The function g is defined as follows. For any 3 digit integer (written xyz),
. If c and k are 3 digit integers, and , what is the value of c - k?
A. 400
B. 320
C. k/16c
D. 40
E. Cannot be determined
As an example, consider 325. .
We are given that f(c) = 16f(k). Let c be the integer lmn, and k be the integer pqr.
[spoiler]
That is, since 16 is a power of 2 (and not divisible by 3 or 5), the only difference between the 2 numbers must be in the first digit, the hundreds digit.
Since the tens' and ones' digits are the same, when we subtract, they will cancel out. (e.g. 353 - 153 = 200). l = p+4, so c must be four hundred greater than k.
Algebraically:
100l + 10m + k - (100p + 10q + r) = ? (We determined that m = q, and k = r, so those cancel.)
100l - 100p = ?
Substitute l = p + 4
100(p + 4) - 100p = 100p + 400 - 100p = 400.[/spoiler]
Cannot be determined.
. If c and k are 3 digit integers, and , what is the value of c - k?
A. 400
B. 320
C. k/16c
D. 40
E. Cannot be determined
As an example, consider 325. .
We are given that f(c) = 16f(k). Let c be the integer lmn, and k be the integer pqr.
[spoiler]
That is, since 16 is a power of 2 (and not divisible by 3 or 5), the only difference between the 2 numbers must be in the first digit, the hundreds digit.
Since the tens' and ones' digits are the same, when we subtract, they will cancel out. (e.g. 353 - 153 = 200). l = p+4, so c must be four hundred greater than k.
Algebraically:
100l + 10m + k - (100p + 10q + r) = ? (We determined that m = q, and k = r, so those cancel.)
100l - 100p = ?
Substitute l = p + 4
100(p + 4) - 100p = 100p + 400 - 100p = 400.[/spoiler]
Cannot be determined.
