When integer n is divided by 15, the remainder is 5

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

When integer n is divided by 15, the remainder is 5

by Vincen » Mon Jan 29, 2018 3:03 am

When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?

I. 3n
II. 5n
III. 4n + 10

A. I Only
B. II Only
C. III Only
D. I & II Only
E. I, II & III

The OA is the option B.

What is the formula that I should use here to solve this DS question? Experts, I would appreciate your help here? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Mon Jan 29, 2018 3:03 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Mon Jan 29, 2018 6:58 am

Vincen wrote:When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?

I. 3n
II. 5n
III. 4n + 10

A. I Only
B. II Only
C. III Only
D. I & II Only
E. I, II & III

Many integer properties questions can be solved by testing values

When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

When integer n is divided by 15, the remainder is 5.
So, some possible values of n are: 5, 20, 35, 50, 65, ....

Which of the following has a remainder of 10 when divided by 15 ?
Let's test a possible value of n.

Try n = 5
I. 3n = 3(5) = 15. When we divide 15 by 15, we get remainder 0. So, statement I does NOT satisfy the requirement.
ELIMINATE answer choices A, D and E

II. 5n = 5(5) = 25. When we divide 25 by 15, we get remainder 10. So, statement II DOES satisfy the requirement.

III. 4n + 10 = 4(5) + 10 = 30. When we divide 30 by 15, we get remainder 0. So, statement III does NOT satisfy the requirement.
ELIMINATE answer choice C

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Jan 30, 2018 10:36 am

Vincen wrote:When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?

I. 3n
II. 5n
III. 4n + 10

A. I Only
B. II Only
C. III Only
D. I & II Only
E. I, II & III

We can create the equation in which Q = quotient:

n = 15Q + 5

Let's now analyze each Roman Numeral:

I. 3n

3n = 45Q + 15

(45Q + 15)/15 = 3Q + 1

We see that 3n is evenly divisible by 15, so the remainder is 0.

II. 5n

5n = 45Q + 25

(45Q + 25)/15 = (45Q + 15)/15 + 10/15 + 3Q + 1 + 10/15

We see that the remainder is 10, so II is true.

III. 4n + 10

4n + 10 = 60Q + 20 + 10 = 60Q + 30

(60Q + 30)/15 = 4Q + 2

We see that 4n + 10 is evenly divisible by 15, so the remainder is zero.

Answer: B

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