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Math Expert V
Joined: 02 Sep 2009
Posts: 58327
If t is the sum of three consecutive positive integers, is t a  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 60% (01:50) correct 40% (01:48) wrong based on 119 sessions

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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.

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Math Expert V
Joined: 02 Aug 2009
Posts: 7958
Re: If t is the sum of three consecutive positive integers, is t a  [#permalink]

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Bunuel wrote:
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.

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
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Math Expert V
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Posts: 58327
Re: If t is the sum of three consecutive positive integers, is t a  [#permalink]

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chetan2u wrote:
Bunuel wrote:
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.

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

The question in the source says "sum", not "product".
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Math Expert V
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Posts: 7958
Re: If t is the sum of three consecutive positive integers, is t a  [#permalink]

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1
Bunuel wrote:
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.

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
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Re: If t is the sum of three consecutive positive integers, is t a  [#permalink]

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(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
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Re: If t is the sum of three consecutive positive integers, is t a  [#permalink]

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asethi wrote:
(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

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.
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Re: If t is the sum of three consecutive positive integers, is t a  [#permalink]

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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

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Re: If t is the sum of three consecutive positive integers, is t a  [#permalink]

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Bunuel wrote:
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.

(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. Re: If t is the sum of three consecutive positive integers, is t a   [#permalink] 12 Oct 2019, 02:52
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