It is currently 24 Jun 2017, 17:33

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If a is a positive integer and 20 < a < 100, is a^3 − a

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Moderator
Moderator
User avatar
S
Joined: 01 Sep 2010
Posts: 3211
If a is a positive integer and 20 < a < 100, is a^3 − a [#permalink]

Show Tags

New post 29 Aug 2013, 08:54
1
This post received
KUDOS
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

67% (02:27) correct 33% (01:55) wrong based on 143 sessions

HideShow timer Statistics

If a is a positive integer and 20 < a < 100, is a^3 − a divisible by 15?

(1) The units digit of a is 9.
(2) The tens digit of a is 3.
[Reveal] Spoiler: OA

_________________

COLLECTION OF QUESTIONS AND RESOURCES
Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection - The Next Generation 3. Bunuel Signature Collection ALL-IN-ONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos
Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Reading-comprehension_Oldy but goldy question banks


Last edited by Bunuel on 29 Aug 2013, 08:56, edited 1 time in total.
Expert Post
1 KUDOS received
Math Expert
User avatar
D
Joined: 02 Sep 2009
Posts: 39662
Re: If a is a positive integer and 20 < a < 100, is a 3 − a [#permalink]

Show Tags

New post 29 Aug 2013, 09:04
1
This post received
KUDOS
Expert's post
If a is a positive integer and 20 < a < 100, is a^3 − a divisible by 15?

In order an integer to be divisible by 15 it should be divisible by both 3 and 5.

(1) The units digit of a is 9 --> \(a^3-a=(a-1)a(a+1)\) --> out of 3 consecutive integers ((a-1), a, and (a+1)), one must be divisible by 3 and as the units digit of a is 9, then the units digit of a+1 is 0, so a+1 is divisible by 5. Thus a^3-a is divisible by 15. Sufficient.

(2) The tens digit of a is 3. If a=30, then the answer is YES but if a=32 ((a-1)a(a+1)=31*32*33), then the answer is NO. Not sufficient.

Answer: A.
_________________

New to the Math Forum?
Please read this: 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?
Extra-hard Quant Tests with Brilliant Analytics

Current Student
avatar
Joined: 21 Oct 2013
Posts: 193
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Re: If a is a positive integer and 20 < a < 100, is a^3 − a [#permalink]

Show Tags

New post 04 Mar 2014, 04:08
(1) units digit of a is 9. If you raise 9 to some power, it repeats this pattern: 9^1=9 9^2= 81 9^3 =...9. Hence, if we raise a number with the units digit 9 to the power of 3, the outcome will also have the units digit of 9. If we then substract the number with the units digit 9, the outcome will have the units digit 0. Hence div. by 15, SUFF.

(2) Tens digit a three: It's thus 31,32,33...or 39. 31^3-31 would be div. by 15, 32^3 - 32 not. IS.

Answer A.
Senior Manager
Senior Manager
avatar
Joined: 20 Dec 2013
Posts: 267
Location: India
Re: If a is a positive integer and 20 < a < 100, is a^3 − a [#permalink]

Show Tags

New post 04 Mar 2014, 05:26
From S1:We can infer that a^3-a=(a-1)*a*(a+1) which are 3 consecutive integers.So they're always divisible by 3 in the range of 'a' given.We just need to prove that any one or more of these will have 5 as a factor too.
S1 gives that 'a' ends with 9 so (a+1) will end with 0.always div by 5.Hence suff.

From S2:we get that 'a' will be in the range of 30s.We could consider 2 simple egs. (30,31,32)-Ans Yes.
While (31,32,33)-And No.Not sufficient.

Option A.

Posted from my mobile device
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 15956
Premium Member
Re: If a is a positive integer and 20 < a < 100, is a^3 − a [#permalink]

Show Tags

New post 19 Mar 2015, 12:14
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

BSchool Forum Moderator
User avatar
P
Joined: 12 Aug 2015
Posts: 2185
GMAT ToolKit User Premium Member CAT Tests
Re: If a is a positive integer and 20 < a < 100, is a^3 − a [#permalink]

Show Tags

New post 15 Mar 2016, 10:21
Here If we write doen A^3-A as A (A+1)(A-1) => we can say that A is sufficient
remember we need to check only 3 values for the pattern of 3
hence 39=> yes
49=> yes
59=> yes
hence A
statement 2 can be discarded as for 39 => yes
else for 32 => NO
_________________

Give me a hell yeah ...!!!!!

Re: If a is a positive integer and 20 < a < 100, is a^3 − a   [#permalink] 15 Mar 2016, 10:21
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic Is integer x<−20? zxcvbnmas 1 06 Feb 2016, 22:17
5 Experts publish their posts in the topic If n is an integer and 100 < n <200, what is the value of n? RadhaKrishnan 9 05 Oct 2016, 23:03
1 Experts publish their posts in the topic The positive integers are such that p < q r < s < hussi9 3 20 May 2011, 06:32
6 Experts publish their posts in the topic If n is an integer and 100 < n < 200, what is the value amitjash 11 23 Feb 2017, 07:02
If n is an integer and 100 < n <200, what is the value kirankp 2 01 Jan 2010, 17:37
Display posts from previous: Sort by

If a is a positive integer and 20 < a < 100, is a^3 − a

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.