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GMATGuruNY
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Start with the smallest possible prime factors: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
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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Hi Apoorva@5,
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.
GMAT assassins aren't born, they're made,
Rich
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.
GMAT assassins aren't born, they're made,
Rich
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OptimusPrep
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For the length to be 6, the number of prime factors should be maximum. Hence we need to use maximum 2'sApoorva@5 wrote: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
The numbers can be 2^6 = 64 and 2^5*3 = 96
For any other number less than 100, the length will be less than 6
Correct option: C
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Matt@VeritasPrep
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Start with the smallest possibility:
2 * 2 * 2 * 2 * 2 * 2 = 64
Then find the next smallest, which would be replacing one 2 with a 3:
2 * 2 * 2 * 2 * 2 * 3 = 96
Then find the next smallest, which would two replacements:
2 * 2 * 2 * 2 * 3 * 3 = 144
This is too big, so we've found them all!
2 * 2 * 2 * 2 * 2 * 2 = 64
Then find the next smallest, which would be replacing one 2 with a 3:
2 * 2 * 2 * 2 * 2 * 3 = 96
Then find the next smallest, which would two replacements:
2 * 2 * 2 * 2 * 3 * 3 = 144
This is too big, so we've found them all!
