XAT Quantitative Aptitude and Data Interpretation (QA & DI) Previous Year Questions (PYQs): 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 Previous Year Questions (PYQs) (3 chapters)
Arithmetic: Percentages, Profit & Loss, Ratio & Proportion, Time & Work, Speed, Time & Distance Previous Year Questions (PYQs) (4 chapters)
Data Interpretation: Graphs, charts, tables requiring insightful analysis Previous Year Questions (PYQs) (4 chapters)
Geometry & Mensuration: Lines, Circles, Polygons, 3D Figures Previous Year Questions (PYQs) (3 chapters)
Modern Math: Probability, Permutations & Combinations Previous Year Questions (PYQs) (3 chapters)

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

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

Nadeem’s age is a two-digit number X, squaring which yields a three-digit number,whose last digit is Y.

Consider the statements below: Statement I: Y is a prime number Statement II: Y is one-third of X To determine Nadeem’s age uniquely:

A.
either of I and II, by itself, is su cient.
B.
only II is su cient, but I is not.
C.
only I is su cient, but II is not.
D.
it is necessary and su cient to take I and II together.
E.
even taking I and II together is not su cient.

Correct Answer:

Step-by-Step Solution

Key idea: Evaluate each statement independently to see if it yields a unique value for Nadeem's age, then check if they are sufficient together.

Step 1: Define constraints. Nadeem's age $X$ is a two-digit number ( $10 \leq X \leq 99$ ). $X^{2}$ is a three-digit number, so $100 \leq X^{2} \leq 999$ , which means $10 \leq X \leq 31$ . $Y$ is the last digit of $X^{2}$ .

Step 2: Analyze Statement I. $Y$ is a prime number. The possible last digits of any perfect square are 0, 1, 4, 5, 6, 9. The only prime among these is 5. So $Y = 5$ . If $X^{2}$ ends in 5, $X$ must end in 5. Within the range $10 \leq X \leq 31$ , $X$ can be 15 or 25. Statement I alone is not sufficient.

Step 3: Analyze Statement II. $Y$ is one-third of $X$ , so $X = 3 Y$ . Since $Y$ is a possible last digit of a square (0, 1, 4, 5, 6, 9), we test these:

If $Y = 4$ , $X = 12$ . $1 2^{2} = 144$ (ends in 4). Valid.
If $Y = 5$ , $X = 15$ . $1 5^{2} = 225$ (ends in 5). Valid.
If $Y = 9$ , $X = 27$ . $2 7^{2} = 729$ (ends in 9). Valid.

Statement II gives $X \in {12, 15, 27}$ , so it is not sufficient alone.

Step 4: Analyze Statements I and II together. From I, $X \in {15, 25}$ . From II, $X \in {12, 15, 27}$ . The only common value is $X = 15$ .

Step 5: Conclusion. Both statements together are necessary and sufficient to uniquely determine Nadeem's age.

Answer: D

chapter

XAT Quantitative Aptitude and Data Interpretation (QA & DI) Previous Year Questions (PYQs): 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

Nadeem’s age is a two-digit number X, squaring which yields a three-digit number,whose last digit is Y. Consider the statements below: Statement I: Y is a prime number Statement II: Y is one-third of X To determine Nadeem’s age uniquely:

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