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Can you help with this problem? Thanks!

This topic has 2 expert replies and 2 member replies
yumi2012 Senior | Next Rank: 100 Posts
Joined
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64 messages
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Can you help with this problem? Thanks!

Post Tue Sep 03, 2013 7:07 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

Diagnostic Test
Question: 13
Page: 22
Difficulty: 650

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ganeshrkamath Master | Next Rank: 500 Posts
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Post Tue Sep 03, 2013 8:03 pm
yumi2012 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

Diagnostic Test
Question: 13
Page: 22
Difficulty: 650
s/t = 64.12
s = 64t + 0.12t
0.12t = 3*4/100 * t
= 3/25 * t

For 0.12t to be an integer, t should be 25,50,75,100,...
So 0.12t = 3,6,9,12,....
So the remainder 0.12t is always a multiple of 3.

Choose E

Cheers

_________________
Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attempt-750-in-2-months-t268332.html#688494

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GMAT/MBA Expert

Post Tue Sep 03, 2013 8:42 pm
Quote:
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
When one positive integer is divided by another, we typically represent what's left over either as a REMAINDER or as a DECIMAL.
There is a relationship between the two representations:

Remainder/Divisor = Decimal.

When 5 is divided by 2:
Remainder representation: 5/2 = 2 R1.
Decimal representations: 5/2 = 2.5.
Remainder/Divisor = 1/2.
Decimal = .5.
Since the two values are equal:
Remainder/divisor = decimal.

We should write the decimal representation AS A FRACTION IN ITS MOST REDUCED FORM.

In the problem above:
Remainder = R
Divisor = t
Decimal = .12 = 12/100 = 3/25.
Plugging these values into remainder/divisor = decimal, we get:
R/t = 3/25.

Since R/t is in its most reduced form, we know that t must be a multiple of 25 and that R must be a multiple of 3.
Only answer choice E is a multiple of 3.

The correct answer is E.

Similar problems:
http://www.beatthegmat.com/quotient-remainder-problem-t101371.html
http://www.beatthegmat.com/remainder-t176105.html

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Java_85 Master | Next Rank: 500 Posts
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Post Tue Sep 03, 2013 8:50 pm
Nice question!

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Post Mon Mar 19, 2018 3:39 pm
yumi2012 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
This problem will be best solved using the remainder formula. Let’s first state the remainder formula:

When positive integer x is divided by positive integer y, if integer Q is the quotient and r is the remainder, then x/y = Q + r/y.

In this problem we are given the following:

s/t = 64.12

We can simplify this to read as the remainder formula:

s/t = 64 + 0.12

s/t = 64 + 0.12

s/t = 64 + 12/100

s/t = 64 + 3/25

Because Q is always an integer, we see that Q must be 64, and thus the remainder r/y must be 3/25. We can now equate r/y to 3/25 and determine a possible value for r.

r/y = 3/25

Note that some equivalent values for r/y could be 6/50 or 9/75 or 12/100, and so forth. Note that in all cases, the value of r is a multiple of 3.

Of the answer choices, the only multiple of 3 is 45, so that is a possible value of r.

Answer: E

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