Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 19 Jul 2019, 13:51

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

If a, b, and c are consecutive integers and 0 < a < b < c, is the prod

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Board of Directors
User avatar
D
Joined: 01 Sep 2010
Posts: 3421
If a, b, and c are consecutive integers and 0 < a < b < c, is the prod  [#permalink]

Show Tags

New post 27 Jul 2017, 08:18
1
Top Contributor
21
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

51% (02:00) correct 49% (01:55) wrong based on 713 sessions

HideShow timer Statistics


If a, b, and c are consecutive integers and 0 < a < b < c, is the product abc a multiple of 8 ?

(1) The product ac is even.

(2) The product bc is a multiple of 4.

_________________
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7764
If a, b, and c are consecutive integers and 0 < a < b < c, is the prod  [#permalink]

Show Tags

New post 27 Jul 2017, 08:31
2
3
carcass wrote:
If a, b, and c are consecutive integers and 0 < a < b < c, is the product abc a multiple of 8 ?

(1) The product ac is even.

(2) The product bc is a multiple of 4.



hi,

If a, b, and c are consecutive integers and 0 < a < b < c, is the product abc a multiple of 8
TWO cases..
A) a and c are even AND b is ODD.... abc will always be multiple of 8 or rather 24.. ans will be YES
B) a and c are ODD and b is even.. if b is multiple of 8.. YES otherwise NO


lets see the statements
(1) The product ac is even.
this MEANS a and c are even..
falls under category A above..
always YES
sufficient

(2) The product bc is a multiple of 4

either b is multiple of 4, ans can be YES or NO case B
OR c is multiple of 4, ans will be YES.. case A
different answers possible
insuff

A
_________________
General Discussion
Intern
Intern
avatar
B
Joined: 26 Mar 2017
Posts: 17
Location: India
Schools: Great Lakes '19
GMAT 1: 580 Q47 V23
GPA: 3.1
Re: If a, b, and c are consecutive integers and 0 < a < b < c, is the prod  [#permalink]

Show Tags

New post 27 Jul 2017, 08:34
1
I Think answer is A

Statement 1:
ac is even -> a and c are even and b is odd, minimum possible values of abc is 2*3*4.
Sufficient

Statement 2:
bc multiple of 4 --> b can be 4.. c can be 5.... so a can be 3, which gives abc=60
not sufficient

Answer A
Intern
Intern
avatar
Joined: 28 Oct 2017
Posts: 2
Re: If a, b, and c are consecutive integers and 0 < a < b < c, is the prod  [#permalink]

Show Tags

New post 01 Dec 2017, 15:58
I don't get why a and c are even AND b is ODD.... abc will always be multiple of 8 or rather 24, could you explain me please
Retired Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1196
Location: India
GPA: 3.82
GMAT ToolKit User Reviews Badge
Re: If a, b, and c are consecutive integers and 0 < a < b < c, is the prod  [#permalink]

Show Tags

New post 01 Dec 2017, 20:38
analuisa wrote:
I don't get why a and c are even AND b is ODD.... abc will always be multiple of 8 or rather 24, could you explain me please


Hi analuisa

as the numbers are consecutive, so \(a\), \(b\), \(c\) can take two options -

Case 1: Even, Odd, Even OR

Case 2: Odd, Even, Odd

Statement 1: as \(ac\) is even, so it has to be Case 1

Now let \(a=2k\) (even number) so \(b=2k+1\) and \(c=2k+2=2(k+1)\), where \(k\) is any number greater than \(0\) (because \(0<a<b<c\))

Hence \(ac=2k*2(k+1)=4k(k+1)\)

so if \(k\) is odd then \(k+1=even\), hence \(4k(k+1)\) will be a multiple of \(8\)

if \(k\) is even then \(4k\) will be a multiple of \(8\). Therefore \(abc\) is a multiple of \(8\) because \(ac\) is a multiple of \(8\). Sufficient

Statement 2: \(bc\) is a multiple of \(4\). so it could be multiple of \(8\) such as \(16,24,32\) etc. or it could not be a multiple of \(8\) such as \(20, 28\) etc.. Insufficient

Option A
Director
Director
avatar
P
Joined: 31 Jul 2017
Posts: 515
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: If a, b, and c are consecutive integers and 0 < a < b < c, is the prod  [#permalink]

Show Tags

New post 01 Dec 2017, 21:29
1
carcass wrote:
If a, b, and c are consecutive integers and 0 < a < b < c, is the product abc a multiple of 8 ?

(1) The product ac is even.

(2) The product bc is a multiple of 4.


The Best would be to plug in by numbers.

