Number systems

IMO E

I dont know whether my method is a genuine one, This is the way I solved:
s/t = 64.12
we can write 6412/100 =3206/50 = 1603/25

So when 1603 divided by 25 we see remainder 3.

Now see the options there is only one option which is a multiple of 3. Thus the answer is E

narik11 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) 4
(b) 2
(c) 8
(d) 20
(e) 45

When one number doesn't divide evenly into another number, we can represent what's left over either as a decimal (5/2 = 2.5) or as a remainder (5/2 = 2 R 1). The problem above is testing the relationship between the decimal representation and the remainder representation. Here's the relationship:

decimal * divisor = remainder

Let's revisit 5/2 = 2.5. If we multiply the decimal (.5) by the divisor (2), we get .5 * 2 = 1, which is the remainder if we represent the division as 5/2 = 2 R1.

In the problem above the decimal is .12, the divisor is t, and the remainder is one of the answer choices. So .12t = answer choice. The problem stipulates that t must be an integer. Which answer choice will result in an integer value for t?

Only answer choice E works:
.12t = 45
t =45/.12 = 4500/12 = 375.

The correct answer is E.

GMATGuruNY wrote:

narik11 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) 4
(b) 2
(c) 8
(d) 20
(e) 45

When one number doesn't divide evenly into another number, we can represent what's left over either as a decimal (5/2 = 2.5) or as a remainder (5/2 = 2 R 1). The problem above is testing the relationship between the decimal representation and the remainder representation. Here's the relationship:

decimal * divisor = remainder

Let's revisit 5/2 = 2.5. If we multiply the decimal (.5) by the divisor (2), we get .5 * 2 = 1, which is the remainder if we represent the division as 5/2 = 2 R1.

In the problem above the decimal is .12, the divisor is t, and the remainder is one of the answer choices. So .12t = answer choice. The problem stipulates that t must be an integer. Which answer choice will result in an integer value for t?

Only answer choice E works:
.12t = 45
t =45/.12 = 4500/12 = 375.

The correct answer is E.

Thanks GMATGuruNY!! Now it is much clear, but the way I did is it acceptable or may fail sometimes?

shovan85 wrote:

GMATGuruNY wrote:

narik11 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) 4
(b) 2
(c) 8
(d) 20
(e) 45

When one number doesn't divide evenly into another number, we can represent what's left over either as a decimal (5/2 = 2.5) or as a remainder (5/2 = 2 R 1). The problem above is testing the relationship between the decimal representation and the remainder representation. Here's the relationship:

decimal * divisor = remainder

Let's revisit 5/2 = 2.5. If we multiply the decimal (.5) by the divisor (2), we get .5 * 2 = 1, which is the remainder if we represent the division as 5/2 = 2 R1.

In the problem above the decimal is .12, the divisor is t, and the remainder is one of the answer choices. So .12t = answer choice. The problem stipulates that t must be an integer. Which answer choice will result in an integer value for t?

Only answer choice E works:
.12t = 45
t =45/.12 = 4500/12 = 375.

The correct answer is E.

Thanks GMATGuruNY!! Now it is much clear, but the way I did is it acceptable or may fail sometimes?

My pleasure. Try your approach on the following question, which tests the same concept:

https://www.beatthegmat.com/remainder-ru ... tml#270804

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

0.12t = 45
t =45/.12 = 4500/12 = 375.

The correct answer is E.

imho, we can avoid time-consuming division by checking answer choices quickly.
since 12 has 3 and we need an integer as a result of division, we can see than only E has 3 in common. it is for a lazy one like me hehe