Digits

[greenwich]

If n is a positive integer, what is the tens digit of n?

(1) The hundreds digit of 10n is 6.
(2) The tens digit of n+1 is 7.

Please provide explanations.

[Rahul@gurome]

(1) The hundreds digit of 10n is 6 means 10n = 6(tens place)(units place); tens place can take the digits from 0 to 9 but units place has to be the digit 0 as n is a positive integer.
So, n = 6(tens place)
We can see that the tens digit of n will always be 6.
[If not clear take an example: Let 10n = 620, then n = 62. If we take 10n = 602 then n cannot be an integer as n = 602/10 = 60.2]
So, (1) is SUFFICIENT.

(2) The tens digit of n+1 is 7 so N can be 69 to 78, so tenth place of n is either 6 or 7. Since we don't have a unique answer, so (2) is NOT SUFFICIENT.

The correct answer is [spoiler](A)[/spoiler].

[greenwich]

(1) The hundreds digit of 10n is 6 means 10n = 6(tens place)(units place); tens place can take the digits from 0 to 9 but units place has to be the digit 0 as n is a positive integer.
So, n = 6(tens place)
We can see that the tens digit of n will always be 6.
[If not clear take an example: Let 10n = 620, then n = 62. If we take 10n = 602 then n cannot be an integer as n = 602/10 = 60.2]
So, (1) is SUFFICIENT.

(2) The tens digit of n+1 is 7 so N can be 69 to 78, so tenth place of n is either 6 or 7. Since we don't have a unique answer, so (2) is NOT SUFFICIENT.

The correct answer is [spoiler](A)[/spoiler].

I am missing something here. The tens digit of 69 (6+1=7), but the tens digit of 78 (7+1 =8, not 7). Can you explain further?

[sanju09]

If n is a positive integer, what is the tens digit of n?

(1) The hundreds digit of 10n is 6.
(2) The tens digit of n+1 is 7.

Please provide explanations.

(1) The hundreds digit of 10n happens to be the tens digit of n. Sufficient

(2) This gives a range of values for the tens digit of n, it could be either 6 or 7. Insufficient


[spoiler]A[/spoiler]

[Rahul@gurome]

I am missing something here. The tens digit of 69 (6+1=7), but the tens digit of 78 (7+1 =8, not 7). Can you explain further?

If we take n = 69, then 10n = 10(69) = 690; here hundreds digit of 10n is 6 and tens digit of n = 6.
But if we take n = 78, then 10n = 10(78) = 780; this is not possible as hundreds digit of 10n is not 6, it's 7 here, but according to statement (1), hundreds digit of 10n is 6.
Does that help?

[sanju09]

I am missing something here. The tens digit of 69 (6+1=7), but the tens digit of 78 (7+1 =8, not 7). Can you explain further?

You are treating n as a digit here, big silent mistake

We enter (2) with a liberty that at minimum, n is 10. But here we discover that at minimum, n is 69, because tens digit of 69 + 1 is 7, and (2) holds true up to 78 only, because tens digit of 78 + 1 is still 7. Hence, the tens digit of n as seen through (2) could be either 6 or 7.

Hence, insufficient

[sanju09]

I am missing something here. The tens digit of 69 (6+1=7), but the tens digit of 78 (7+1 =8, not 7). Can you explain further?

If we take n = 69, then 10n = 10(69) = 690; here hundreds digit of 10n is 6 and tens digit of n = 6.
But if we take n = 78, then 10n = 10(78) = 780; this is not possible as hundreds digit of 10n is not 6, it's 7 here, but according to statement (1), hundreds digit of 10n is 6.
Does that help?

We switch to (2) with no hang-overs of (1)