OG12, #107, pp.167

[BillGator97]

If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2^i 3^k 5^m 7^p then i + k + m + p =

(a) 4
(b) 7
(c) 8
(d) 11
(e) 12

Isn't the correct answer (a) 4?

The answer key says it's (d) 11.

k, m, and p all must be 1 for their respective bases to remain in the range 1-8.

i can be 0, 1, 2, or 3, but the only value when added to the other three that yields an answer choice is 1, which makes the four letters total 4.

[ajith]

If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2^i 3^k 5^m 7^p then i + k + m + p =

(a) 4
(b) 7
(c) 8
(d) 11
(e) 12

Isn't the correct answer (a) 4?

The answer key says it's (d) 11.

k, m, and p all must be 1 for their respective bases to remain in the range 1-8.

i can be 0, 1, 2, or 3, but the only value when added to the other three that yields an answer choice is 1, which makes the four letters total 4.

x=1*2*3*4*5*6*7*8

= 2*4*8*6*3*5*7
= 2*2^2*2^3*2*3*3*5*7
= 2^7*3^2*5*7

i = 7; k = 2; m =1; p=1

sum = 11

[BillGator97]

Ah, thank you!