If a, b, and c are consecutive integers and 0

Question

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.

chetan2u · Accepted Answer

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 because both are even and one of a or c will surely be a multiple of 4....ans will be YES
numbers can be 2a, 2a+1, 2a+2....product = 2a*(2a+1)*2(a+1)=4*a*(a+1)*(2a+1)...one of a or a+1 will be even. 
B) a and c are ODD and b is even.. if b is multiple of 8.. YES otherwise NO 
2a-1,2a,2a+1.....if a is a multiple of 4, 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

niks18 · Answer

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

Manbarasan · Answer

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

analuisa · Answer

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

rahul16singh28 · Answer

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.

chetan2u · Answer

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

KrishnakumarKA1 · Answer

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.

Izzyjolly · Answer

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

Archit3110 · Answer

given a, b, c are consecutive integers ;

#1 product ac is even ; so they will be in 2^3 least value eg 2<3<2^2 ; 2^2<5<2*3 ; so always yes

#2 product bc is multiple of 4 ; 2,3,4 ; yes ; 3,4,5 ; no insufficient ;

option A is sufficient

ArindamLucky · Answer

St 1 will include all sets where a and c both are even like
(2,3,4) (4,5,6) and not like (7,8,9)

So it helps

St 2

For st 2 one set can be (4,5,6) this fulfils 1 but breaks st2 hence insufficient

Posted from my mobile device

Basshead · Answer

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

Three consecutive integers can be even * odd * even or odd * even * odd. If a = even, then product abc will be a multiple of 8.

(1) The product ac is even.

This statement tells us even * odd * even. SUFFICIENT.

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

Lets test numbers:
a = 2, b = 3, c = 4; multiple of 8
a = 3, b = 4, c = 5; not multiple of 8

INSUFFICIENT.

Answer is A.

Hoozan · Answer

Similar question: https://gmatclub.com/forum/a-b-c-are-co ... fl=similar

ScottTargetTestPrep · Answer

Solution:

We need to determine whether the product abc is a multiple of 8, given that a, b, and c are consecutive integers. 
If a is even, then abc is a multiple of 8 since a is a multiple of 4 and c is a multiple of 2, or vice versa. 
If a is odd, then b must be a multiple of 8 in order for abc to be a multiple of 8.

Statement One Alone:

Since ac is even, either a or c is even. However, since a, b and c are consecutive integers, then ac is even means both a and c are even. From our stem analysis, we see that ac itself is a multiple of 8 and hence abc is a multiple of 8. Statement one alone is sufficient.

Statement Two Alone:

This is not sufficient. For example, if bc = 12 with c = 4, then abc = 2 x 3 x 4 = 24 is a multiple of 8. However, if bc = 20 with b = 4, then abc = 3 x 4 x 5 = 60 is not a multiple of 8.

Answer: A

DUMDUM21 · Answer

I did a silly mistake in this one. solve 1 and then solve 2 separately before combining them and save yourself from silly mistakes.

bumpbot · Answer

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

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