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Approach

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Approach

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How to approach such questions?
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Quote:
For any positive integer n the length is defined as the number of prime numbers whose product equals n. So for 75 the length is 3 since 75 = 3 * 5 * 5. How many 2-digit numbers have a length of 6?

a) None
b) One
c) Two
d) Three
e) Four
Start with smallest possible prime factors:
2*2*2*2*2*2 = 64.
2*2*2*2*2*3 = 96.
Since the product must be less than 100, only the two numbers above are possible. If we increase any of the factors, the product will be greater than 100.

The correct answer is C.

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Hi eitijan,

When deciding how to approach a GMAT question, it's important to take advantage of ALL of the information presented. Here, you'll notice that the answer choices are SMALL, meaning that there can only be 0 to 4 possible numbers that fit the description given in the prompt. We're told to multiply 6 prime numbers together and get a total that is only 2 digits (less than 100). There just can't be that many ways for that to happen (and we know there's not, from the answer choices). From here, rather than trying to randomly find numbers that fit, we have to work in reverse and think about what multiplying primes together would get us. The other explanations show you the specific numbers, so I won't rehash that here.

The take-away from this prompt is that you should keep your thinking flexible. Be ready to come up with ways to deal with the problem that aren't what you learned in "math class." That way of thinking is essential to scoring at a high level on the GMAT.

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Rich

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eitijan wrote:
How to approach such questions?
Hmmm... This is an example of a "strange operator" question, as they call them on the GMAT Prep Now video series. I can't think of any way to approach this other than to test all possibilities, starting with the smallest. This is a question that at first glance looks challenging, but is really fairly easy.

The smallest possible product of six prime factors is 2^6, which is 64. This is a two-digit number.

The next smallest is (2^5)(3), which is 96. This is a two-digit number.

The next smallest is (2^4)(3^2), which is 144. This is a three-digit number. Since no other product of six prime factors can possibly be less than this value, we can stop testing here.

The answer is C.

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I'd say test the cases. The answers imply that there aren't very many, so we'd start from the smallest (2⁶), then work our way up: 2⁵ * 3, 2⁴ * 3², ...

Luckily for us, not even 2⁴ * 3² works, so we're done pretty quickly.

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