Aptitude - Numbers - Discussion

Discussion :: Numbers - General Questions (Q.No.61)

61. 

When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?

[A]. 339
[B]. 349
[C]. 369
[D]. Data inadequate

Answer: Option B

Explanation:

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

13p + 11 = 17q + 9

17q - 13p = 2

q = 2 + 13p
17

The least value of p for which q = 2 + 13p is a whole number is p = 26
17

x = (13 x 26 + 11)

   = (338 + 11)

   = 349


Subhseh said: (Jul 31, 2010)  
Please explain the method to find out the least value of p here.

Jainendra said: (Sep 8, 2011)  
Please explain I couldn't understand how he get maximum value.

Anup Gupta said: (Sep 19, 2011)  
Why we consider only minimum ?

Narendra said: (Sep 29, 2011)  
Explain the reason or any guessing that we can take. If I take here p=9 it also works.

Naveenkumar said: (Oct 17, 2011)  
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.

Raman said: (Apr 16, 2012)  
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

Raj said: (May 26, 2013)  
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.

Deep said: (Jul 13, 2013)  
Please explain the method to find out the least value of p here?

Arun said: (Jan 23, 2014)  
Please tell how to find the minimum value of p. Is there any alternative method to solve this problem?we cannot predict the value.

Faneal said: (Apr 17, 2014)  
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.

Sunny Wilson said: (Aug 23, 2014)  
Instead solving the problem use plugin methods to answer quickly.

Sweta said: (Sep 7, 2014)  
@Sunny wilson, can you please explain the plugin method here ?

Pratikshya said: (Feb 11, 2015)  
I am not able to understand why p is taken as 26? please help me.

Raihan said: (Feb 27, 2015)  
Please explain p=26 how?

Arvind said: (Jun 19, 2015)  
How to get the least value p here?

Aparna said: (Jun 30, 2015)  
I did not get please explain me anyone.

Kanijv said: (Aug 6, 2015)  
Here p=9 also works but the thing is that there is no option for that only p=26 we have the answer.

Shashank said: (Aug 9, 2015)  
How the value of P becomes 26?

Vrunda said: (Aug 27, 2015)  
How is possible in p=26?

Rajani said: (Mar 10, 2016)  
How we get the value of p=26?

Please explain.

Sonu Shaw said: (Apr 15, 2016)  
How p = 26? Please explain that step.

Ravi said: (Jun 18, 2016)  
How are you taking p as 26? Please explain.

Shubham said: (Aug 23, 2016)  
@Ravi.

We have to satisfy the condition so that q should be greater than 1 that is why we take p =2, putting p =2 = 13 * 2 = 26 which is equal to p.

Ramesh Mariyada said: (Nov 22, 2016)  
Is there any shortcut method to solve this problem?

Justin said: (Dec 8, 2016)  
Please explain the value of P.

Puja said: (Jul 19, 2017)  
One of the easy ways is check options.

349-11 = 338,
Now,338/13 = 26,
Also,349-9 = 340,
340/17 = 20.

Hence from checking opt. B it is right option.
I hope it is clear to all.

Shruti Mohite said: (Jul 11, 2018)  
Please explain the method, how p=26 came?

Naina said: (Aug 11, 2018)  
How does p=26 appears? explain me.

Sudhanshu said: (Sep 2, 2018)  
Here, The Least value for p is 9 which will give us q as 7 and the result will be 128.

Jayalakshmi J said: (Sep 17, 2018)  
How come p=26?

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