January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 31 Aug 2011
Posts: 162

If n is an nonnegative integer is 10^n+8 divisible by 18?
[#permalink]
Show Tags
Updated on: 18 Dec 2013, 10:56
Question Stats:
42% (01:06) correct 58% (01:28) wrong based on 226 sessions
HideShow timer Statistics
If n is an nonnegative integer is 10^n+8 divisible by 18? (1) n is a prime number (2) n is even m11 q13 will post my doubt and OA after some discussion.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
If you found my contribution helpful, please click the +1 Kudos button on the left, I kinda need some =)
Originally posted by PUNEETSCHDV on 18 Dec 2013, 10:43.
Last edited by Bunuel on 18 Dec 2013, 10:56, edited 1 time in total.
Renamed the topic, edited the question and added the OA.



Intern
Joined: 08 Sep 2012
Posts: 5

Re: If n is an nonnegative integer is 10^n+8 divisible by 18?
[#permalink]
Show Tags
18 Dec 2013, 11:18
Will go with A. 2 gives diff answers for zero n non zero



Intern
Joined: 16 Jun 2011
Posts: 29

Re: If n is an nonnegative integer is 10^n+8 divisible by 18?
[#permalink]
Show Tags
18 Dec 2013, 11:47
[quote="PUNEETSCHDV"]If n is an nonnegative integer is 10^n+8 divisible by 18?
(1) n is a prime number (2) n is even
IMO A
1) 10^n+8 will never divisible by 18 if n is prime no. define no means A is sufficient 2) n is even, if n=10, 10^n+8 is divisible by 18, but if n=2 it is not, two diff ans, means not sufficient



Math Expert
Joined: 02 Sep 2009
Posts: 52231

If n is an nonnegative integer is 10^n+8 divisible by 18?
[#permalink]
Show Tags
19 Dec 2013, 00:23
PUNEETSCHDV wrote: If n is an nonnegative integer is 10^n+8 divisible by 18? (1) n is a prime number (2) n is even m11 q13 will post my doubt and OA after some discussion. If n is an nonnegative integer is 10^n+8 divisible by 18?Notice that 10^n+8 is divisible by 18 for any positive value of n. In this case 10^n+8=even+even=even so it's divisible by 2. Also, in this case, the sum of the digits of 10^n+8 is 9 so its divisible by 9. Since 10^n+8 divisible by both 2 and 9 then it's divisible by 2*9=18 (the LCM of 2 and 9) too. On the other hand if n=0 then 10^n+8=1+8=9, so in this case 10^n+8 is not divisible by 9. (1) n is a prime number > n is a positive integer. Sufficient. (2) n is even > n can be zero as well as any positive even number. Not sufficient. Answer: A.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 09 Nov 2013
Posts: 72

Re: If n is an nonnegative integer is 10^n+8 divisible by 18?
[#permalink]
Show Tags
19 Dec 2013, 21:32
please use brackets as 10^n+8 is quiet confusing between 10^(n+8) or (10^n)+8



Manager
Joined: 15 Aug 2013
Posts: 53

Re: If n is an nonnegative integer is 10^n+8 divisible by 18?
[#permalink]
Show Tags
20 Dec 2013, 02:57
Notice that 10^n + 8 will have sum of digits = 9. Since, no matter what value 'n' may take, we will have 1 + 8 + 0 (depending on n) = 9. Now this no will be even since last digit is 8 => divisible by 2. Hence, no of the form 10^n + 8 is always divisible by 18 when n > 0. Only for n =0, the no becomes 9 which is not divisible by 18.
Stmt1 > sufficient based on above, we know n is not equal to 0. Stmt2 > insufficient since n =0 (even no) is not divisible by 18 while others will be.
Hence (A)



Manager
Joined: 04 Oct 2013
Posts: 169
Concentration: Finance, Leadership
GMAT 1: 590 Q40 V30 GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)

Re: If n is an nonnegative integer is 10^n+8 divisible by 18?
[#permalink]
Show Tags
04 Feb 2015, 00:54
PUNEETSCHDV wrote: If n is an nonnegative integer is 10^n+8 divisible by 18? (1) n is a prime number (2) n is even m11 q13 will post my doubt and OA after some discussion. Notice we are considering nonnegative numbers. We have to test 0 as well. every positive integer power of 10 yields a reminder of 10. statement 1: a prime is always a positive integer, thus reminder when 10^n is divided by 18 is 10; reminder when 8 is divided by 18 is 8. You can perform operations with reminders as long as you correct the excess (in case R>=divisor) R10+R8 = R18. Adjusting the excess you have R0, thus 10^prime+8 is a multiple of 18. Sufficient. statement 2: n is even, since we are dealing with nonnegative numbers, zero is even. Assume n=0 and R=9 Not sufficient. Answer A
_________________
learn the rules of the game, then play better than anyone else.



Senior Manager
Status: Math is psychological
Joined: 07 Apr 2014
Posts: 416
Location: Netherlands
GMAT Date: 02112015
WE: Psychology and Counseling (Other)

If n is an nonnegative integer is 10^n+8 divisible by 18?
[#permalink]
Show Tags
07 Feb 2015, 03:31
wastedyouth wrote: PUNEETSCHDV wrote: If n is an nonnegative integer is 10^n+8 divisible by 18?
(1) n is a prime number (2) n is even
IMO A
1) 10^n+8 will never divisible by 18 if n is prime no. define no means A is sufficient 2) n is even, if n=10, 10^n+8 is divisible by 18, but if n=2 it is not, two diff ans, means not sufficient The above justification in red is wrong, right? The point is that in case 2 "n" could be zero, as zero is an even number. In this case, 10^0 = 1 and 1+8=9, which is not divisible by 18 (it gives 1/2). In every other case we get a "yes". So, this statement is not sufficient. In case 1 it is always divisible by 18, because any positive power of 10 (except for 1 of course) would only add zeroes at the end of 10, and 8 would be added to that. Only by testing n=2, 100+8=108 and 108/18=6 we answer the question as "yes". Then, ANS is A.



NonHuman User
Joined: 09 Sep 2013
Posts: 9419

Re: If n is an nonnegative integer is 10^n+8 divisible by 18?
[#permalink]
Show Tags
03 Nov 2018, 07:23
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If n is an nonnegative integer is 10^n+8 divisible by 18? &nbs
[#permalink]
03 Nov 2018, 07:23






