Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Sep 2008
Posts: 102

If b is the product of three consecutive positive integers c
[#permalink]
Show Tags
18 Apr 2009, 20:43
Question Stats:
69% (01:19) correct 31% (01:28) wrong based on 385 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.




Senior Manager
Joined: 08 Jan 2009
Posts: 310

Re: multiple of 3 consecutive number..............
[#permalink]
Show Tags
19 Apr 2009, 03:16
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.




GMAT Tutor
Joined: 24 Jun 2008
Posts: 1345

Re: If b is the product of three consecutive positive integers
[#permalink]
Show Tags
04 Nov 2010, 16:24
tatane90 wrote: 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. 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.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Retired Moderator
Joined: 20 Dec 2010
Posts: 1879

Re: Number :DS
[#permalink]
Show Tags
01 Jun 2011, 09:51
pkmme wrote: 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. 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"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Director
Joined: 01 Feb 2011
Posts: 671

Re: Number :DS
[#permalink]
Show Tags
03 Jun 2011, 18:57
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.



Senior Manager
Joined: 16 Dec 2011
Posts: 368

Re: If b is the product of three consecutive positive integers
[#permalink]
Show Tags
26 Aug 2012, 07:31
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.



SVP
Joined: 06 Sep 2013
Posts: 1851
Concentration: Finance

Re: If b is the product of three consecutive positive integers
[#permalink]
Show Tags
06 Oct 2013, 11:00
milind1979 wrote: 24. 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. 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)



Retired Moderator
Joined: 29 Apr 2015
Posts: 862
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Re: If b is the product of three consecutive positive integers c
[#permalink]
Show Tags
14 Jul 2015, 13:02
milind1979 wrote: 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. 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
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.



Retired Moderator
Joined: 06 Jul 2014
Posts: 1248
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

If b is the product of three consecutive positive integers c
[#permalink]
Show Tags
14 Jul 2015, 13:41
reto wrote: milind1979 wrote: 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. 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?"
_________________
Simple way to always control time during the quant part. How to solve main idea questions without full understanding of RC. 660 (Q48, V33)  unpleasant surprise 740 (Q50, V40, IR3)  antidebrief



SVP
Joined: 26 Mar 2013
Posts: 1777

Re: If b is the product of three consecutive positive integers c
[#permalink]
Show Tags
14 Jul 2015, 14:51
reto wrote: milind1979 wrote: 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. 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 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 plugin 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



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2649

Re: If b is the product of three consecutive positive integers c
[#permalink]
Show Tags
16 Mar 2016, 05:44



SVP
Joined: 26 Mar 2013
Posts: 1777

If b is the product of three consecutive positive integers c
[#permalink]
Show Tags
13 Feb 2018, 03:16
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




If b is the product of three consecutive positive integers c &nbs
[#permalink]
13 Feb 2018, 03:16






