If The Product of 3 Consecutive Integers is 210, Then The Sum of The Two GMAT Problem Solving

Question: If the product of 3 consecutive integers is 210, then the sum of the two smaller integers is?

(A) 5
(B) 11
(C) 12
(D) 13
(E) 18

Correct Answer: B
Solution and Explanation:
Approach Solution 1:

The problem statement states that:

Given:

• The product of 3 consecutive integers is 210.

Find out:

• The sum of the two smaller integers.

There are 3 consecutive integers.

The sum of 2 consecutive integers can be 5 i.e 3 + 2 = 5.
Therefore, we can say, 2*3*4 = 24. But it fails to satisfy the condition stated in the question.
The sum of 2 consecutive integers can be 11 i.e 5 + 6 =11.
The sum of 2 consecutive integers cannot be 12.
The sum of 2 consecutive integers can be 13 i.e 6 + 7= 13.
The sum of 2 consecutive integers cannot be 18

If we consider 6 and 7 are the two smaller integers, 3rd will be 8 in this case.
Therefore, 6*7*8 will not produce 210.

Thus, 3 consecutive integers will be 5*6*7 = 210.
Hence, the sum of 2 smaller integers will be 11

Approach Solution 2:

The problem statement informs that:

Given:

• The product of 3 consecutive integers is 210.

Find out:

• The sum of the two smaller integers.

Since the product of 3 consecutive integers is 210, we can say:
=> 210=(x-1)(x)(x+1)
=> x^3 - 210 = x
The next perfect cube of 210 is 6^3 = 216
216 - 210 = 6 = x
x - 1 = 5
5 + 6 = 11
Therefore, the sum of the two smaller integers = 11.

Approach Solution 3:

The problem statement indicates that:

Given:

• The product of 3 consecutive integers is 210.

Find out:

• The sum of the two smaller integers.

This problem can be solved with the most easier and quicker approach.
Let’s do the factorization of 210.
210 = 5* 6 * 7
Therefore, it implies that they are three consecutive integers.
Hence, the sum of the two smaller integers will be 5+ 6 = 11.

“If the product of 3 consecutive integers is 210, then the sum of the”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “Kaplan GMAT Math Workbook”. The GMAT Problem Solving questions help the candidates to improve their basic math concepts. The candidates can boost their mathematical learning by practising from the GMAT Quant practice papers that will enable them to score high in the exam.

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