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Problem Of The Week 8

with 3 comments

Let x and y be real nos such that

[x] + 3{y}=3.9 and

{x} + 3[y]=3.4

[z] and {z} have their usual meanings.

Find the number of ordered pairs (x,y).

a) 0                    b) 1                   c) 2                     d)  3                        e) none of these

Written by Rahul

August 29, 2008 at 11:43 am

Posted in Number Thoery, Problem of the week

Tagged with , ,

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3 Responses

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  1. i guess there is no such pair :|

    nidhi

    August 29, 2008 at 5:13 pm

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  2. Now adding the given equations, We get x+3y = 7.3

    Now [x] can be 1,2 or 3 and [y] should be equal to 1 as -1<{x}<1

    Now suppose [x] =1,
    we get {y} as 29/30 using 1st equation and hence y = 59/30 (Since [y]=1) and substituting in the equation, we get x=1.4

    Similarly when [x] = 2, we get x = 2.4 and y= 49/30

    when [x] = 3 we get x = 3.4 and y = 1.3

    So total three solutions, answer choice (d)..Really good questions Implex, keep ‘em coming:)

    Celebrating Life

    August 29, 2008 at 5:15 pm

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  3. Rightly done Bhaskar
    @ Nidhi, Have a look at the solution above, if you have doubts, we can handle it !

    outtimed

    August 29, 2008 at 5:18 pm

    Reply

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