Timed CAT Practice: Numerical Operations & Percentages

Hello! In the previous lesson, you used percentage multipliers to handle successive changes and worked backward from a final value to the original. Today the task changes: you will use those methods in a 40-minute set of ten CAT previous-year QA questions. The questions also draw on the numerical fluency you built earlier—fractions, cancellation, and checking whether an answer is plausible.

This is a topic-focused sprint, not a full QA section. Your aim is to find a sound setup quickly, make deliberate decisions about when to move on, and finish with a record you can use in the next revision lesson.

Set up the sprint

Have a timer and scratch paper ready. The questions below are paraphrased from CAT previous-year questions; their numerical conditions, answer choices, and MCQ or TITA formats are retained. Do not open the answer-checking resource or the video until the timer stops.

Use the 40 minutes as follows:

1. First 2 minutes: Scan all ten questions. Mark the ones whose setup you can see immediately.
2. Next 32 minutes: Solve in any order. If you cannot identify a useful setup after about 75 seconds, mark the question and move on. Return if time permits.
3. Final 6 minutes: Revisit marked questions and check bases, units, and answer format. Do not replace a reasoned MCQ answer with an unsupported guess.

Questions 2, 3, and 5 are TITA: write a number rather than selecting an option. Record an answer for each attempted question, even if you are unsure, and note any question that consumed unusually long.

The 40-minute CAT previous-year set

Start your timer now. Keep your working: it will be more useful than your score when you review errors.

1. CAT 2017, Slot 2 — MCQ. A factory finds that $15\%$ of its shirts are defective. It sells $20\%$ of the remaining shirts domestically and has $8840$ shirts left for export. How many shirts did it produce?
   Choices: A. $13600$ · B. $13000$ · C. $13400$ · D. $14000$

2. CAT 2017, Slot 1 — TITA. Someone puts $50\%$ of their monthly savings in fixed deposits. Of what remains, $30\%$ goes into stocks; the rest goes into a savings account. The fixed-deposit and savings-account amounts total ₹$59500$. Find the total monthly savings.

3. CAT 2019, Slot 2 — TITA. Student A scored $10\%$ less than B; B scored $25\%$ more than C; and C scored $20\%$ less than D. If A scored $72$, what was D’s score?

4. CAT 2020, Slot 2 — MCQ. A shopper buys the same quantities of rice and wheat in May as in April. Rice and wheat prices rise by $20\%$ and $12\%$, respectively, increasing the combined bill by ₹$150$. April’s rice bill was ₹$450$. What is May’s wheat bill?
   Choices: A. ₹$590$ · B. ₹$580$ · C. ₹$560$ · D. ₹$570$

5. CAT 2021, Slot 2 — TITA. A box contains $450$ balls, each white or black. Metallic white balls and metallic black balls are equal in number. If $40\%$ of the white balls and $50\%$ of the black balls are metallic, how many balls are non-metallic?

6. CAT 2019, Slot 1 — MCQ. A student initially scores $40\%$ of the maximum marks. A review raises that score by $50\%$, but it remains $35$ marks below the pass mark. If the post-review score were raised by another $20\%$, it would be $7$ marks above the pass mark. What percentage of the maximum marks is needed to pass?
   Choices: A. $75\%$ · B. $80\%$ · C. $60\%$ · D. $70\%$

7. CAT 2021, Slot 2 — MCQ. An investment of ₹$10000$ loses value in its first year, but its remaining balance is greater than ₹$5000$. In the second year, that balance grows at a percentage rate five times the first year’s loss rate. The investment finishes $35\%$ above its initial value. What was the first-year loss percentage?
   Choices: A. $15\%$ · B. $5\%$ · C. $10\%$ · D. $70\%$

8. CAT 2024, Slot 3 — MCQ. After two successive salary increases, the salary is $187.5\%$ of its starting value. The percentage rate of the second increase was twice the rate of the first. What was the first increase rate?
   Choices: A. $27.5\%$ · B. $30\%$ · C. $25\%$ · D. $20\%$

9. CAT 2021, Slot 1 — MCQ. A large box of chocolate sells for twice the price of a small box, but its selling price per gram is $12\%$ lower. Approximately what percentage greater is the chocolate’s weight in the large box than in the small box?
   Choices: A. $127\%$ · B. $135\%$ · C. $124\%$ · D. $144\%$

10. CAT 2018, Slot 1 — MCQ. Passing requires $45\%$ of a maximum score $N$. A candidate scores $36$, which is $68\%$ below the pass mark. Which range contains $N$?
    Choices: A. $N\le 200$ · B. $243\le N\le 252$ · C. $N\ge 253$ · D. $201\le N\le 242$

Stop the timer before going further. Write down your attempted count, the questions you skipped, and any answer for which you were uncertain about the percentage base.

Check answers without losing the diagnostic

Use the CAT portion of 2IIM’s CAT Questions | CAT Arithmetic Questions to check your ten answers. Its answer appears immediately below each question, so approach this section only after the sprint. For now, check the answer and the corresponding question; save full explanation-reading and error correction for the next lesson. The page also contains non-PYQ practice questions near the top—begin instead at its line announcing questions from actual CAT papers.

If question 9 was difficult to set up, you can watch this short explanation after checking your answer. Focus on the relationship between total box price, price per gram, and weight—not on the assumed numerical values themselves.

Carry the result into revision

Record three brief facts beside each wrong, skipped, or uncertain question: what you tried first, where you got stuck or changed course, and whether the issue was setup, arithmetic, base selection, or time. A correct answer reached by a guess is worth flagging too. Do not treat this ten-question score as a percentile estimate; it is a snapshot of methods under a time limit.

The key takeaway from today is practical: numerical fluency helps only when it serves the right interpretation of the question. “Percent of the remainder,” “percent below the pass mark,” and “price per gram” each specify a different base. In the next lesson, you will correct this timed set, recall the methods without notes, and update a weakness log so the next round of practice targets what actually cost you time or accuracy.