Question

Let p and q be two positive integers. For some fixed
integer n, the set {n - 1, 3n - 19, 38 - 5n, 7n – 45
represents {p, 2p, q, 2q} but not necessarily in that order.
Find the value of n.​

Answer 1

Given : p and q be two positive integers. For some fixed integer n, the set {n - 1,3n - 19, 38 - 5n, 7n - 45} represents {p, 2p, q, 2q}

To Find :  value of n

Solution:

{n - 1, 3n - 19, 38 - 5n, 7n - 45}

 

p,  2p,  q, 2q  

38 - 5n > 0  =>  5n < 38  => n ≤ 7

7n - 45 > 0  => n  ≥ 7

Hence only possible value on n is 7

{n - 1, 3n - 19, 38 - 5n, 7n - 45}

( 6 ,  2  , 3 ,  4)

4 = 2 * 2

6 = 2 * 3  

Hence p,  2p,  q, 2q     ( p and q can be 2 and 3 in any order )

So value of n is  7

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