Problem Solving

If s and t are positive integer such that s/t=64.12, which of the following could be the remainder when s is devided by t?

A-2
B-4
C-8
D-20
E-45

Please provide detail explanation.It's 11th OG problem but i m not happy with the explanation. need some alternate explanation.

Here is my explanation it is a big long winded but once the logic is clear it does not take a long time. I am a newbie GMAT preppie and have come across this problem in the OG guide.

The trick here and in most other problems is to construct equations to solve the problem.

1) s/t = 64.12 means that the remainder is Zero

2) Dividend = (Divisor*Numerator) + Remainder

3) Dividend = s; Divisor = t ; Numerator = 64 ( 0.12 is not taken as the numerator as remainder will be zero); Remainder = R

4) Using above formula - s=64t+R ( 1rst equation) and as in the question s = 64.12t (2nd equation)

5) Equating both the 's' equations

64t + R = 64.12t
R = 64.12t - 64t
R = 0.12t

t = R/0.12

6) The critical thing over here is that s & t are positive integars hence by slotting in all the values for R from the options given one of them should give a integar ( ie. it should be divisible by 0.12 without a remainder)

7) Hence we have five options

2/0.12; 4/0.12; 8/0.12; 20/0.12; 45/0.12

OR rewriting them

200/12; 400/12; 800/12; 2000/12; 4500/12

8) To find if the above numbers are divisible by 12 they should be divisible by 2&6(2*6 = 12)

Only 4500 is divisible by both 2 & 6 and hence 12.

So answer is E (45)

You can double check it by substituting the remainder 45 in the 2 equations. (No.4 in my explanation)
t = 375, s = 24045 which are positive integars

ash_maverick wrote:If s and t are positive integer such that s/t=64.12, which of the following could be the remainder when s is devided by t?

A-2
B-4
C-8
D-20
E-45

Please provide detail explanation.It's 11th OG problem but i m not happy with the explanation. need some alternate explanation.

Remember this rule: Every positive integer s divided by another positive integer t yields a quotient of q and a remainder of r, which is an integer from 0 to t-1.

For example, when 20 is divided by 7, the quotient is 2 and the remainder is 6. We often write 20/7=2 + 6/7

In general, s/t=q+r/t

Here s/t=64.12, so r/t=0.12, where r and t are both integers.

100r=12t => t=25r/3

Since t must be an integer, r must be a multiple of 3. Of the answer choices, only 45 fits the bill!

If s and t are positive integer such that s/t=64.12, which of the following could be the remainder when s is devided by t?

A-2
B-4
C-8
D-20
E-45

s /t = 64.12 = 6412/100 = 3206/50 = 1603/25. Here the remainder is 3. Thus any multiple of 3 can be the remainder.

Hope this helps!

Ok...i am just not getting the concept behind this problem. What is this question trying to test?

ash_maverick wrote:If s and t are positive integer such that s/t=64.12, which of the following could be the remainder when s is devided by t?

A-2
B-4
C-8
D-20
E-45

Please provide detail explanation.It's 11th OG problem but i m not happy with the explanation. need some alternate explanation.

let's rewrite info

s=64t+.12

the remainder is .12 which can be rewritten as 12/100 or 3/25. The question asks which answer choice could possibly be the remainder. well, the remainder has to retain the ratio 3/25. So the remainder could be 6/50 or 9/75, etc. It has to be a multiple of 3. The only choice thats a multiple of 3 is E.

You got this man!

By using a long division model, it can be seen that
the remainder after dividing s by t is s - 64t:
t) s
t
s t
−
−
64
64
64
Th en, the given equation can be written as 64.12t = s.
By splitting portions of t into its integer multiple
and its decimal multiple, this becomes
64t + 0.12t = s, or 0.12t = s - 64t, which is the
remainder. So, 0.12t = remainder. Test the answer
choices to find the situation in which t is an
integer.
A 0.12t = 2 or t = 16.67 NOT an integer
B 0.12t = 4 or t = 33.33 NOT an integer
C 0.12t = 8 or t = 66.67 NOT an integer
D 0.12t = 20 or t = 166.67 NOT an integer
E 0.12t = 45 or t = 375 INTEGER
Th e correct answer is E.

ash_maverick wrote:If s and t are positive integer such that s/t=64.12, which of the following could be the remainder when s is devided by t?

A-2
B-4
C-8
D-20
E-45

Please provide detail explanation.It's 11th OG problem but i m not happy with the explanation. need some alternate explanation.

Well I think if s/t = 64.12
--> s/t = 64.12 = 6412/100 = 1603/25 = Q + 3 (Q = quotient)
so 3 is the remainder here. Now try to find the factor 3 in the given options . we see that there is factor of 3 in 45 only . So 45 can be an ans.
Hence I would go with E