N is positive integer and hundredth digit of 10N is 6

Question

N is positive integer and hundredth digit of 10N is 6.If N and N+13 is multiple of 13 then N+13 tenth digit is 7. Now what is the unit digit of N.

A.7
 B.5
 C.8
 D.4
 E.0

GyanOne · Answer

This question should be re-framed by specifying that N is a two digit positive integer.

1) If the hundred's digit of 10N is 6 => the ten's digit of N is 6. 
2) The ten's digit of N+13 is 7 => the one's digit of N is 5

The one's digit of N is 5 because for the ten's digit of N to be 6, and the ten's digit of N+13 to be 7, the addition of 13 to N must be causing a carry of 1 to the ten's column. Therefore 3 must be getting added to the ten's column. Now, if the one's digit is X, we must choose X in such a way that 60+X and 70+(X+3) are both divisible by 13. This is possible when X=5.

Option (B), provided that this number is two digit number (not given in the question).

If this is not a two digit number, then the numbers 260 and 273 will also satisfy this criteria and in that case the units digit will be 0, 364 and 377 will also satisfy with the units digit being 4, 663 and 676 will also satisfy with the units digit being 3....... so there is no unique answer for the units digit in that case.

vsrsankar · Answer

My take:
Hundredth digit of 10N is 6 => tenth digit of N is 6
N+13 tenth digit is 7 => unit digit of N shall be between 0 and 6 (inclusive of 0,6)
The only answer options possible are 0,4,5
We know that 65 is divisible by 13. And no other additional clue is given we can conclude the unit digit to be '5'
Answer option 'B'

vomhorizon · Answer

From the information given :

N = multiple of 13 ...

N + 13 = Multiple of 13 , with the tenth place being 7 ...

10N has a 100th unit as 6 ...

Multiples of 13 = ( 13 x 2 = 26 , 13 x 3 = 39, 13x4 = 52 , 13x5 = 65, 13x6 = 78, 13x9 = 78, 13x10 = 130...) ..

Out of these we need to find a number which when added to 13 yields a unique number whose tenth place is occupied by a 7.. We have 65 as that number so will select it to test it out ..

65+13 = 78 , tenth place is 7 .. So 1 condition is met ...

Lets multiply 10 by N we get 10 x 65 = 650 ..The hundredth unit is 6 , so the second condition has been met...

after satisfying 1 and 2 we know that n = 65 , the units digit of n is 5 (B)

Ousmane · Answer

N = tu, 10N = tu0, t = 6, N = 6u; N + 13 = 6u + 13 = 73 + u =13k (because N+13 is multiple of 13)
u = 13k - 73 = 5 for k= 6
Brother Karamazov

kassim · Answer

Hello,

I didn't understand why the tens digit 6 if the hundredth digit of 10N is 6.

For me I assumed that it's a 3 digit number and the hundredth digit of N is 6

Can anyone please explain more?

Best,
Kassim

mau5 · Answer

We know that N is an integer. Let N = abc.Now, 10*N = abc0. As you can notice, the value of the each of the digit shifts place wise. Initially, the units digit of N was c, which is now 0. The tens unit of N was b, which is now at the hundred's place.Thus, when we know that the hundred's digit after multiplication by 10 is 6, then by similar analogy, we can say that the tens place of N must be 6.
You can actually pick up numbers with tens digit as 6, and multiply by 10 to get an idea. Also, for this particular thing, it doesn't matter if N is a 2 digit number or a 10 digit number.

Hope this helps.

kassim · Answer

Hi,

Thank you for your help. I don't know why I assumed that 10N is 3 digit number or more as one hundred and N not 10 times N.

Now it's Crystal clear

Thank you

N is positive integer and hundredth digit of 10N is 6

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