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Digits

by greenwich » Tue Sep 07, 2010 3:22 pm
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.
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by Rahul@gurome » Tue Sep 07, 2010 3:41 pm
(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].
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by greenwich » Wed Sep 08, 2010 2:37 pm
Rahul@gurome wrote:(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?
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by sanju09 » Wed Sep 08, 2010 8:34 pm
greenwich wrote: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]
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by Rahul@gurome » Wed Sep 08, 2010 11:00 pm
greenwich wrote: 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?
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by sanju09 » Wed Sep 08, 2010 11:40 pm
greenwich wrote: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
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by sanju09 » Wed Sep 08, 2010 11:42 pm
Rahul@gurome wrote:
greenwich wrote: 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)
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