What is the least value of the positive integer n?

Question

I. The units digit of n is equal to the units digit of sum of n and (n + 1).
II. n is the square of a single digit odd prime number.

Archit3110 · Answer

#1
 The units digit of n is equal to the units digit of sum of n and (n + 1).
2n+1
for n= 9 only we get this relation satisfied
18+1 ; 19 unit digit is same as 9 single digit
sufficient
#2
n is the square of a single digit odd prime number
again true for value = 3,7 square ; 9,,25,49
least value is 9
sufficeint
IMO D

m1033512 · Answer

IMO D

from Statement 1 , we have n = 9,19,29 and n+1 = 10,20,30 among them the least is 9 sufficient

From Statement 2 ,

the square of single digit prime number which means n = 3 only , sufficient

Render · Answer

Hi, could you clarify how exactly you arrived at the number  n=9 ? Did you have to check every number from 0 to 9?

Thank you.

nick1816 · Answer

Statement 1- If n has the same unit digit as that of the sum of n and n+1, then unit digit of n must be 9. (9+0=9)
The least positive integer whose unit digit is 9=9
Sufficient

Statement 2- n is square of single digit prime numbers. Possible values are 9, 25 and 49
Least value of n is 9
(sufficient)

Karmesh · Answer

Since we know the number is 2n+1, we can conclude it is ODD. So, we have to check only the odd number i.e 1,3,5,7,9  . It will hardly take 10-15 sec.

CareerGeek · Answer

I. The units digit of n is equal to the units digit of sum of n and (n + 1)

Units digit of n+1 should be 0
Different possibilities of n = 9, 19, 29, . . . .
Least value of n = 9

Sufficient

II. n is the square of a single digit odd prime number.
--> n = 3^2 = 9
Only 1 possibility, n = 3

Sufficient

IMO Option D

Pls Hit Kudos if you like the solution

mweber · Answer

Hello, my original thinking when I read this problem was that you don't even need to solve anything because no matter what the conditions are, it asks for the least possible value therefore there is only going to be one value that satisfies the statements and thus each will be sufficient.. could someone confirm or deny this methodology? It almost seems too simple... Thanks!

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What is the least value of the positive integer n?

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