What Is The Sum Of 3 Consecutive Integers? GMAT Data Sufficiency

Question: What is the sum of 3 consecutive integers?

(1) The sum of the 3 integers is less than the greatest of the 3 integers.
(2) Of the 3 integers, the ratio of the least to the greatest is 3.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: (B)

Approach Solution : 1

Statement - 1 : The sum of the 3 integers is less than the greatest of the 3 integers

We can write, n+n+1+n+2 < n+2
=> 3n+3

Finally, 3n

Now plug in the values for n. (It is clear that positive integers are out of question, so let us begin with negative values)

When n =−1, we have −3<−2 (yes)
When n=−2, we have −6<−3 (yes)

We can note that there are two possibilities.

Therefore this statement is not sufficient.

Statement - 2 : Of the 3 integers, the ratio of the least to the greatest is 3

We can write that, n/n + 2 = 3
=> n = 3(n+2)
=> n = 3n+6
=> −2n = 6
=> n = −3

The process is complete and we have the first integer. And so we can write the rest as this is a consecutive series.

Therefore this statement is sufficient

Approach Solution : 2

Statement - 1 : The sum of the 3 integers is less than the greatest of the 3 integers

This statement is met by various sets of three consecutive integers. Here are two situations.

Scenario A :The numbers are {-1, 0, 1}. The sum in this instance is zero, and zero is smaller than the largest number in the set (1). The integers' sum equals zero, thus the answer to the target question is 0.

Scenario B: The figures are {2, 1, 0}. Since -3 is less than the largest number in the set, the sum in this instance is -3. The answer to the target question is -3 because the total number of integers.

With this we cannot have a certain answer to the target question.

Therefore this statement is not sufficient.

Statement - 2 : Of the 3 integers, the ratio of the least to the greatest is 3

Allow x to be the smallest number.
Thus, x + 1 equals the middle number.
And x + 2 equals the largest integer.

As an example, we can write, x/(x+2) = 3
Add x + 2 to both sides of the equation to get, x = 3x + 6

3x subtracted both sides yields, -2x = 6
=> x = -3.

Because x is the smallest integer, we now understand that the next three numbers are {3, 2, 1} respectively.
The sum of the numbers will be, (-3) + (-2) + (-1) = -6, which is the answer to the target question.

Therefore this statement is sufficient

Approach Solution : 3

Statement - 1 : The sum of the 3 integers is less than the greatest of the 3 integers

We can write (x−1) + x + (x+1) < (x+1)
So, 3x => 2x<1
=> x<1/2

With this we have no definite value for x.

Therefore this statement is not sufficient.

Statement - 2 : Of the 3 integers, the ratio of the least to the greatest is 3

We can write (x−1) / (x+1) = 3

So x = −2 and therefore the three numbers are −1,−2,−3

The sum of them is −6.

Therefore this statement is sufficient.

“What is the sum of 3 consecutive integers?” - is a subject covered in the GMAT quantitative reasoning section. There are 31 questions in the GMAT Quant section. A problem statement is followed by two factual statements in GMAT data sufficiency questions. Two-fifths of the total 31 GMAT Quant questions, or 15 questions, are devoted to the topic of data sufficiency.

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