If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d?
1) 10^d is a factor of f
2) d > 6
[spoiler]Answer: C[/spoiler]
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Factor Problem
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neoshichhadva
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cans
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f=30!
A) 10^d is factor of 30!
d=1, true, d=2, true. Insufficient
B) d>6 d=7,8,... insufficient
A&B) 30! = (10)^7 * n where n is not multiple of 10.
d>6.
d=7, 10^7 is factor of 30!
10^8 is not....
Sufficient
d=7
IMO C
A) 10^d is factor of 30!
d=1, true, d=2, true. Insufficient
B) d>6 d=7,8,... insufficient
A&B) 30! = (10)^7 * n where n is not multiple of 10.
d>6.
d=7, 10^7 is factor of 30!
10^8 is not....
Sufficient
d=7
IMO C
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sl750
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f = 30!
Statement 1
30!/10^d = Integer. d=1,2,3,4,5,6. Insufficient
Statement 2. d>6 Insufficient
1+2
d>6
Look at the factors of 5 in 30! 5, 10,15,20,25,30. There are a total of 7 5's in 30!. There are sufficient 2's as well to ensure that we obtain an integer
Therefore in order for 30!/(2^d)(5^d) to be an integer. d=7 Sufficient
Statement 1
30!/10^d = Integer. d=1,2,3,4,5,6. Insufficient
Statement 2. d>6 Insufficient
1+2
d>6
Look at the factors of 5 in 30! 5, 10,15,20,25,30. There are a total of 7 5's in 30!. There are sufficient 2's as well to ensure that we obtain an integer
Therefore in order for 30!/(2^d)(5^d) to be an integer. d=7 Sufficient
