If b is the product of three consecutive positive integers c

Product of any 3 consecutive numbers will be a multiple of 3;
If c=1; b=1*2*3=6; b is not a multiple of 24.
If c=23, b=23*24*25; b is a multiple of 24.
Not Sufficient.

Ans: "E"

b = c(c+1)(c+2)

1. Not sufficient

1 2 3 product is not a multiple of 24
2 3 4 product is a multiple of 24

2. Not sufficient

1 2 3 product is not a multiple of 24
3 4 5 product is not a multiple of 24

23 24 25 product is a multiple of 24

together
all the examples considered in 2 can be considered (As product of 3 consecutive integers will always be a multiple of 3) . So not sufficient.

Answer is E.

Product of 3 consecutive integers will always be divisible by 3!=6. Statement 1 does not provide any additional information, and definitely it is not sufficient. When taken both the statements together, b will not be multiple of 24 for c = 1, and b will be multiple of 24 for c = 23. So, together not sufficient. Answer will be E.

The product of three consecutive consecutive integers will ALWAYS be divisible by 3!. Hence will always have 3 as one of its factors.
Statement (1) is useles.

Now for being a multiple of 24 we need an 8, given that we know we'll get a 3 already. So if c is odd then c+1 must be a multiple of 8. If c is even then 'c' must be a multiple of 4, so that (c)*(c+2) = 8

Statement (2) c is odd. Well this is the first case right? But we don't know if C+1 is a multiple of 8. So Insuff

(1) and (2) together. Statement 1 doesn't help at all so we're stuck in the same spot. Hence (E)

Dear Community

How do not run the risk that when testing both statements together (multiple of 3 and c is odd):

1 * 2 * 3 = 6 > Answer NO
3 * 4 * 5 = 60 > Answer NO
5 * 6 * 7 = 210 > Answer NO

If one is under time pressure, one would stop here and come to the conclusion that together 1+2 are sufficient. However its not.

Is it just about plugging in one more > 7 * 8 * 9 or is there a way, which tells me that i should not stop after three plug in's?

Thanks

Hello reto. Picking numbers is a very bad way of solution such tasks.
You should remember that product of 3 consecutive integers will be always divisible on 3 and always contain at least 1 even integer (or 2 even integers)

So 1 statement is just the same information that we already know from the tasks: b is multiple of 3 because it is a product of 3 cosecutive numbers
2 statement says to us that c = odd then c+1 = even and c+2 is again odd
So we can infer that b has 3 as a factor and 2 as a factor so it will be multiple of 6
But this all information that we have so we can't say if b will be divisible by 24.

By this approach you will be really sure that you found correct answer.
And with picking numbers you will be always has some hesitations: "What if I need to check some different numbers?"

Hi Reto,
When you try to plug numbers. You need to pick smart numbers that work. However, knowing some rules is really beneficial such as consecutive numbers rules. When I solve the problem by plunging numbers I will do the following ( I will detail my thoughts to help you):

Statement 1: b is a multiple of 3
C=1 ......> 1*2*3= 6 multiple of 3.........Answer to question NO
C=2.......> 2*3*4=24 multiple of 3 &24 Answer to question YES

Statement 1 is Insufficient.. then you can go to examine to statement 2. However, I would not use C=2 in my plug-in process because when you see Statement 2 it gives me impression (comes from practice) that you can focus your effort to look for other odd numbers. look to 24. it is easy to infer that any 3 consecutive number containing 24 will be multiple of 24 So choose C=23.......> 23*24*25 is multiple of 24... Answer to the question YES

So we reached same result Statement 1 is Insufficient with 2 odd numbers

Statement 2: c is odd.
When you look to you work above with C=1 & C=23. Statement 2 is Insufficient

Combining 1+2, C=odd number & multiple of 3, then look to your work above .........both are Ins.... Answer is E.

Another alternation is to start with Statement 2 with smart numbers also near 24 and then look into Statement 1.

I hope it helps

Here choose c=1 and c=23 to discard both the statements and we can easily say that E is the answer

If b is the product of three consecutive positive integers c, c + 1, and c + 2, is b a multiple of 24 ?

(1) b is a multiple of 3

Let c=1, c + 1= 2, c + 2 = 3...........B =3 ............Answer is NO

Let c=2, c + 1= 3, c + 2 = 4...........B =24 ............Answer is Yes

Insufficient

(2) c is odd

Let c=1, c + 1= 2, c + 2 = 3...........B =3 ............Answer is NO

Let c=7, c + 1= 8, c + 2 = 9...........B =No need to calculate is has (8*3)............Answer is Yes

Insufficient

Combine 1& 2

Use 2 cases above.....No conclusive answer

Insufficient

Answer: E

whoever posted this question is wrong.

statement one is: b is a multiple of 8 not 3

That question is here: https://gmatclub.com/forum/if-b-is-the- ... fl=similar

Product of three consecutive integers is always a multiple of !3
From 1
b=3*4*5 answer-NO
b=24*25*26-Yes
From 2
b=3*4*5- NO
b=25*26*27-yes
From 1 and 2
Yes and No
E:)

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