A Quality Control Analyst Collected 200 Measurements Of Length GMAT Problem Solving

Question: A quality control analyst collected 200 measurements of length. The range of the 200 measurements is 17 centimeters, and one of the measurements is 49.5 centimeters. Which of the following could be another one of the 200 measurements, in centimeters?

1. 32.0
2. 33.0
3. 34.0

1. I only
2. II only
3. III only
4. II and III only
5. I, II and III

“A quality control analyst collected 200 measurements of length”- is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT quant section improves the mathematical and analytical proficiency of the candidates. This GMAT quantitive section measures the candidates’ primary concepts of arithmetic, algebra and geometry. The students must possess solid qualitative skills in order to crack GMAT Problem Solving questions. The mathematical problems of the GMAT Quant topic in the problem-solving part can be solved by better concepts of mathematical calculations. The candidates can increase their knowledge by answering more questions from the “GMAT Official Guide Quantitative Review”.

Solution and Explanation:

Approach Solution 1:

The problem statement suggests that

Given:

• A quality control analyst collected 200 measurements of length
• The range of the 200 measurements is 17 centimeters
• one of the measurements is 49.5 centimeters

Find out:

• The another one of the 200 measurements.

we can say from the given statement of the question,
the range of feasible values will be from 49.5 - 17 to 49.5 + 17
= 32.5 to 66.5

Therefore, the value of options II and III lie within the range.

Hence, D is the correct answer.

Approach Solution 2:

The problem statement informs that

Given:

• A quality control analyst gathered 200 measurements of length
• The coverage of the 200 measurements is 17 centimeters
• one of the measurements is 49.5 centimeters

Find out:

• The value of another one of the 200 measurements.

Let's assume the measurement 49.5 is the maximum number.

Then the minimum value of measurement will be equal to the subtraction of 49.5 to 17.

Therefore, 49.5 - 7 = 32.5,

Thus option one- 32 does not satisfy the condition. Option II and III are therefore the correct answers since the number 33.0 and 34.0 is greater than 32.5.

Hence, D is the correct option.

Approach Solution 3:

The problem statement illustrates that

Given:

• A quality control analyst gathered 200 measurements of length
• The coverage of the 200 measurements is 17 centimeters
• one of the measurements is 49.5 centimeters

Find out:

• The value of another one of the 200 measurements.

Let’s consider 49.5 as the largest measurement.

Therefore, the smallest measurement will be 49.5 - 17 centimeters

= 32.5 cm.

Thus it can be inferred that any measurement that lies between 49.5 cm and 32.5 cm will be the measurement of the 200 measurements.
Options II and III cite the numbers 33.0 and 34.0 respectively which are one of the 200 measurements as it lies within the range of 49.5 cm and 32.5 cm.

Hence, D is the correct answer.

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