Equation

Expert replies

dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

by dtweah » Mon May 18, 2009 3:40 pm

. The equation 5x + 51y = 551 has two solution pairs where x and y are positive integers. One solution pair is (100,1). If (x,y) is the other solution pair then x + y equals
(a) 43
(b) 62
(c) 55
(d) 75
(e) 67

Like this post

Source: Beat The GMAT — Problem Solving | Mon May 18, 2009 3:40 pm

francopiccolo: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Dec 11, 2008 12:02 am; Thanked: 1 times

by francopiccolo » Mon May 18, 2009 4:58 pm

Working on the equation:

x = 551 - 51y

y must be such that 51y is 51 + a multiple of 5 so it is y = 1 + 5k

For k = 1 the solution is (49,6), thus the sum is 55.

Like this post

singhr10: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Fri Mar 28, 2008 3:57 pm

by singhr10 » Mon May 18, 2009 5:00 pm

Is OA = c
Well the answer is 55

55*6 = 306 and the remaining 245/5 = 49

So X+Y = 49+5 = 55

Like this post

dumb.doofus: Master | Next Rank: 500 Posts; Posts: 435; Joined: Sat Sep 27, 2008 2:02 pmFollowed by: 1 member; Location: San Jose, CA; Thanked: 43 times; GMAT Score:720

by dumb.doofus » Tue May 19, 2009 12:09 am

To write this in terms of x we get
x = (551 - 51y)/5

For x to be an integer.. 551-51y needs to be a multiple of 5.. for that to happen it should either end with a 0 or a 5..

For ending with a 0 51*y should yield a number ending with 1.. we already know that 1 satisfies it.. the next number would be 11.. but that gives a number greater than 551.. so can't take that..

So now we should check another number that when subtracted from 551 should yield a number ending with 5.. so that means, 51y should be a number ending with 6..
the closest we have is itself.. and so that gives us y =6 and x = 49

total = 55.

Notice that the next number after 6 would be 16 and that too will give a number greater than 551, so not allowed..

One love, one blood, one life. You got to do what you should.
https://dreambigdreamhigh.blocked/
https://gmattoughies.blocked/

Like this post

Svedankae: Master | Next Rank: 500 Posts; Posts: 101; Joined: Tue Apr 07, 2009 12:30 am; Thanked: 2 times; GMAT Score:750

by Svedankae » Tue May 19, 2009 1:41 am

how long do top scorers take on these kinds of questions? are these the questions considered "hard" or does it get way harder than that? i found the solution by working my way up from 1 until i reached 6.... but i guess to score high one needs to do it a smart way like you guys :-/

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review