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by oquiella » Thu Dec 24, 2015 8:20 am
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: E

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by vinit2shah » Fri Dec 25, 2015 9:41 pm
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


Explanation :

A remainder is a non-negative integer.
For eg., 6/4 = 1.5 Or when 6 is divided by 4 the quotient is 1 and the remainder is 2
Dividend = Divisor * Quotient + Remainder.

6 = 4*1 + 2
Another way of putting this is 6 = 4*1 + 4*0.5
= 4(1 + 0.5).
What I mean is the quotient is the part before the decimal(for this eg, it is 1) and the remainder is part after the decimal times the divisor, i.e. 0.5 * 4

So in the given question, when s is divided by t, the quotient is 64 and the remainder is .12 * t.
And t, the divisor, is an integer too, as given in the question. Now using the options
1. .12t = 2, i.e., t = 2/.12 = not an integer
2. .12t = 4, i.e., t= 4/.12 = not an integer.
And so on, .12t = 45 , i.e. t = 45/.12 = an integer.
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by Brent@GMATPrepNow » Sat Dec 26, 2015 10:25 am
oquiella 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.


Answer: E

Cheers,
Brent
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by Brent@GMATPrepNow » Sat Dec 26, 2015 10:26 am
Here's a very similar question: https://www.beatthegmat.com/og-13-ps-95- ... 81925.html
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