BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

Good DS.

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Fri Oct 18, 2013 5:58 pm
Hi rakeshd347,

This DS question has a great little Number Property behind it, although most people don't realize it. Sometimes the best way to figure out that a pattern exists is to PROVE it.

Here, we're told that N is a NON-NEGATIVE integer (so it can be either 0 or a positive integer). We're asked if (10^N) + 8 is evenly divisible by 18? This is a Yes/No question.

I'm going to show you the pattern right up front:
If N = 0, then 10^0 + 8 = 9 and the answer is NO
If N = 1, then 10^1 + 8 = 18 and the answer is YES
If N = 2, then 10^2 + 8 = 108 and the answer is YES (pattern: 108 = 18 + 90)
If N = 3, then 10^3 + 8 = 1008 and the answer is YES (pattern: 1008 = 108 + 900)
If N = 4, then 10^4 + 8 = 10008 and the answer is YES (pattern: 10008 = 1008 + 9000)

18 divides evenly into 90, so it divides into 900, 9000, etc.
As N gets bigger, each total = a multiple of 90 + the prior total, so 18 will ALWAYS divide evenly into the total. The "exception" is when N = 0.

Fact 1: N is prime.
We have proof (in the above list) that the answer is ALWAYS YES.
Fact 1 is SUFFICIENT

Fact 2: N is even
If N = 0, then the answer is NO
If N = 2, then the answer is YES
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members
Thanked: 448 times
GMAT Score:650

by theCodeToGMAT » Fri Oct 18, 2013 11:44 pm
(10^n + 8)/18

= (10^n + 8 + 10 - 10)/18

= (10^n - 10 + 18)/18

= 10(10^(n-1))/18 + 18/18

To find: (10^(n-1) - 1)/9

For every value greater than 1 the equation is true as all digits will result in "9"

Statement 1:
N > 1
SUFFICIENT

Statement 2:
N can be 0
INSUFFICIENT

Answer [spoiler]{A}[/spoiler]
R A H U L
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Sat Oct 19, 2013 6:47 am
rakeshd347 wrote:If n is an non-negative integer, is (10^n)+8 divisible by 18?

(1) n is a prime number.

(2) n is even.
Target question: Is (10^n)+8 divisible by 18?

This is a great candidate for rephrasing the target question.

IMPORTANT: In order for (10^n)+8 to be divisible by 18, it must be divisible by 9 AND by 2.
The good thing is that (10^n)+8 is already divisible by 9 for ALL non-negative integer values of n.
We know this because all integers divisible by 9 are such that the sum of their digits is divisible by 9. For example, 504, 11709 and 8838 are divisible by 9 because the sums of their integers are 9, 18 and 27 (respectively), and 9, 18 and 27 are all divisible by 9.

Let's examine some values of (10^n)+8
n = 0: (10^n)+8 = 1 + 8 = 9
n = 1: (10^n)+8 = 10 + 8 = 18
n = 2: (10^n)+8 = 100 + 8 = 108
n = 3: (10^n)+8 = 1000 + 8 = 1008
n = 4: (10^n)+8 = 10000 + 8 = 10008
As you can see, the sum of the digits of (10^n)+8 will ALWAYS be 9. So, (10^n)+8 is ALWAYS divisible by 9.

So, as you can see, we've already taken care of the "divisible by 9" part.
So, in order to determine whether (10^n)+8 is divisible by 18, we need only determine whether (10^n)+8 is divisible by 2.
This means we can rephrase the target question as follows:

REPHRASED target question: Is (10^n)+8 even? (i.e., divisible by 2)

Since 8 is ALWAYS even, we can see that (10^n)+8 will be even whenever (10^n) is even. Furthermore, we can see that (10^n) will be even as long as n ≠ 0. In other words, (10^n) will be even AS LONG AS n > 0. So, we can rephrase the target question one last time.

REPHRASED target question: Is n > 0 ?

Now that we've taken a moment to rephrase the target question to such a great extent, the statements should take no time at all to analyze.

Statement 1: n is a prime number.
In n is prime, then n is definitely greater than zero
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: n is even
case a: n = 2, in which case n is greater than zero
case b: n = 0, in which case n is not greater than zero
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

NOTE: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Sun Dec 18, 2016 10:52 am

by Kamakshi Chawla » Sat Dec 24, 2016 10:10 am
But what we study is 0 is either odd not even.
So in that case even statement 2 is sufficient and answer is D.
Am i right?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Sun Dec 18, 2016 10:52 am

by Kamakshi Chawla » Sat Dec 24, 2016 10:12 am
Brent@GMATPrepNow wrote:
rakeshd347 wrote:If n is an non-negative integer, is (10^n)+8 divisible by 18?

(1) n is a prime number.

(2) n is even.
Target question: Is (10^n)+8 divisible by 18?

This is a great candidate for rephrasing the target question.

IMPORTANT: In order for (10^n)+8 to be divisible by 18, it must be divisible by 9 AND by 2.
The good thing is that (10^n)+8 is already divisible by 9 for ALL non-negative integer values of n.
We know this because all integers divisible by 9 are such that the sum of their digits is divisible by 9. For example, 504, 11709 and 8838 are divisible by 9 because the sums of their integers are 9, 18 and 27 (respectively), and 9, 18 and 27 are all divisible by 9.

Let's examine some values of (10^n)+8
n = 0: (10^n)+8 = 1 + 8 = 9
n = 1: (10^n)+8 = 10 + 8 = 18
n = 2: (10^n)+8 = 100 + 8 = 108
n = 3: (10^n)+8 = 1000 + 8 = 1008
n = 4: (10^n)+8 = 10000 + 8 = 10008
As you can see, the sum of the digits of (10^n)+8 will ALWAYS be 9. So, (10^n)+8 is ALWAYS divisible by 9.

So, as you can see, we've already taken care of the "divisible by 9" part.
So, in order to determine whether (10^n)+8 is divisible by 18, we need only determine whether (10^n)+8 is divisible by 2.
This means we can rephrase the target question as follows:

REPHRASED target question: Is (10^n)+8 even? (i.e., divisible by 2)

Since 8 is ALWAYS even, we can see that (10^n)+8 will be even whenever (10^n) is even. Furthermore, we can see that (10^n) will be even as long as n ≠ 0. In other words, (10^n) will be even AS LONG AS n > 0. So, we can rephrase the target question one last time.

REPHRASED target question: Is n > 0 ?

Now that we've taken a moment to rephrase the target question to such a great extent, the statements should take no time at all to analyze.

Statement 1: n is a prime number.
In n is prime, then n is definitely greater than zero
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: n is even
case a: n = 2, in which case n is greater than zero
case b: n = 0, in which case n is not greater than zero
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

NOTE: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100



But what we study is 0 is either odd not even.
So in that case even statement 2 is sufficient and answer is D.
Am i right?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Sat Dec 24, 2016 2:05 pm
Hi Kamakshi Chawla,

On a Number Line, integers follow the same pattern in either direction: odd-even-odd-even-odd-even, etc.

-3 = odd
-2 = even
-1 = odd
0 = even
1 = odd
2 = even
etc.

So 0 IS even. It is NEITHER positive nor negative though - it's what is referred to as a 'null value.'

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Sat Dec 24, 2016 5:13 pm
If integer y can be written as the product 2k, for some integer k, then y is EVEN.
For example, since we can write 6 as (2)(3), we can conclude that 6 is even.
Likewise, since we can write -10 as (2)(-5), we can conclude that -10 is even.

Similarly, since we can write 0 as (2)(0), we can conclude that 0 is even.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1