must be true?

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Apr 08, 2011 1:34 am

When the integer n is divided by 2, the quotient is u and the remainder is 1. When the integer n is divided by 5, the quotient is v and the remainder is 3. Which one of the following must be true?
(A) 2u + 5v = 4
(B) 2u - 5v = 2
(C) 4u + 5v = 2
(D) 4u - 5v = 2
(E) 3u - 5v = 2

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Source: Beat The GMAT — Problem Solving | Fri Apr 08, 2011 1:34 am

HSPA: Legendary Member; Posts: 1101; Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members; Thanked: 47 times; GMAT Score:640

by HSPA » Fri Apr 08, 2011 1:52 am

2u+1 = 5v+3 = n

First take: 640 (50M, 27V) - RC needs 300% improvement
Second take: coming soon..
Regards,
HSPA.

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Apr 08, 2011 4:03 am

sanju09 wrote:When the integer n is divided by 2, the quotient is u and the remainder is 1. When the integer n is divided by 5, the quotient is v and the remainder is 3. Which one of the following must be true?
(A) 2u + 5v = 4
(B) 2u - 5v = 2
(C) 4u + 5v = 2
(D) 4u - 5v = 2
(E) 3u - 5v = 2

To solve this question, we must know how to "Rebuild the Dividend"
The property goes like this: If A divided by B is C with remainder D, then BC + D = A
Example: Since 17 divided by 5 is 3 with remainder 2, then (5)(3)+2 = 17

We can apply this to the question:

When n is divided by 2, the quotient is u and the remainder is 1 --> 2u + 1 = n
When the integer n is divided by 5, the quotient is v and the remainder is 3 --> 5v + 3 = n

We now have two equations set equal to n, so we can conclude that 2u+1 = 5v+3

When we rearrange the terms, we get 2u-5v=2 (B)

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