XAT Quantitative Aptitude and Data Interpretation (QA & DI) Notes: Syllabus, Unit-wise Weightage and Study Order

XAT Quantitative Aptitude and Data Interpretation (QA & DI): 5 units and 17 chapters, a study order by exam weight and 0 practice questions.

Units in XAT Quantitative Aptitude and Data Interpretation (QA & DI)

Algebra: Equations, Functions, Progressions Notes (3 chapters)
Arithmetic: Percentages, Profit & Loss, Ratio & Proportion, Time & Work, Speed, Time & Distance Notes (4 chapters)
Data Interpretation: Graphs, charts, tables requiring insightful analysis Notes (4 chapters)
Geometry & Mensuration: Lines, Circles, Polygons, 3D Figures Notes (3 chapters)
Modern Math: Probability, Permutations & Combinations Notes (3 chapters)

All Quantitative Aptitude and Data Interpretation (QA & DI) chapters

One Solved Question from Each Quantitative Aptitude and Data Interpretation (QA & DI) Chapter

Question 1 · Quantitative Aptitude and Data Interpretation (QA & DI) NAT

Let $n$ be a positive integer such that $n^{3} + 2 n^{2} + 3 n + 4$ is a perfect cube. What is the sum of all possible values of $n$ ?

Correct Answer:

Step-by-Step Solution

Key idea: This is a perfect power bounding problem. For large $n$ , the expression lies strictly between consecutive cubes, so only small $n$ need checking. Modular arithmetic eliminates remaining candidates.

Step 1: Compare with nearby cubes. Note $(n + 1)^{3} = n^{3} + 3 n^{2} + 3 n + 1$ .

Our expression: $E (n) = n^{3} + 2 n^{2} + 3 n + 4$ .

Difference: $(n + 1)^{3} - E (n) = n^{2} - 3$ .

For $n \geq 2$ , $n^{2} - 3 > 0 \Rightarrow E (n) < (n + 1)^{3}$ .

Step 2: Compare with $n^{3}$ . Clearly $E (n) > n^{3}$ for $n > 0$ .

So for $n \geq 2$ , $n^{3} < E (n) < (n + 1)^{3}$ . Thus $E (n)$ cannot be a perfect cube for $n \geq 2$ .

Step 3: Check $n = 1$ : $E (1) = 1 + 2 + 3 + 4 = 10$ , not a cube.

Step 4: No positive integer $n$ satisfies the condition. Sum of all possible values is 0.

Step 5: Verify no edge cases missed. For $n = 0$ (not positive), $E (0) = 4$ , not cube. Negative $n$ excluded by problem.

Answer: 0

chapter

XAT Quantitative Aptitude and Data Interpretation (QA & DI) Notes: Syllabus, Unit-wise Weightage and Study Order

XAT Quantitative Aptitude and Data Interpretation (QA & DI): 5 units and 17 chapters, a study order by exam weight and 0 practice questions.

A question from this chapter

Question 1

Let n be a positive integer such that n^{3} + 2 n^{2} + 3 n + 4 is a perfect cube. What is the sum of all possible values of n ?

Free preview ends here

Login to view the complete notes

Creating an account is free. You get the rest of this chapter, step-by-step solutions, and a study plan built around the topics you are actually weak at.

Why MastersUp

Personalised first. High quality throughout.

Most platforms hand everyone the same content. Here the content moves with your performance, topic by topic.

Built around you, not around a syllabus PDF

Every answer you give moves your topic-level intelligence rate. The next question, the next revision card and tomorrow's plan all change with it.

Revision that hits your weak spots

We only revise topics you have actually attempted and are still below the safe bar on — never the same chapter on repeat.

Questions calibrated to the real exam

Each question carries a measured toughness. You are served a rung above your current level, so practice keeps stretching you.

Notes written for recall, not for volume

Full lesson cards for first study, curated short-note cards for the last mile — with derivations, traps and exam patterns marked.

One place for everything

Notes, chapter practice, previous-year questions, test series and full-length papers — all feeding one picture of your preparation.

Honest progress

No vanity streaks. Progress here means chapters mastered and accuracy that held up on harder questions.

Unlock the whole course

Full notes and short notes, the complete question bank with worked solutions, mock tests, full-length papers, and an adaptive plan that rebuilds itself as you improve.

View all plans Start free