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What is the least value of the positive integer n? 16 May 2019, 00:48
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85% (hard)

Question Stats:

44% (02:06) correct 56% (02:10) wrong based on 350 sessions

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What is the least value of the positive integer n?

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.
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D
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What is the least value of the positive integer n? 17 May 2019, 02:55
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kiran120680
What is the least value of the positive integer n?

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.
Show more

#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
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What is the least value of the positive integer n? 17 May 2019, 09:28
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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
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What is the least value of the positive integer n? 20 May 2019, 14:37
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kiran120680
What is the least value of the positive integer n?

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.

#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
Show more


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.
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What is the least value of the positive integer n? 21 May 2019, 04:09
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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)
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What is the least value of the positive integer n? 21 Jun 2019, 09:41
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kiran120680
What is the least value of the positive integer n?

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.

#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


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.
Show more

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 [even number can't have the same units digit as an odd number]. It will hardly take 10-15 sec.
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What is the least value of the positive integer n? 21 Jun 2019, 12:00
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kiran120680
What is the least value of the positive integer n?

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.
Show more


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

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What is the least value of the positive integer n? 22 Jun 2019, 07:44
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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? 12 Feb 2023, 12:43
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