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 Post subject: GMAT Number Theory
PostPosted: Thu Sep 09, 2010 3:56 am 
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Joined: Sun May 30, 2010 3:15 am
Posts: 424
The prime factors of a number, n, can be listed. For example, the prime factors of 12 are 2, 2, 3, as 12 = 2 × 2 × 3. For which of the following integers is the mode, of the prime factors, 5?
A. 440
B. 512
C. 620
D. 740
E. 750

(E) To solve this question we will evaluate each number
(A) 440 = 2 × 2 × 2 × 5 × 11, the mode of the
prime factors, 2, 2, 2, 5, 11, is 2.
(B) Since 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2, the mode of the prime factors is 2.
(C) Since 620 = 2 × 2 × 5 × 31, the mode of the prime factors (2, 2, 5, 31) is 2.
(D) Since 740 = 2 × 2 × 5 × 37, the mode of the prime factors (2, 2, 5, 37) is 2.
(E) Since 750 = 2 × 3 × 5 × 5 × 5, the mode of the prime factors (2, 3, 5, 5, 5)
is 5.
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The key with this question is trying to decide which one to do first. 750 = 250 × 3. We know that any number which is 5 squared is what you should start with. The same would hold true if you had a question asking about the number of factors of 2. A square based on 2 such as 64 would have more than a number that had 2s and 3s.


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 Post subject: Re: math (test 5, question 37): number theory
PostPosted: Thu Sep 09, 2010 4:15 am 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
If you see that 750 is a good choice to start first - why not. If it doesn't turn out to be the right one - then you can pick up another one and evaluate it. And so on.

In order to pick such choice to start first you still need to do some calculations to evaluate which one to choose. It is up to:
- if you are good at fast evaluating - do so and pick the number to start with.
- picking at random or start from (A) to (E) will lead you to right answer in about the same time

Note, that if the question asked you about "what number has the most number of distinct prime multipliers" or something similar then you would need to do calculations for all the answer choices no matter what order you decide to go.


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