If t is the sum of three consecutive positive integers, is t a

Question

If t is the sum of three consecutive positive integers, is t a multiple of 24?

(1) The smallest of the 3 integers is even. 
(2) t is a multiple of 3.

chetan2u · Answer

Hi  Bunuel ,
although this too can be a question but looking at t as a multiple of 24, I am sure you meant  product and not sum of three consecutive positive integers

Bunuel · Answer

The question in the source says "sum", not "product".

chetan2u · Answer

Hi,
t is the sum of three consecutive positive integers,...
only one thing is for sure that the sum will be a multiple of 3,  since one number will leave a remainder of 0, next 1 and the third one 2... 
lets check the statement..
1) The smallest of the 3 integers is even..
this tells us that the integers are even, odd,even..
therefore the sum will be odd...
and no odd number can be a multiple of 24..
so ans to Q is NO and suff...

2) t i sa multiple of 3..
nothing new.. ie is already known.. insuff

ans A

asethi · Answer

(1) The smallest of the 3 integers is even. 
 2,3,4...Suffcient
(2) t is a multiple of 3.
 1,2,3 or 2,3,4 ....Insuff.

Ans:A

FightToSurvive · Answer

Hi,

I do understand that you have read the question wrong " its the sum of three consecutive integers NOT product"

In any case, the answer will be A because of the following logic:

St (1) says " smallest of the 3 integers is even" that means it must be even,odd,even which gives odd as a result and we know that 24 doesnt give odd as a multiple. Hence A is sufficient.
St (2) says, t is a multiple of 3 which doesnt help. Hence Not sufficient.

Mo2men · Answer

If t is the sum of three consecutive positive integers, is t a multiple of 24?

Let the three integers x, x+1, x+2

t=x + x+1 + x+2=3x + 3= 3 (x+1)

(1) The smallest of the 3 integers is even.

x= even which means = 3 (even +1) = 3 * odd =odd. Therefore, t can't be multiple of 24 as it can't contain any even factor.

Sufficient

(2) t is a multiple of 3.

From our previous work above, we know the it is already multiple of 3 but no info about x.

Let x = 0.........t = 3 *1 =3 is NOT multiple of 24

Let x= 7........ t= 3 * 8=24 is multiple of 24

Insufficient

Answer: A

siddharthkapoor · Answer

(1) t=Even+odd+even=Odd
No odd number is a multiple of 24, which is an even number. 
Thus, sufficient.

(2) t=3k
So, t=3,6,9,12,....24.27, and so on.
As we can see, t can or can not be a multiple of 24.
Thus, insufficient.

Therefore, answer is option A.

dimri10 · Answer

T=X-1+X+X+1=3X , so the stem is T=3X
1. the smallest number is EVEN, so x-1 is even and x is ODD.

3*ODD will always yield an odd number, so it can not be multiple of 24 . Sufficient

2. T=3K and from the stem T=3X
3k=3t so if k=t=8, ie. then t is a multiple of 24 (3*8) 
but if k=t=7 or 9 , i.e then t is not (3*7=21. 3*9=27) not sufficient.
so A

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If t is the sum of three consecutive positive integers, is t a

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If t is the sum of three consecutive positive integers, is t a

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