Three consecutive integers are selected from the integers 1 to 50, inc

Question

Three consecutive integers are selected from the integers 1 to 50, inclusive. What is the sum of the remainders that result when each of the three integers is divided by x ?

(1) When the greatest of the consecutive integers is divided by x, the remainder is 0.

(2) When the least of the consecutive integers is divided by x, the remainder is 1.

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JerryAtDreamScore · Answer

Statement 1 Alone:

We don't have much information, insufficient.

Statement 2 Alone:

The remainder of the middle integer divided by x could be 2 or 0. Insufficient.

Both Statements Combined:

The remainder of the middle integer divided by x could be 2 or 0, while the remainder from statement 1 is 0. We cannot have consecutive integers both having a remainder of 0 as that would mean x = 1. Thus we must have the remainder of 2 for the middle integer. Then the sum of remainders must be 3. (We can also infer x = 3) Sufficient.

Answer: C

nikhilvsh · Answer

This is what I did -

question analysis -

remainder r, needs to be 0<=r<x,

Now,
St 1 - If the largest number has remainder 0, the middle number will give a remainder of x-1, and the smallest number will give a remainder of x-2.

Since we do not know x, we do not know the value of the sum, 2x-3.

St2 - least number gives remainder 1.
what if x=2? the remainders would be 1 0 1. If x>2, remainders would be 1 2 3, if x=3, remainders would be 1 2 0. So St 2 is not sufficient.

St1 + St2

x-2=1, so x=3. And sum of the remainders, 2x-3 = 3.

ScottTargetTestPrep · Answer

Question Stem Analysis:

We choose three consecutive integers between 1 and 50, inclusive, and we need to determine the sum of the remainders when each integer is divided by x. No other information is provided in the question stem.

Statement One Alone:

\Rightarrow  When the greatest of the consecutive integers is divided by x, the remainder is 0.

If x = 1, then the remainder when each of the integer is divided by x is 0. Thus, the answer is 0 + 0 + 0 = 0 in this case.

If x = 3, then the remainder when the middle integer is divided by x is 2, and the remainder when the smallest integer is divided by x is 1. Thus, the answer is 1 + 2 + 0 = 3 in this case.

Since there are more than one possible answers, statement one alone is not sufficient.

Eliminate answer choices A and D.

Statement Two Alone:

\Rightarrow  When the least of the consecutive integers is divided by x, the remainder is 1.

If x = 3, then the remainder when the middle integer is divided by x is 2, and the remainder when the largest integer is divided by x is 0. In this case, the answer is 1 + 2 + 0 = 3.

If x > 3, then the remainder when the middle integer is divided by x is 2, and the remainder when the largest integer is divided by x is 3. In this case, the answer is 1 + 2 + 3 = 6.

Since there are more than one possible answers, statement two alone is not sufficient.

Eliminate answer choice B.

Statements One and Two Together:

If the the remainder when the smallest integer is divided by x is 1 and the remainder when the largest integer is divided by x is 0, then the remainder when the middle integer is divided by x can only equal 2. Thus, the sum of the three remainders is 1 + 2 + 0 = 3.

Statements one and two together are sufficient.

Answer: C

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Three consecutive integers are selected from the integers 1 to 50, inc

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