Aptitude - Numbers - Discussion

Here p=9 also works but the thing is that there is no option for that only p=26 we have the answer.

I did not get please explain me anyone.

How to get the least value p here?

Please explain p=26 how?

I am not able to understand why p is taken as 26? please help me.

@Sunny wilson, can you please explain the plugin method here ?

Instead solving the problem use plugin methods to answer quickly.

x = 13p + 11 and x = 17q + 9.

The general case is,
x = 221a + 128 which give x = 349 for the least value of a = 1.

Let's try to demonstrate that!

Difference d > 0 get p = q + d and q = p - d.

We will replace q (into the second equality of x) to get p as function of d:
13p + 11 = 17(p-d) + 9 => 4p = 17d + 2.

We see now that d is even, so d = 2k and p = q + 2k.

4p = 17 x 2k + 2.

After dividing the above equality by 2 we will remark that k has an odd value so we will replace it by 2a+1.

2p = 17k + 1.

So k = 2a + 1 and p = q + 2(2a+1).

2p = 17(2a+1) + 1 => p = 17a + 9.

Replacing p in x = 13p + 11 will lead to the expected result.

x = 13(17a+9) + 11 => x = 221a + 128.

Please tell how to find the minimum value of p. Is there any alternative method to solve this problem?we cannot predict the value.

Please explain the method to find out the least value of p here?