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

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

by Azzaya » Mon Jul 31, 2017 8:28 am

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Hi all,

I am having a hard time understanding how Statement (2) is being explained, can someone please explain this in detail as I don't understand how n equals either 70 or 69, and how the statement is being incorporated in the explanation, how is n+1=7 being used in realizing statement (2) is NOT SUFFICIENT?

Target Question:

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

Statement (1): The hundreds digit of 10n is 6.

Statement (2): The tens digit of n + 1 is 7.

How Statement (1) is explained (This one I understand) :
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.

How Statement (2) is explained:

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.

Any reply is highly appreciated!

Thank you all for the great support and insight!
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by [email protected] » Mon Jul 31, 2017 11:11 am

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Hi Azzaya,

When dealing with DS questions, you have to consider the various possibilities (based on whatever information you're given to work with in the two Facts) - so that you can properly determine the correct answer.

Here, we're told that N is a positive integer. We're asked for the TENS DIGIT of N. Fact 2 gives us the additional information that (N+1) has a TENS DIGIT of 7.... So what COULD N be under these circumstances?

There are 10 possibilities (and remember - (N+1) has a tens digit of 7....)
N COULD be....
69
70, 71, 72, 73, 74, 75, 76, 77, 78

In the first example, N has a TENS DIGIT of 6
In the other nine examples, N has a TENS DIGIT of 7
Since there are two difference answers to the given question, Fact 2 is INSUFFICIENT.

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Rich
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by Jay@ManhattanReview » Mon Jul 31, 2017 9:54 pm

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Azzaya wrote:Hi all,

I am having a hard time understanding how Statement (2) is being explained, can someone please explain this in detail as I don't understand how n equals either 70 or 69, and how the statement is being incorporated in the explanation, how is n+1=7 being used in realizing statement (2) is NOT SUFFICIENT?

Target Question:

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

Statement (1): The hundreds digit of 10n is 6.

Statement (2): The tens digit of n + 1 is 7.

How Statement (1) is explained (This one I understand) :
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.

How Statement (2) is explained:

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.

Any reply is highly appreciated!

Thank you all for the great support and insight!
Though Rich has beautifully explained this, here's my take.

Statement 2: The tens digit of (n + 1) is 7.

Since the tens digit of (n + 1) is 7, the number (n + 1) could be anything from 70 to 79. We see that for each of the numbers 70, 71, 73, ..., 79, the tens digit is '7.'

If (n+1) is anything from 70 to 79, then n is anything from (70 - 1 =) 69 to (79 - 1 =) 78.
We see that the tens digit of n could be 6 or 7. No unique value. Insufficient.

Hope this helps!

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by Brent@GMATPrepNow » Fri Sep 01, 2017 2:13 pm

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

Statement (1): The hundreds digit of 10n is 6.
Statement (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

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

by Scott@TargetTestPrep » Mon May 31, 2021 1:07 pm

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Azzaya wrote: ↑
Mon Jul 31, 2017 8:28 am
 Hi all,

I am having a hard time understanding how Statement (2) is being explained, can someone please explain this in detail as I don't understand how n equals either 70 or 69, and how the statement is being incorporated in the explanation, how is n+1=7 being used in realizing statement (2) is NOT SUFFICIENT?

Target Question:

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

Statement (1): The hundreds digit of 10n is 6.

Statement (2): The tens digit of n + 1 is 7.

How Statement (1) is explained (This one I understand) :
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.

How Statement (2) is explained:

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.

Any reply is highly appreciated!

Thank you all for the great support and insight!
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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