• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Most awarded test prep in the world
Now free for 30 days

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

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

tagged by: Brent@GMATPrepNow

This topic has 3 expert replies and 0 member replies
Azzaya Newbie | Next Rank: 10 Posts
Joined
13 Jul 2017
Posted:
2 messages

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

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.

Thank you all for the great support and insight!

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11278 messages
Followed by:
1225 members
5254
GMAT Score:
770
Fri Sep 01, 2017 2:13 pm
Quote:
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

Cheers,
Brent

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!

### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
Joined
22 Aug 2016
Posted:
976 messages
Followed by:
20 members
470
Mon Jul 31, 2017 9:54 pm
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.

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!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Singapore | London | Dubai | and many more...

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9184 messages
Followed by:
472 members
2867
GMAT Score:
800
Mon Jul 31, 2017 11:11 am
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.

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

### Best Conversation Starters

1 lheiannie07 112 topics
2 ardz24 71 topics
3 Roland2rule 69 topics
4 LUANDATO 53 topics
5 swerve 45 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 GMATGuruNY

The Princeton Review Teacher

154 posts
2 Rich.C@EMPOWERgma...

EMPOWERgmat

107 posts
3 Jeff@TargetTestPrep

Target Test Prep

106 posts
4 Scott@TargetTestPrep

Target Test Prep

98 posts
5 EconomistGMATTutor

The Economist GMAT Tutor

91 posts
See More Top Beat The GMAT Experts