Problem Solving

The "length of the integer" refers to the number of prime factors, not necessarily distinct, that x has(If x=60, the length of x would be 4 because 60=2*2*3*5). what is the greatest possible length of integer z if z<1080?

A.13
B.10
C. 9
D. 7
E. 6

I think, 1024 which is < 1080 will have maximum length.

1024 = 2.2.2....10times..

so the maxium length would be 10.

so my answer is B

That answer is correct. To expand a bit on the reasoning:

Your goal is to get the maximum length subject to the constraint z < 1080. To do this, use the smallest possible prime number (2) to build up the length. Multiply 2 by itself until the product is as close to 1080 as possible without going over. Since 2^10 = 1024, 10 is correct.

IMO B


2^10=1024

srini1988 wrote:The "length of the integer" refers to the number of prime factors, not necessarily distinct, that x has(If x=60, the length of x would be 4 because 60=2*2*3*5). what is the greatest possible length of integer z if z<1080?

A.13
B.10
C. 9
D. 7
E. 6

Here we see that we have to find the greatest possible length if the integer z. So to increase the number we should first try to use smallest number possible prime number.
so lets start with (2)^10 = 1024 < 1080.
If we try any other combination like 3, 5 in it we will get smaller length.

Hence Correct Ans is B