Number Properties - Advanced

davo45 wrote:Q1
a and b are integers such that a/b =3.45. If R is the remainder of a/b, which of the following could NOT be equal to R?

a) 3 b)9 c)36 d)81 E)144


Thanks and regards

Charles

davo45 wrote:
Q2
When 15 is divided by y, the remainder is y - 3. If Y must be an integer, what are all the
possible values of y?

Understand the remainder,y, must be at least 3 and y at most can only be 18.

From this point you could pick numbers, dividing 15 by these numbers to check to see whether the
remainder is 3 lower than the number you have picked. Only 15 divided by 3,6,9, and 18 yield remainders
three less than the divisor:
15 = (5 x3) + 0
15 = (2 x 6) + 3
15 = (1 x 9) + 6
15 = (0 x 18) + 15

Remainder of 0 is 3 less than divisor of 3.
Remainder of 3 is 3 less than divisor of 6.
Remainder of 6 is 3 less than divisor of 9.
Remainder of 15 is 3 less than divisor of 18.


answer is 3,6,9,18. Still dont understand.

Please explain.

Thanks and regards

Charles

Q1
a and b are integers such that a/b =3.45. If R is the remainder of a/b, which of the following could NOT be equal to R?

a) 3 b)9 c)36 d)81 E)144

I understand how to derive the equation to 20 X R = 9 X b.

Step-by-step method for dealing with remainder questions when picking numbers or plugging in answers doesn't apply:

1) Rephrase as equation: remainder = decimal x divisor
R = .45b

2) Rephrase decimal using 10^-x
R = 45 x 10^-2b

3) Prime factor all terms
R = 3^2 x 5 x 2^-2 x 5^-2 x b

4) Combine terms
R = 2^-2 x 3^2 x 5^-2 x b

5) Rephrase as ratio/fraction:
R/b = 3^2/5 x 2^2

We now know that R must be a multiple of 9 (and that b must be multiple of 20).[/u]

aljaz11 wrote:15/y = i (i is integer) + (y-3)/y --> 15/y = i + 1 -3/y --> 15/y +3/y = i + 1 --> 18/y = i + 1;
y= 18/(i+1), y can be an integer if and only if 18 divided by (i+1) gives an integer; this is possible when i has the following values {0,1,2,5,8,17}. Total six values for i and six values for y {18,9,6,3,2,1}


can you please clarify me how did you come to (y-3)/y ? everything else from there is clear but in the question it says:: When 15 is divided by y, the remainder is y - 3. I just can not understand how did you come to (y-3)/y

aljaz11 wrote:hi, yes that was what i was asking you about

i must admit i still dont comprehend the (y-3)/y im trying hard

you gave an example:
15 is divided by 2 the remainder is 1 or 1/15.... i do understand that remainder of 1 is 1/15 of 15 (or 1part out of 15) but if we divide 15 by 2 we get 7 and the remainder is a whole number 1 (or 15/15...thats where i am confused with 1/15)

im just having trouble trying to cross this gap.... thanks for the help!!