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 Post subject: GMAT Number Theory
PostPosted: Wed Apr 10, 2013 12:57 am 
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Let p be the product of the positive integers between 1 and 7, inclusive. How many distinct prime factors does p have?
A. 1
B. 2
C. 3
D. 4
E. 5

(D) is the correct answer. The first step is to determine which product we are actually concerned with. The positive integers between 1 and 7 inclusive are 7, 6, 5, 4, 3, 2, 1. We don't have to multiply them out just yet. We can break them up in to their prime components:
7 × 6 × 5 × 4 × 3 × 2 × 1 = 7 × (2 × 3) × 5 × (2 × 2) × 3 × 2 × 1.
Notice that the only prime factors that appear are 2, 3, 5 and 7 (remember that 1 is not a prime number).

-------------
Why do we not count 1 as a prime number?


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 Post subject: Re: GMAT Number Theory
PostPosted: Wed Apr 10, 2013 12:58 am 
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Number 1 is not prime by definition.

A prime number is a positive integer that is divisible only by itself and 1, number 1 itself is not a prime number.


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 Post subject: Re: GMAT Number Theory
PostPosted: Wed Apr 10, 2013 12:58 am 
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When the question stated 'between 1 and 7', I assumed that meant the numbers between 1 and 7, not inclusive. When the question is stated like so, should I always assume that this would include 1 and 7 on the GMATs?


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 Post subject: Re: GMAT Number Theory
PostPosted: Wed Apr 10, 2013 12:59 am 
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First of all, note, that this question has the word "inclusive" in it.

Secondly, if the phrase was "between 1 and 7" it would mean "between 1 and 7, NOT inclusive".

So if the phrase is "between 1 and 7", then 1 < x < 7.
If the phrase is "between 1 and 7, inclusive", then 1 ≤ x ≤ 7.


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