Last visit was: 16 Sep 2024, 21:44 It is currently 16 Sep 2024, 21:44
Toolkit
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

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.

# Is the integer r divisible by 3?

SORT BY:
Tags:
Show Tags
Hide Tags
Senior Manager
Joined: 01 May 2007
Posts: 484
Own Kudos [?]: 1470 [38]
Given Kudos: 0
Senior Manager
Joined: 23 Sep 2007
Posts: 394
Own Kudos [?]: 1546 [7]
Given Kudos: 0
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3709
Own Kudos [?]: 17779 [5]
Given Kudos: 165
General Discussion
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21832
Own Kudos [?]: 11872 [3]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Is the integer r divisible by 3? [#permalink]
1
Kudos
2
Bookmarks
Hi metskj127,

The GMAT will sometimes test you on concepts that you know, but in ways that you're not used to thinking about (as is the case here).

This specific concept can appear in other ways. When most people think of "multiples", they only think of POSITIVE multiples.

eg. Multiples of 10: 10, 20, 30, 40, etc.

But 10x0 is ALSO a multiple of 10, so the above list should INCLUDE the number 0. Don't be surprised if this exact issue shows up in one of your DS questions on Test Day...

GMAT assassins aren't born, they're made,
Rich
Senior Manager
Joined: 05 Jan 2008
Posts: 352
Own Kudos [?]: 3754 [1]
Given Kudos: 0
Re: Is the integer r divisible by 3? [#permalink]
1
Kudos
A

you atleast have one integer divisible by 3 for every 3 consecutive numbers, the question says 4 consecutive numbers thus A

Stmt-2 does not provide any info thus insufficient
Intern
Joined: 14 Mar 2015
Posts: 4
Own Kudos [?]: [0]
Given Kudos: 0
Re: Is the integer r divisible by 3? [#permalink]
jimmyjamesdonkey
Is the integer r divisible by 3?

(1) r is the product of 4 consecutive integers.
(2) r < 25

For Statement 1, why couldn't the 4 integers by 0, 1, 2, 3? In which case, r=0.
Director
Joined: 26 Oct 2016
Posts: 506
Own Kudos [?]: 3426 [0]
Given Kudos: 877
Location: United States
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE:Education (Education)
Re: Is the integer r divisible by 3? [#permalink]
a) r is the product of 4 consecutive positive integers.

Multiples of 3 are 3,6,9,12...
any set of 4 positive integers will have a multiple of 3.

say 1,2,3,4 has 3
8,9,10,11 has 9(a multiple of 3)

Hence a) alone is sufficient

b) r < 25
It doesn't matter if r is less than 25 or not.

Hence A is the correct choice
Intern
Joined: 06 Jan 2021
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 0
Re: Is the integer r divisible by 3? [#permalink]

(1) four consecutive integers -> 2 odd integers & 2 even integers -> product and therefore r is even -> r can't be devisible by 3 since it's even -> SUFFICIENT
Intern
Joined: 06 May 2021
Posts: 22
Own Kudos [?]: 5 [0]
Given Kudos: 12
Location: United States
GMAT 1: 640 Q41 V37
GMAT 2: 710 Q48 V39
GPA: 3.94
Re: Is the integer r divisible by 3? [#permalink]
marvinsxntos But 12 is even and is divisible by 3.
24 is even and divisible by 3.

marvinsxntos

(1) four consecutive integers -> 2 odd integers & 2 even integers -> product and therefore r is even -> r can't be devisible by 3 since it's even -> SUFFICIENT
Intern
Joined: 15 Mar 2021
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 16
GMAT 1: 710 Q48 V39
GPA: 3.98
Re: Is the integer r divisible by 3? [#permalink]
Can someone help out here, please? I keep seeing Answer A is sufficient, but I'm not getting that in my execution of the problem:

Q: Is "R" divisible by 3?

1) (1) r is the product of 4 consecutive integers.

