Operations on Rational Numbers

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Jeevanantham: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sun Apr 08, 2012 12:44 am; Thanked: 1 times

Operations on Rational Numbers

by Jeevanantham » Sun May 27, 2012 3:28 am

If s and t are positive numbers 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.

Source : OG . Please explain the way to solve this problem. What is the key point in this problem to start up solving it.

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Source: Beat The GMAT — Problem Solving | Sun May 27, 2012 3:28 am

aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 am; Location: Pune, India; Thanked: 186 times; Followed by:29 members

by aneesh.kg » Sun May 27, 2012 3:40 am

Jeevanantham wrote:If s and t are positive numbers 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.

Source : OG . Please explain the way to solve this problem. What is the key point in this problem to start up solving it.

Let's discuss a few concepts first.

Any number N can be represented by:
N = Divisor*Quotient + Remainder
Dividing LHS and RHS by Divisor,
(N/Divisor) = Quotient + (Remainder/Divisor)
(N/Divisor) = Integral Part + Decimal Part
Any number when divided by another number leaves an Integral Part and a Decimal Part. The Integral Part = Quotient whereas the Decimal Part = (Remainder)/(Divisor)

Lets return to this problem.
Decimal Part = 0.12 = (Remainder)/t
Remainder = 0.12t = 3t/25
The Remainder has to be a multiple of 3 (and 't' has to be a multiple of 25).

Among the options given, there is just one option that is a multiple of 3.
[spoiler](E)[/spoiler] is correct.

Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
Facebook Page: https://www.facebook.com/GMATPad

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Jeevanantham: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sun Apr 08, 2012 12:44 am; Thanked: 1 times

by Jeevanantham » Sun May 27, 2012 3:55 am

Thanks for your reply.

But How come 0.12t = 3t/25 ? I did not get this point alone.

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aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 am; Location: Pune, India; Thanked: 186 times; Followed by:29 members