Aptitude - Numbers - Discussion

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

Please explain I couldn't understand how he get maximum value.

Why we consider only minimum ?

Explain the reason or any guessing that we can take. If I take here p=9 it also works.

Here we have to use options 339=13p+11, p is not a whole number, like that we have to use options, at 349=13p+11, p is whole number.

So simple 339/13 remainder is 1
349/13 remainder is 11 & same when we divide by 349/17 remainder is 9
So answer is B

Its true that we can get answer by using options. But if the options are not available then we have to use formula. Then we must know how to get least value of P.

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

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

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.