Ex. 1: 0, 1, 2, 3; Product is 0; suff.

Ex. 2: 1, 2, 3, 4; Product is 24; suff.

Ex. 3: -2, -1, 0, 1; Product is 2; insuff.

2) r < 25

Ex. 2 and Ex. 3 above fit this criterion, therefore insuff.

3) Together, both provide a product less than 25, abiding by consecutive integers, with a result of "maybe", therefore "insufficient" together.

Intern
Joined: 06 May 2021
Posts: 22
Own Kudos [?]: 5 [0]
Given Kudos: 12
Location: United States
GMAT 1: 640 Q41 V37
GMAT 2: 710 Q48 V39
GPA: 3.94
Is the integer r divisible by 3? [#permalink]
In your example 3, the correct product is zero (-2*-1*1*0) since anything times zero is zero. Therefore since zero is divisible by 3, example 3 is sufficient as well.
GMATJudoka

GMATJudoka
Can someone help out here, please? I keep seeing Answer A is sufficient, but I'm not getting that in my execution of the problem:

Q: Is "R" divisible by 3?

1) (1) r is the product of 4 consecutive integers.

Ex. 1: 0, 1, 2, 3; Product is 0; suff.

Ex. 2: 1, 2, 3, 4; Product is 24; suff.

Ex. 3: -2, -1, 0, 1; Product is 2; insuff.

2) r < 25

Ex. 2 and Ex. 3 above fit this criterion, therefore insuff.

3) Together, both provide a product less than 25, abiding by consecutive integers, with a result of "maybe", therefore "insufficient" together.

Posted from my mobile device
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4127
Own Kudos [?]: 9620 [0]
Given Kudos: 96
Q51  V47
Is the integer r divisible by 3? [#permalink]
GMATJudoka
Ex. 3: -2, -1, 0, 1; Product is 2; insuff.

The product here is 0, not 2, so that's why your calculations led you to an incorrect answer.

In general, the product of n consecutive integers is always divisible by n!, so here, the product of our 4 consecutive integers is automatically divisible by 4! = 24, and in particular is divisible by 3, so Statement 1 is sufficient. There is no reason to consider zero separately.

There are two posts above that carry an 'Expert' tag that might be misleading, so to clarify:

- one post says "zero is divisible by any integer", which is definitely true if you rephrase it to say "zero is divisible by any positive integer", but is only true, as written, if you use a definition of divisibility that is not universally accepted: by some definitions, zero is divisible by zero, and by some definitions, zero is not divisible by zero. For GMAT purposes, it's best just to think: "you can never divide by zero, so nothing is divisible by zero", though that's not an issue you'll really ever need to worry about regardless.

- another post says "don't be surprised if this exact issue shows up... on test day." I'm not even sure what that means, but there is no reason whatsoever to be concerned about "issues" around zero in divisibility questions of this type. For one thing, zero follows all of the divisibility rules followed by any other positive numbers - for example, the product of n consecutive integers is always divisible by n!, whether zero is allowed to be among those integers or not. Or as another example, "multiples of 7 are 7 apart" is still true when you include zero among your multiples of seven. So you're generally just wasting time if you consider zero as a separate case in questions like this. But there's another reason you should be especially surprised if this "exact issue shows up on test day": almost all GMAT divisibility questions are restricted to positive integers only. It's normally not even permitted for any of your numbers to be zero.

While there are many unrealistic prep company questions that test certain exceptions about zero, it is almost impossible to find any official questions that do. Prep materials that encourage test takers to spend time separating out zero as a special case in questions like the one in this thread are just using up a test taker's time during a test, time that could be spent more profitably on a different question.

Posted from my mobile device
Non-Human User
Joined: 09 Sep 2013
Posts: 34880
Own Kudos [?]: 881 [0]
Given Kudos: 0
Re: Is the integer r divisible by 3? [#permalink]
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.
Re: Is the integer r divisible by 3? [#permalink]
Moderator:
Math Expert
95555 posts