If $s$ and $t$ are positive integers such that $\dfrac{s}{t} = 64.12,$ which of the following could be the remaind

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Thu Jan 14, 2021 12:16 pm

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If $s$ and $t$ are positive integers such that $\dfrac{s}{t} = 64.12,$ 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

Source: Official Guide

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Source: Beat The GMAT — Problem Solving | Thu Jan 14, 2021 12:16 pm

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8175; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If $s$ and $t$ are positive integers such that $\dfrac{s}{t} = 64.12,$ which of the following could be the rem

by Scott@TargetTestPrep » Wed Jan 20, 2021 2:47 pm

Vincen wrote: ↑
Thu Jan 14, 2021 12:16 pm
If $s$ and $t$ are positive integers such that $\dfrac{s}{t} = 64.12,$ 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

Source: Official Guide

Solution:

We see that s = 64.12t = 64t + 0.12t. Therefore, 0.12t = 12t/100 = 3t/25 must be the remainder. Since 3 is not a multiple of 25, t must be a multiple of 25 (so that 3t/25 will be an integer). In that case, t/25 is an integer, and 3t/25 = 3 * t/25 must be a multiple of 3. Because the only multiple of 3 in the given choices is 45, then 45 could be the remainder when s is divided by t.

Answer: E

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swerve: Legendary Member; Posts: 2560; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: If $s$ and $t$ are positive integers such that $\dfrac{s}{t} = 64.12,$ which of the following could be the rem

by swerve » Thu Jan 21, 2021 2:55 am

Vincen wrote: ↑
Thu Jan 14, 2021 12:16 pm
If $s$ and $t$ are positive integers such that $\dfrac{s}{t} = 64.12,$ 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

Source: Official Guide

Here, we have

$\dfrac{s}{t} = 64.12$
$s = t\cdot 64.12$
$s = 64t + t\cdot 0.12$

So, when $s$ is divided by $t$ then we will get $t\cdot 0.12$ as reminder (as $t\cdot 0.12$ will be less than $t$)

Now $t$ is an integer and $0.12$ is $12\cdot 0.01$ which means it is $3\cdot$something
So, only answer choices which are multiple of $3$ are contenders.

Therefore, E

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