Aptitude and Reasoning Interview Questions 2026

Before you ever get to a coding round or a technical interview, most companies filter thousands of applicants down to a manageable number using an aptitude test, and this round eliminates more candidates than any other single stage in the entire placement process. It's also the round students prepare for the least seriously, since it feels like "just math," right up until the actual test gives you 20 questions in 20 minutes and half the room runs out of time on question 12.

This page covers the four areas that show up in essentially every aptitude round, quantitative aptitude, logical reasoning, verbal ability, and data interpretation, with solved examples for each, plus how the round is actually structured at major recruiters, time management strategy, and a realistic preparation plan.

Why the Aptitude Round Eliminates More Candidates Than Any Other Stage

Companies hiring in bulk, TCS, Infosys, Wipro, Cognizant, Capgemini, and similar, can't personally interview every applicant, so the aptitude test acts as the first, high-volume filter before anyone even looks at your resume in detail. It's used to check:

• Whether you can work through numerical problems quickly and accurately under real time pressure
• Whether you can think logically and spot patterns, which correlates reasonably well with general problem-solving ability
• Whether your written English is strong enough for a role that'll involve documentation, emails, and client communication
• Whether you can read and correctly interpret data presented in tables, charts, and graphs, a skill that shows up constantly in real reporting and analysis work

Who This Page Is For

• Students preparing for TCS NQT, Wipro Elite/Turbo, Infosys, Cognizant GenC, Capgemini, and similar off-campus and on-campus drives
• Anyone who's strong at coding but has never seriously practiced quantitative aptitude or verbal reasoning
• Candidates who've failed an aptitude round before due to running out of time, not lack of knowledge

Related Resources

• Group Discussion Topics and Tips
• HR Interview Questions
• Advanced Placement Interview Questions

How the Aptitude Round Is Typically Structured

Formats vary by company, but most off-campus drives follow a broadly similar pattern:

• TCS NQT: Numerical ability, verbal ability, reasoning ability, plus a separate coding section, all timed and sectional (you often can't go back to a previous section once time runs out for it).
• Wipro Elite/Turbo: Quantitative aptitude, logical reasoning, and verbal ability, followed by a coding round, with Elite (for CS/IT branches) and Turbo (for non-CS branches) having slightly different weightings.
• Infosys: A quant and logical reasoning section, a verbal section, and a separate pseudocode-based logical ability section that tests reading and tracing through code-like logic without requiring actual programming.
• Capgemini: A verbal, logical, and quantitative aptitude section, followed by a separate technical/coding assessment.
• Cognizant GenC: Aptitude, verbal, and logical reasoning, similar in structure to the others, followed by coding.

The common thread across all of them: sectional time limits, negative marking is common in some formats, and you're almost always racing the clock more than the actual difficulty of the questions.

Quantitative Aptitude

1. In an election between two candidates, the winner got 60% of the votes and won by 4,000 votes. What was the total number of votes cast?

The winning margin represents the difference between the two vote shares, 60% minus 40% equals 20%, and that 20% corresponds to the 4,000 vote margin. So the total number of votes is 4,000 divided by 0.20, which is 20,000. This "margin equals percentage difference" pattern is one of the most common election/percentage question types, once you spot it, the calculation itself is quick.

2. A shopkeeper marks an item 40% above its cost price, then offers a 10% discount on the marked price. What is his actual profit percentage?

Assume the cost price is 100 for easy calculation. The marked price is 100 + 40% = 140. After a 10% discount on that marked price, the selling price is 140 × 0.90 = 126. Since the cost price was 100, the profit is 126 − 100 = 26, so the profit percentage is 26%. The key habit worth building here is always assuming a cost price of 100 when a problem only gives you percentages, it makes the arithmetic dramatically simpler.

3. Pipe A can fill a tank in 12 hours, and Pipe B can fill it in 15 hours. Working together, how long will they take to fill the tank?

Pipe A's rate is 1/12 of the tank per hour, Pipe B's rate is 1/15 per hour. Working together, their combined rate is 1/12 + 1/15, which, using a common denominator of 60, is 5/60 + 4/60 = 9/60 = 3/20 of the tank per hour. Time taken is the reciprocal of that combined rate, 20/3 hours, which is 6 hours and 40 minutes.

4. A train 150 meters long crosses a pole in 15 seconds. What is its speed in km/hr?

Since the train only needs to cross its own length to pass a stationary pole, the distance covered is simply 150 meters. Speed equals distance divided by time, 150/15 = 10 meters per second. To convert to km/hr, multiply by 18/5 (the standard conversion factor), 10 × 18/5 = 36 km/hr.

