BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members

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

by Vincen » Thu Jan 14, 2021 12:16 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 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 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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Legendary Member
Posts: 2499
Joined: Sun Oct 29, 2017 2:04 pm
Followed 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
Top
Post new topic Post Reply
• Page 1 of 1