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# Rules 1. Time yourself 2. Write the solution on a seperate

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CEO
Joined: 15 Aug 2003
Posts: 3469
Followers: 61

Kudos [?]: 702 [0], given: 781

Rules 1. Time yourself 2. Write the solution on a seperate [#permalink]  08 Mar 2004, 16:05
Rules

1. Time yourself
2. Write the solution on a seperate sheet

The number of positive integer valued pairs (x, y), satisfying 4x-17y = 1 and x < 1000 is:

1. 59
2. 57
3. 55
4. 58
SVP
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
Followers: 5

Kudos [?]: 41 [0], given: 0

It sure took more than 2 minutes because I did a mistake while calculating.

Assume 4x-17y = 0 so x = approx 4y
Make x = 1000 then y = 250. So max value y can take is 250

Now if we see the relation between x and y
we have to have odd number from 17y and even number from 4x and the difference should be 1
one such (x,y) pair is (13,3) and another is (30,7)
The space between each succesive y is 4
So max number of pairs can be 250/4 = approx 62
Only the 58 comes close to this

So I will go wtih 58.
Manager
Joined: 11 Oct 2003
Posts: 102
Location: USA
Followers: 1

Kudos [?]: 0 [0], given: 0

Graph it.. [#permalink]  08 Mar 2004, 17:55
hmm..i could be wrong..at 58

Last edited by mantha on 08 Mar 2004, 18:00, edited 1 time in total.
CEO
Joined: 15 Aug 2003
Posts: 3469
Followers: 61

Kudos [?]: 702 [0], given: 781

Lets rearrange
x = (y+1)/4 + 4y
Now we are looking for integer values of x,
Therefore, (y+1)/4 must be an integer.
At x=1000, y+1 =236.2
So what i am looking for is number of multiples of 4 between 0 & 236.

Now u can calculate that there are 59 mutiples of 4 between 0 & 236.

Good try. More to come.

questions?

Last edited by Praetorian on 08 Mar 2004, 18:00, edited 1 time in total.
SVP
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
Followers: 5

Kudos [?]: 41 [0], given: 0

Hi Praetorian

I meant 59. But my method is crude I guess.

Anand.
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