5. Divide ₹1,200 among A, B, and C in the ratio 2:3:5.

The total number of parts is 2 + 3 + 5 = 10. Each part is worth 1,200/10 = 120. So A gets 2 × 120 = 240, B gets 3 × 120 = 360, and C gets 5 × 120 = 600, which correctly sums back to 1,200.

6. Find the compound interest on ₹10,000 at 10% per annum for 2 years, compounded annually.

The amount after compounding is Principal × (1 + rate)^time, so 10,000 × (1.1)² = 10,000 × 1.21 = 12,100. The compound interest is the amount minus the original principal, 12,100 − 10,000 = ₹2,100. A quick sanity check worth knowing, simple interest for the same numbers would be exactly ₹2,000, compound interest is always slightly higher because the second year earns interest on the first year's interest too.

7. The average of 5 numbers is 20. If one number is excluded, the average of the remaining 4 numbers becomes 18. What is the excluded number?

The total of the original 5 numbers is 5 × 20 = 100. The total of the remaining 4 numbers is 4 × 18 = 72. The excluded number is the difference, 100 − 72 = 28.

8. In how many distinct ways can 5 people be seated in a row?

This is a straightforward permutation problem, arranging 5 distinct people into 5 distinct positions, which is 5 factorial, 5! = 5 × 4 × 3 × 2 × 1 = 120 ways.

9. Two dice are rolled together. What is the probability that the sum of the numbers shown is 7?

There are 6 × 6 = 36 total equally likely outcomes when rolling two dice. The combinations that sum to 7 are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1), which is 6 favorable outcomes. Probability is favorable outcomes divided by total outcomes, 6/36, which simplifies to 1/6.

10. Find the largest number that divides both 245 and 1029, leaving a remainder of 5 in each case.

If a number leaves remainder 5 when dividing 245 and 1029, it must divide (245 − 5) = 240 and (1029 − 5) = 1024 exactly. So the answer is the HCF of 240 and 1024. Breaking both down, 240 = 16 × 15 and 1024 = 16 × 64, and since 15 and 64 share no common factors, the HCF is 16.

11. Find the LCM of 12, 18, and 24.

Break each number into prime factors, 12 = 2² × 3, 18 = 2 × 3², 24 = 2³ × 3. The LCM takes the highest power of each prime that appears, 2³ × 3² = 8 × 9 = 72.

12. The ratio of the present ages of A and B is 3:5. After 6 years, the ratio becomes 2:3. Find A's present age.

Let A's age be 3x and B's age be 5x. After 6 years, (3x + 6)/(5x + 6) = 2/3. Cross-multiplying, 9x + 18 = 10x + 12, which gives x = 6. So A's present age is 3 × 6 = 18 years.

13. A and B invest ₹5,000 and ₹8,000 respectively in a business for one year. If the total profit is ₹3,900, find A's share.

Since both invested for the same duration, profit is split purely in the ratio of their investments, 5,000:8,000, which simplifies to 5:8, a total of 13 parts. A's share is 3,900 × (5/13) = ₹1,500.

14. In what ratio should tea worth ₹60/kg be mixed with tea worth ₹80/kg so that the resulting mixture is worth ₹65/kg?

Using the alligation rule, the ratio is (cost of dearer − mean price) : (mean price − cost of cheaper), which is (80 − 65) : (65 − 60) = 15 : 5 = 3 : 1. So the cheaper tea (₹60/kg) and the dearer tea (₹80/kg) should be mixed in the ratio 3:1.

15. A boat's speed in still water is 10 km/hr, and the stream's speed is 2 km/hr. Find the time taken to travel 24 km downstream.

Downstream, the boat's effective speed is the sum of its own speed and the stream's speed, 10 + 2 = 12 km/hr. Time is distance divided by speed, 24/12 = 2 hours.

16. A shopkeeper offers successive discounts of 20% and 10% on an item marked at ₹1,000. Find the final selling price.

Successive discounts are applied one after another, not simply added together. After the first 20% discount, the price is 1,000 × 0.80 = 800. After the second 10% discount on that new price, it's 800 × 0.90 = ₹720. Note this is different from a flat 30% discount, which would have given ₹700, successive discounts are always slightly less aggressive than adding the percentages directly.

17. Find the area of a circle with radius 7 cm (use π = 22/7).

Area of a circle is π r², so 22/7 × 7 × 7 = 22 × 7 = 154 cm². Using 22/7 specifically with a radius that's a multiple of 7 is a deliberate, common exam pattern, since it makes the arithmetic clean.

18. Find the volume of a cube with a side length of 5 cm.

Volume of a cube is side³, so 5³ = 5 × 5 × 5 = 125 cm³.

