neha shekhawat 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
Let's examine a few things about remainders and decimal conversions.
7/4 = 1
3/4 = 1
.75. When we divide 7 by
4, the remainder is
3, and
.75 =
3/
4.
32/5 = 6
2/5 = 6
.4. When we divide 32 by
5, the remainder is
2, and
.4 =
2/
5.
58/20 = 2
18/20 = 2
.9. When we divide 58 by
20, the remainder is
18, and
.9 =
18/
20.
As you can see, there is an important relationship between the remainder and the decimal part of the conversion.
64
.12 = 64
12/100 = 6412/100. So, it's possible that s/t = 6412/100, in which case the remainder is
12 when s is divided by t.
Check the answer choices. . . nope, 12 is not one of the options.
Also, recognize that 64
.12 = 64
12/100 = 64
3/25 = 1603/25. So, it's possible that s/t = 1603/25, in which case the remainder is
3 when s is divided by t.
Check the answer choices. . . nope, 3 is not one of the options.
At this point, we should recognize that we can get
ANY MULTIPLE OF 3 as the remainder.
For example, 64
.12 = 64
12/100
= 64
3/25
= 64
6/50
= 3206/50 = s/t, in which case the remainder is
6 when s is divided by t.
Or...64
.12 = 64
12/100
= 64
3/25
= 64
9/75
= 4809/75 = s/t, in which case the remainder is
9 when s is divided by t.
And so on.
Since only one answer choice (
E) is
A MULTIPLE OF 3,
E must be the correct answer.
Aside: Here's further proof:
64
.12 = 64
12/100
= 64
3/25
= 64
45/375
= 24045/375 = s/t, in which case the remainder is
45 when s is divided by t.
Cheers,
Brent
