If b is the product of three consecutive positive integers c

Question

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,
(2) c is odd.

tkarthi4u · Accepted Answer

given

b = c * c+1 * c+2 is B a mutiple of 24

stmt 1 :

b is a mutiple of 3

when c =1 b =6 not a mutiple of 24
when c =2 b= 24 yes mutiple.

Not sufficient.

stmt 2 :

c is odd 
when c =1 not a mutiple
when c = 7 b = 504 yes mutiple of 24

Not sufficient.

Togther Not sufficient . So it is E.

Good to remember this rule.

The product of 3 consecutive positive integer whose first number is even is divisible by 24.

IanStewart · Answer

I'm not sure where you got the OA from here, but the answer certainly is not A. When you multiply three consecutive integers, one of those integers must be a multiple of 3, so b is always going to be a multiple of 3; Statement 1 tells us nothing useful at all. The answer here is E; if c = 1, then b = 1*2*3, and b is not a multiple of 24, whereas if c=7, then b=7*8*9 = 7*24*3, and b is a multiple of 24.

fluke · Answer

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"

Spidy001 · Answer

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.

doe007 · Answer

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.

jlgdr · Answer

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)

reto · Answer

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

Harley1980 · Answer

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?"

Mo2men · Answer

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

stonecold · Answer

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

Mo2men · 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

Amureabc · Answer

whoever posted this question is wrong.

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

Bunuel · Answer

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

satya2029 · Answer

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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If b is the product of three consecutive positive integers c

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