How Challenging It Is to Design Aptitude Test Questions: A Case of Wrong Question Design

Look at the following wrongly designed question:

Version 1:

A lady has a son who is 28 years old. Four years ago, she was 3 times as old as her son. What will be her son's age 4 years from now?

A. 9 B. 10 C. 12 D. 14 E. 16

The problem:

Who is 28 years old? Since “who” modifies “son,” it’s the son who is 28 years old. Well, then the answer must be 28 + 4 = 32 years. Well, there’s no option as 32!

It’s a poorly drafted question.?

Version 2:

A lady has a son and is 28 years old. Four years ago, she was 3 times as old as her son. What will be her son's age 4 years from now?

A. 9 B. 10 C. 12 D. 14 E. 16

The problem:

Who is 28 years old? It’s the lady. However, there is an ambiguity. Though the sentence “A lady has a son and is 28 years old” is not grammatically incorrect, it may be confusing as to whether the son or the lady is 28 years old.

Version 3:

A lady is 28 years old. Four years ago, she was 3 times as old as her son. What will be her son's age 4 years from now?

A. 9 B. 10 C. 12 D. 14 E. 16

Correct solution 1:

Who is 28 years old? It’s the lady. No confusion at all. The reference to the son is taken care of in the following sentence.?

Let’s solve this question.

Say the present age of the son = x

Thus, four years ago, (28 – 4) = 3(x – 4)

x = 12 years (present age)

Thus, 4 years from now, the son will be x + 4 = 12 + 4 = 16

The problem:

From the mathematical logic point of view, there is no issue with the question; however, from the social logic point of view, there is an issue. It’s unethical to endorse a 28-year-old lady with a 12-year-old son. She gave birth at the age of 16—a minor!

Version 4:

A lady is 28 years old. Four years ago, she was 6 [changed to 6 from 3] times as old as her son. Four years from now, what will be her son's age?

A. 9 B. 10 C. 12 D. 14 E. 16

Correct solution 2:

Say the present age of the son = x

Thus, four years ago, (28 – 4) = 6(x – 4)

x = 8 years (present age)

Thus, 4 years from now, the son will be x + 4 = 8 + 4 = 12

The problem:

Though this is a nicely drafted and ethically acceptable question (the 28-year-old lady has an 8-year-old son), the question writer did not apply his brain to design options.

Think like a student:

Test makers must also think like test takers. What if students commit mistakes while solving the question? Well, then the test maker must design such incorrect options.

Incorrect solution 1:

What if the student did not decrease the present age of the son by 4 years while setting up the equation? The answer would then be different.

Let’s solve this in this incorrect way.

Say the present age of the son = x

Thus, four years ago, (28 – 4) = 6x

x = 4 years (current age)

Thus, 4 years from now, the son will be x + 4 = 4 + 4 = 8 (there must be an option as 8)

Incorrect solution 2:

What if the student solved the question as given in “Incorrect solution 1,” but in a hurry he did not calculate the son’s age 4 years from now? Well, in that case, his incorrect answer would be 4 (there must be an option as 4).

Incorrect solution 3:

What if the student mixed up 4 and 6 while setting up the equation? The answer would then be different.

Let’s solve this in this incorrect way.

Say the present age of the son = x

Thus, four years ago, (28 – 6) = 4(x – 6)

x = 11.5 years (present age)

Thus, 4 years from now, the son will be x + 4 = 11.5 + 4 = 15.5 (there must be an option as 15?).

Incorrect solution 4:

What if the student solved the question as given in “Incorrect solution 3,” but in a hurry he did not calculate the son’s age 4 years from now? Well, in that case, his incorrect answer would be 11.5 (there must be an option as 11?).

The final version:

A lady is 28 years old. Four years ago, she was 6 times as old as her son. Four years from now, what will be her son's age?

A. 4 B. 8 C. 11? D. 12 E. 15?

Sign-off thought:

The question I discussed is an easy-level word problem. It’s important to note that being a good instructor and being a good content writer are two different things. The two require different skill sets. This question also highlights why it’s important to study the content of official material or reputed test prep companies.

About me:

I am Shalabh Jain. For the last 10 years, I have been solely dedicated to authoring American test prep content. So far, I've written/edited/reviewed 60+ books/20,000+ pages/10,000+ questions for test prep companies for the GMAT, GRE, SAT, LSAT, ACT, SSAT, ISEE, TOEFL, and IELTS. I also create employee assessment test questions.

Please see my copyright sample questions and other very interesting stuff.

https://www.dropbox.com/sh/10o2lvscrixryhf/AADHstjjLN_iS1LGnnoyZu7Aa?dl=0