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by g.shankaran » Sun Jun 12, 2011 2:16 am
for any +ve integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75 = 3 X 5 X 5. how many two-digit integers have length 6?

1. none
2. 1
3. 2
4. 3
5. 4
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by Calvin123 » Sun Jun 12, 2011 2:55 am
g.shankaran wrote:for any +ve integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75 = 3 X 5 X 5. how many two-digit integers have length 6?

1. none
2. 1
3. 2
4. 3
5. 4
IMO 2. 1

because 2^6=64 if you try to replace any 2 from 3 it will be
2*2*2*2*2*3=106 which is 3 digit no.
so for 2 digit no it will be 64 only, which has 6 length.
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by vinayreguri » Sun Jun 12, 2011 3:01 am
Ans 2. 2 numbers in total.

2*2*2*2*2*2=64
2*2*2*2*2*3=96

I see these questions in MGMAT forums also.
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by Calvin123 » Sun Jun 12, 2011 3:59 am
vinayreguri wrote:Ans 2. 2 numbers in total.

2*2*2*2*2*2=64
2*2*2*2*2*3=96

I see these questions in MGMAT forums also.


My bad.. ans must be 2, i did silly calculation mistake :)
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by Geva@EconomistGMAT » Sun Jun 12, 2011 4:36 am
Calvin123 wrote:
vinayreguri wrote:Ans 2. 2 numbers in total.

2*2*2*2*2*2=64
2*2*2*2*2*3=96

I see these questions in MGMAT forums also.


My bad.. ans must be 2, i did silly calculation mistake :)
Slow down, score more. It's always good to spend an extra 10 seconds taking another look at your logical path before committing to an answer - try to pick up on hidden assumptions that you're making (such as that fact that the prime factors don't need to all be the same, in the case above).
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