Let b = n, a = n-1, c = n+1

Stmnt 1: ac = even, \(n^2\) - 1 =even, Here n can be only a odd number starting from 3,5,7,9,11 etc.. So abc will be Divisible by 8.
Stmnt 2: n(n+1) = 4m.. Here, n can be 3,4,7,8,9,11,13,14.. etc. when n = 3, abc Divisible by 8 but n= 4, abc not divisible by 8.

Hope this Helps.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7764
Re: If a, b, and c are consecutive integers and 0 < a < b < c, is the prod  [#permalink]

Show Tags

New post 01 Dec 2017, 21:48
1
analuisa wrote:
I don't get why a and c are even AND b is ODD.... abc will always be multiple of 8 or rather 24, could you explain me please


Hi...
Three consecutive integers and two even means even, odd, even...
Now since three are consecutive, one of them would surely be a MULTIPLE of 3.
Two of them even means one will be MULTIPLE of 2 and other will be MULTIPLE of atleast 4 so product will be MULTIPLE of atleast 3*2*4=24
_________________
Director
Director
User avatar
S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 541
Location: India
If a, b, and c are consecutive integers and 0 < a < b < c, is the prod  [#permalink]

Show Tags

New post 23 Aug 2018, 23:36
Hi,

Another way to solve this question is trying out numbers.

Always try out few numbers and understand the pattern of the answers.

Here in the question, it’s given, a, b and c are consecutive integers and also positive (0 < a < b < c),

Question: Is product abc a multiple of 8 ?

To be a multiple of 8 , it has to have minimum of three 2’s because of 8 can be written in prime factorization as 2^3

Now, lets try out some numbers,

a, b and c minimum has to be 1,2 and 3. Here the product abc is 6. Not a multiple of 8.

If a, b and c is 2,3 and 4. Then the product abc is 24. Multiple of 8.

Okay, then lets check the next set.

If a,b and c is 3,4 and 5. Then the product abc is 60. Not a multiple of 8.

If a, b and c is 4,5 and 6. Then the product abc is 120. Multiple of 8.

Note 1:

We can note from the above pattern, everytime if a and c is even, then the product abc is a multiple of 8(Infact 24).

Note 2:

Also, if a and c are odd, then the product abc need not be a multiple of 8 but it is an even number.

Statement I is sufficient.

Given, the product ac is even.


Since, a, b and c are consecutive integers. If ac is even, then both a and c has to be even.

So, from the note 1, we can see that product is a multiple of 8.

So sufficient.

Statement II is insufficient.

Given, the product bc is a multiple of 4.


bc is a multiple of 4 means, either b is a multiple of 4 and c is odd or b is odd and c is a multiple of 4.

For example,

If a,b and c is 3,4 and 5. Then the product abc is 60. Not a multiple of 8. But here 4*5 = 20 is a multiple of 4.

If a, b and c is 2,3 and 4. Then the product abc is 24. Multiple of 8. Here 3*4= 12 also a multiple of 4.

So it is insufficient.

So the answer is A.

I alone sufficient.
_________________
GMAT Mentors
Image
Manager
Manager
User avatar
S
Joined: 06 Nov 2016
Posts: 60
Location: Viet Nam
Concentration: Strategy, International Business
GPA: 3.54
Re: If a, b, and c are consecutive integers and 0 < a < b < c, is the prod  [#permalink]

Show Tags

New post 25 Aug 2018, 21:08
1
carcass wrote:
If a, b, and c are consecutive integers and 0 < a < b < c, is the product abc a multiple of 8 ?

(1) The product ac is even.

(2) The product bc is a multiple of 4.


a, b, and c are consecutive integers and 0 < a < b < c --> b=a+1; c=a+2
Question: Is \(a(a+1)(a+2)\) a multiple of 8?

(1) The product \(ac\) is even. -> \(a(a+2)\) is even. Since \(a\) and \(a+2\) are either both odd or both even, we can conclude that \(a\) and \(a+2\) are both even in this case. The product of two consecutive even numbers is a multiple of 8, so \(a(a+2)\) is a multiple of 8. --> \(a(a+1)(a+2)\) is a multiple of 8. --> Sufficient.

(2) The product \(bc\) is a multiple of 4 -> (a+1)(a+2) is multiple of 4.
    If a=2 then a(a+1)(a+2)=2*3*4 -> YES
    If a=3 then a(a+1)(a+2)=3*4*5 -> NO
-> Statement 2 alone is not sufficient.

Answer A
_________________
GMAT Club Bot
Re: If a, b, and c are consecutive integers and 0 < a < b < c, is the prod   [#permalink] 25 Aug 2018, 21:08
Display posts from previous: Sort by

If a, b, and c are consecutive integers and 0 < a < b < c, is the prod

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne