Problem Solving

JDesai01 wrote:If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t?

(a) 2
(b) 4
(c) 8
(d) 20
(e) 45

Answer is E. The gmat explanation is not very practical. Please post advice on how best to solve. Thanks

Agreed- the explanation in the OG is pretty obscure.

When we divide s by t we can always write:

s/t = q + r/t

where q is the 'quotient', and r is the 'remainder', where 0 <= r < t (so 0 <= r/t < 1). That's essentially the definition of the remainder, so is quite important to understand- many remainder questions will be difficult to answer otherwise. If

s/t = 64.12 = 64 + 12/100

then 64 is the quotient, while the fractional part, 12/100, is equal to r/t (compare with the other equation above). This doesn't mean 12 is the remainder, however- that would only be true if t was equal to 100. Still, we can find what values r might take. Rewriting:

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

and if r and t are integers, the primes that divide the right side of this equation must also divide the left- in particular r must be divisible by 3. Only one answer choice is divisible by 3- E, or 45- so it's the only possible value of r among the answer choices.

There are many other possible values for r- any multiple of 3 would have been a possible answer, in fact.

ben2pop wrote:Please Ian can you evaluate the level of difficulty of that question , let say on a scale of 1 to 10 ??

because in my learning , I am always afraid to do only simple questions and not the kind of hard questions that will give me a good grade on the exam !
thx you

I just saw this now; it's definitely a high-level question, as you'd need a very good foundation in both remainders and divisibility to answer it. Someone scoring below 40 (scaled score) in Quant shouldn't bother with this question (yet); you won't see anything as abstract on test day.