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

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Walkabout
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If n is a positive integer, what is the tens digit of n ? [#permalink] New post  Updated on: 01 Jun 2021, 03:31
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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.
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Originally posted by Walkabout on 26 Dec 2012, 05:51.
Last edited by Bunuel on 01 Jun 2021, 03:31, edited 1 time in total.
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BrentGMATPrepNow
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If n is a positive integer, what is the tens digit of n ? [#permalink] New post  Updated on: 09 Sep 2021, 07:20
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Walkabout 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.


Target question: What is the tens digit of n?

Statement 1: The hundreds digit of 10n is 6
Notice what happens when we multiply any positive integer by 10:
34 x 10 = 340
60 x 10 = 600
128 x 10 = 1280
54629 x 10 = 546290
The tens digit in the original number becomes the hundreds digit in the new number.

So, if we're told that the hundreds digit of 10n is 6, then we know that the tens digit in n must be 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The tens digit of n+1 is 7
There are several values of n that meet this condition. Here are two:
case a: n=69 in which case the tens digit of n is 6
case b: n=74 in which case the tens digit of n is 7
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT


Answer = A

Originally posted by BrentGMATPrepNow on 21 Jul 2016, 16:32.
Last edited by BrentGMATPrepNow on 09 Sep 2021, 07:20, edited 1 time in total.
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Bunuel
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Re: If n is a positive integer, what is the tens digit of n ? [#permalink] New post  26 Dec 2012, 05:53
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If n is a positive integer, what is the tens digit of n ?

(1) The hundreds digit of 10n is 6. This implies that the tens digit of n is 6. Sufficient.

(2) The tens digit of n + 1 is 7. If n=70, then the tens digit of n is 7, but if n=69, then the tens digit of n is 6. Not sufficient.

Answer: A.
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Re: If n is a positive integer, what is the tens digit of n ? [#permalink] New post  14 Jan 2013, 00:45
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fozzzy wrote:
How do you solve this one?


(1) The hundreds digit of 10n is 6
SUFFICIENT: If Hundred's place of 10n = 6 then Ten's place of n must be 6
e.g. n=68 tens place 6,
10n=680, hundreds place is 6

(2) The tens digit of n+1 is 7
INSUFFICIENT: If n=69; n+1=70 OR If n=77; n+1=77; i.e. n can have both 6 or 7 as tens place.

Hence choice(A) is the answer.
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Re: If n is a positive integer, what is the tens digit of n ? [#permalink] New post  18 May 2014, 11:11
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let n = ABCD

tens digit = C

1. 10n = ABCD0
given, hundreds digit = 6 (or) C = 6 - sufficient

2. tens digit of n+1 = 7.

consider CD = 69 -> CD+1 = 70 -> C=6 (or)

consider CD = 71 ->CD+1 = 72 -> C = 7

2 cases possible - insuff.

Hence A
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Re: If n is a positive integer, what is the tens digit of n ? [#permalink] New post  09 Sep 2016, 09:59
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Here is my contribution with the reasoning a little more visual for those still struggling. :wink:
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Re: If n is a positive integer, what is the tens digit of n ? [#permalink] New post  25 Jun 2019, 15:32
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I think we have a problem with the question language for statement (2). It could be perceived in two different ways:

(1) "The tens digit of n" + 1 is 7, or
(2) The tens digit of "n + 1" is 7.

Therefore, perception becomes reality to the reader until we use parentheses properly, or at least some kind of technique to unquestionably clarify the idea being communicated. I think this is even more pertinent given that communication is an essential element in business administration.
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Re: If n is a positive integer, what is the tens digit of n ? [#permalink] New post  24 Jul 2020, 14:28
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Isn't it too ambiguous when they say "tens digit of n + 1 = 7"?
I understood that tens digit of n like x, and this x+1=7, so x is 6. Therefore, tens digit of n is 6.

Isn't it also possible to understand the question as I did?

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Re: If n is a positive integer, what is the tens digit of n ? [#permalink] New post  12 Sep 2020, 07:32
Mits555 wrote:
Isn't it too ambiguous when they say "tens digit of n + 1 = 7"?
I understood that tens digit of n like x, and this x+1=7, so x is 6. Therefore, tens digit of n is 6.

Isn't it also possible to understand the question as I did?

Posted from my mobile device

Mits555
No.
The way you are saying it x is a single digit number. However, n is a two digit number, the tens digit of which has to be found.
But, n + 1 ≠ x + 1

Do you mean to say n = x?
No, i guess.

I hope you get the point.
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Re: If n is a positive integer, what is the tens digit of n ? [#permalink] New post  07 Oct 2020, 03:38
OFFICIAL GMAT EXPLANATION

(1) Given that the hundreds digit of 10n is 6, the tens digit of n is 6, since the hundreds digit of 10n is always equal to the tens digit of n; SUFFICIENT.

(2) Given that the tens digit of n + 1 is 7, it is possible that the tens digit of n is 7 (for example, n = 70) and it is possible that the tens digit of n is 6 (for example, n = 69); NOT sufficient.

The correct answer is A; statement 1 alone is sufficient.
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Re: If n is a positive integer, what is the tens digit of n ? [#permalink] New post  12 Oct 2020, 07:58
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Re: If n is a positive integer, what is the tens digit of n ? [#permalink] New post  31 May 2021, 14:06
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Walkabout 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.

Solution:

We need to determine the tens digit of a positive integer n.

Statement One Alone:

Since the hundreds digit of 10n is the tens digit of n, the tens digit of n is therefore 6. Statement one alone is sufficient.

Statement Two Alone:

If the tens digit of n + 1 is 7, the tens digit of n could be 6 or 7. For example, if n = 69, then n + 1 = 70 has a tens digit of 7. In this case, the tens digit of n is 6. On the other hand, if n = 70, then n + 1 = 71 still has a tens digit of 7. In this case, the tens digit of n is 7. Statement two alone is not sufficient.

Answer: A
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Re: If n is a positive integer, what is the tens digit of n ? [#permalink] New post  30 Jun 2021, 15:51
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Statement 1: 10(x)=6xx
needs to be 6x Sufficient

Statement 2:
Could be 69 (nice) 69+1=70 or could be 71+1=72
since two different tens digit (6 or 7) no good.

Ans->A
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Re: If n is a positive integer, what is the tens digit of n ? [#permalink] New post  14 Oct 2021, 11:46
Bunuel
Hi Bunuel,

What if the question didn't mention n is a positive integer. Do you think the answer is still A?

I think even if we consider n is a decimal or a negative number, statement 1 will be sufficient.
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If n is a positive integer, what is the tens digit of n ? [#permalink] New post  01 Dec 2022, 07:56
Walkabout 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.



Algebraic approach:

1) 10n = 100(6) + 10(x) + 0
to make n the subject (since we are trying to find n) we divide the above eq. by 10
n = 10(6) + x + 0
n = 10(6) + x

hence, the tens digit is 6 and this statement is sufficient.

2) n+1 = 10(7) + x
n+1 = 70 + x
n = 69 + x

now if x (the unit's digit) is 0 then n = 69
tens digit of n is 6.
if x is 1 or greater than 1 then n = 70,71,72......
tens digit of n is 7.

hence, statement 2 is not sufficient!
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If n is a positive integer, what is the tens digit of n ? [#permalink]
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