: b < 8 and b > a
There are several values of a and b that satisfy statement 2. Here are two:
Case a: a = 2 and b = 3. In this case, ab = (2)(3) = 6. So, the answer to the target question is YES, ab IS less than 10
Case b: a = 2 and b = 7. In this case, ab = (2)(7) = 14. So, the answer to the target question is NO, ab is NOT less than 10
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: When testing possible cases, always check to see whether you can re-use possible cases from previous statements.
In this case, we can see that the two cases I tested for Statement 1 can be re-used for the statements COMBINED.
Case a: a = 2 and b = 3. In this case, ab = (2)(3) = 6. So, the answer to the target question is YES, ab IS less than 10
Case b: a = 2 and b = 7. In this case, ab = (2)(7) = 14. So, the answer to the target question is NO, ab is NOT less than 10
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
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Re: if a and b denote two prime numbers, is the product ab <10?   [#permalink] 09 Mar 2019, 10:38
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