Are x, y, and z consecutive integers?

Question

(1) The remainder when x + y + z is divided by 3 is 2.
(2) The remainder when xyz is divided by 3 is 1.

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abhishekdadarwal2009 · Answer

IMO D.

Sol:

1.every set of consecutive 3 numbers will be a multiple of 3, example-1+2+3=6 so we will not have 2 as a remainder.
Similarly even if one of the number is 0 then we will have 0 +1+2=3 div by 3 give no remainder. so this option tells us that x,y,z are not consecutive.

2. xyz div by 3 gives remainder 1, so again 1*2*3=6, similarly this will always be a multiple of 3 , and in case of zero our case doesn't stand, so we know that x,y,z are not consecutive.

Both options tell us that the x,y and z are not consecutive.

KaramveerBakshi · Answer

To find: If x,y, and z are consecutive integers.

Solving:

Statements :

(1) x+y+z, when divided by 3, gives the remainder 2.
A - Observation: For any set of 3 consecutive integers, the sum is always divisible by 3. That means the remainder is always 0.
Since the remainder is given as 2; x, y, and z cannot be consecutive integers.

Are x, y, and z consecutive integers? NO.

Sufficient.

(2) Xyz, when divided by 3, give the remainder as 1.
A - Observation: For any set of 3 consecutive integers, the product is always divisible by 3. That means the remainder is always 0.
Since the remainder is given as 1; x, y, and z cannot be consecutive integers.

Are x, y, and z consecutive integers? NO.

Sufficient.

Both statements are independently Sufficient.

Therefore,  Answer (D)

suchita2409 · Answer

The sum or product of three consecutive integers is always divisible by 3.

Stmt 1) says x+y+z is not divisible by 3 as it has remainder 2.
So they are not consecutive.
Sufficient.

Stmt 2) says xyz is not divisible by 3 as it gives remainder 1.
So they arent consecutive.
Sufficient.

D .

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v12345 · Answer

Statement 1: Sufficient 
Addition of three consecutive integers is always divisible by 3 by observation.
But here it leaves remainder of 2.
Hence, x, y, and z are not consecutive integers.
 Statement 2: Sufficient 
Multiplication of three consecutive integers is always divisible by 3 by observation.
But here it leaves remainder of 1.
Hence, x, y, and z are not consecutive integers.
Hence, OA is (D).

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Are x, y, and z consecutive integers?

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Are x, y, and z consecutive integers?

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