Is the integer r divisible by 3?

A

1x2x3x4 or 4x5x6x7 or ...
every 4 consecutive integers contains at least 1 number that is divisible by 3

statement 2: r could be 3 or r could be 5
insuff

Hi metskj127,

You are right about the possibility of 4 integers being 0,1,2,3, in which case r = 0. The question statement asks us about r being divisible by 3 i.e. is the remainder 0 when r is divided by 3. If you divide 0 by 3, the remainder is 0.

Thus, even if r = 0, we can say that r is divisible by 3.

The takeaway from this can be " Zero is divisible by any integer i.e. every integer is a divisor of Zero" as zero divided by anything gives the remainder as zero.

Hope its clear!

Regards
Harsh
_________________

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

For Statement 1, why couldn't the 4 integers by 0, 1, 2, 3? In which case, r=0.

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

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
_________________

Not exactly sure about my approach, but how about:

(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

marvinsxntos But 12 is even and is divisible by 3.
24 is even and divisible by 3.

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.

Cancel Answers "A"/"D".

2) r < 25

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

Cancel Answer "B".

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

ANSWER E is correct

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



Posted from my mobile device

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
_________________

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.
_________________