It is currently 17 Oct 2017, 21:20

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If t is a positive integer, can (t+2)(t-3) be evenly divided by 6?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Manager
Joined: 17 Oct 2016
Posts: 81

Kudos [?]: 33 [0], given: 17

Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38
GPA: 3.05
WE: Pharmaceuticals (Health Care)
If t is a positive integer, can (t+2)(t-3) be evenly divided by 6? [#permalink]

### Show Tags

12 Aug 2017, 03:33
00:00

Difficulty:

65% (hard)

Question Stats:

39% (01:57) correct 61% (02:02) wrong based on 31 sessions

### HideShow timer Statistics

If t is a positive integer, can (t+2)(t-3) be evenly divided by 6?

(1) 5(t^3 +1) is not divisible by 2.

(2) t is a 3-digit number, whose digits are consecutive integers.
[Reveal] Spoiler: OA

_________________

Sometimes you have to burn yourself to the ground before you can rise like a phoenix from the ashes.

Dr. Pratik

Kudos [?]: 33 [0], given: 17

Senior Manager
Joined: 06 Jul 2016
Posts: 412

Kudos [?]: 115 [0], given: 99

Location: Singapore
Concentration: Strategy, Finance
If t is a positive integer, can (t+2)(t-3) be evenly divided by 6? [#permalink]

### Show Tags

12 Aug 2017, 04:48
fitzpratik wrote:
If t is a positive integer, can (t+2)(t-3) be evenly divided by 6?

t > 0
Question is if (t+2)(t-3) are divisible by both 2 and 3?

Quote:
(1) 5(t^3 +1) is not divisible by 2.
(2) t is a 3-digit number, whose digits are consecutive integers.

1) 5($$t^3$$ + 1) ≠ 2n
=> t is even.
If t = 2, (t+2)(t-3) is not divisible by 6
If t = 4, (t+2)(t-3) is divisible by 6
Insufficient.

2) t = abc
where a, b, c are 3 consecutive integers
=> t = 123, 234, 345, 456,...
=> (t+2)(t-3) will always be divisible by 2 and 3, so it's divisible by 6.
=> (t-3) will always be a multiple of 3, as t is a multiple of 3.
=> and for all even integer values of t, (t+2) will be divisible by 2

Sufficient. B is the answer.
_________________

Put in the work, and that dream score is yours!

Kudos [?]: 115 [0], given: 99

Math Forum Moderator
Joined: 02 Aug 2009
Posts: 4967

Kudos [?]: 5455 [0], given: 112

Re: If t is a positive integer, can (t+2)(t-3) be evenly divided by 6? [#permalink]

### Show Tags

12 Aug 2017, 06:59
fitzpratik wrote:
If t is a positive integer, can (t+2)(t-3) be evenly divided by 6?

(1) 5(t^3 +1) is not divisible by 2.

(2) t is a 3-digit number, whose digits are consecutive integers.

Hi..

Let's analyze the main statement...
1) For div by 6, it should be div by both 2 and 3..
2) if t+2 is even T+2-2-2=t-2 should also be even.
3) But t-2 & t-3 should be consecutive integers.. so their product should be even
4) Now we know the product is MULTIPLE of 2
5) We have to check for div by 3!!!

Now let's see the statements..
1) $$5(t^3+1)$$ is NOT div by 2.
So $$t^3 +1$$ is ODD. Hence the is EVEN.
But we are looking for div by 3
Insufficient

2)T is a 3 digit number with consecutive numbers..
3 CONSECUTIVE numbers when added are always div by 3
So t is div by 3 and hence t-3 will also be div by 3.
Now we know product (t-2)(t-3) is div by 3
So SUFFICIENT

B
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5455 [0], given: 112

Re: If t is a positive integer, can (t+2)(t-3) be evenly divided by 6?   [#permalink] 12 Aug 2017, 06:59
Display posts from previous: Sort by

# If t is a positive integer, can (t+2)(t-3) be evenly divided by 6?

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.