19. Find the sum of the first 20 terms of the arithmetic progression 2, 5, 8, 11, ...

This AP has a first term a = 2 and common difference d = 3. The sum of n terms is n/2 × (2a + (n−1)d), so for n = 20, that's 10 × (4 + 19×3) = 10 × (4 + 57) = 10 × 61 = 610.

20. If x + 1/x = 5, find the value of x² + 1/x².

Squaring both sides of the given equation, (x + 1/x)² = x² + 2(x)(1/x) + 1/x² = x² + 2 + 1/x² = 25. So x² + 1/x² = 25 − 2 = 23. Squaring a given sum to find a related expression like this is one of the most reusable algebra tricks in aptitude tests.

21. At what time between 3 and 4 o'clock will the hour and minute hands of a clock be exactly together?

At 3:00, the hour hand is at the 90° mark and the minute hand is at 0°, a 90° gap the minute hand needs to close. The minute hand gains on the hour hand at 5.5° per minute (it moves at 6°/min, the hour hand at 0.5°/min). Time to close a 90° gap is 90 ÷ 5.5 = 16.36 minutes, roughly 16 minutes and 22 seconds. So the hands align at approximately 3:16:22.

22. If today is Monday, what day of the week will it be after 65 days?

Since the week repeats every 7 days, only the remainder after dividing by 7 actually matters. 65 ÷ 7 leaves a remainder of 2 (63 is exactly divisible by 7). Counting 2 days forward from Monday gives Wednesday.

23. A is twice as efficient as B. Working together, they complete a task in 6 days. In how many days can A alone complete it?

Let B's work rate be x (task per day), so A's rate is 2x. Working together, their combined rate is 3x, and since together they finish in 6 days, 3x = 1/6, giving x = 1/18. A's individual rate is 2x = 2/18 = 1/9, meaning A alone would take 9 days.

24. A car covers a certain distance in 5 hours at a speed of 60 km/hr. What speed would it need to cover the same distance in 4 hours?

First find the distance, 60 × 5 = 300 km. To cover that same 300 km in 4 hours instead, the required speed is 300/4 = 75 km/hr.

Logical Reasoning

1. If CAT is coded as 3120, how would DOG be coded using the same logic?

First figure out the coding rule from the given example, C is the 3rd letter of the alphabet, A is the 1st, T is the 20th, which exactly matches 3, 1, 20 written together as 3120. Applying the same rule to DOG, D is the 4th letter, O is the 15th, G is the 7th, giving the code 4-15-7, or 41 57 written together depending on the exact formatting convention used, the core skill being tested is spotting that the "code" is just each letter's alphabetical position.

2. Pointing to a photograph, a man says, "She is the daughter of my grandfather's only son." How is the woman in the photograph related to the man?

The man's grandfather's only son has to be the man's own father (since the man himself is part of that family line and his grandfather would only have one son who is the man's father, assuming standard family structure). So the woman is the daughter of the man's father, which makes her the man's sister.

3. Find the next number in the series: 2, 6, 12, 20, 30, ?

Look at the differences between consecutive terms, 6−2=4, 12−6=6, 20−12=8, 30−20=10, the differences themselves are increasing by 2 each time (4, 6, 8, 10). Following that pattern, the next difference should be 12, so the next number is 30 + 12 = 42. (This particular series is also just n × (n+1) for n = 1, 2, 3, 4, 5, 6, which is a useful pattern to recognize directly.)

4. Statement: All pens are books. All books are tables. Conclusion I: All pens are tables. Conclusion II: Some tables are pens. Which conclusion(s) logically follow?

Both conclusions follow. Since all pens are books, and all books are tables, every pen must also be a table, that's a direct chain, which validates Conclusion I. Since all pens are tables, and pens themselves exist as a group, at least some tables (specifically, the ones that are pens) must be pens, which validates Conclusion II as well, syllogism questions like this are almost always about carefully tracing the chain of "all/some" relationships rather than using outside knowledge about what pens or books actually are.

5. Five friends, A, B, C, D, and E, are sitting in a row facing north. B is to the immediate right of A. C is to the immediate right of B. D is to the immediate right of C. E is at one of the ends. Who is sitting at the other end?

Since B is immediately right of A, C is immediately right of B, and D is immediately right of C, that gives a fixed sequence: A, B, C, D, in that left-to-right order. That's 4 people already placed consecutively, with E being the 5th person at one of the ends. Since A, B, C, D already form one continuous block, E must be at either the far left (before A) or the far right (after D). If E is at one end, A, being the start of the fixed A-B-C-D block, must be at the other end.

6. A man walks 5 km north, then turns right and walks 3 km, then turns right again and walks 5 km. How far is he from his starting point, and in which direction?

Walking 5 km north, then turning right (now facing east) and walking 3 km, then turning right again (now facing south) and walking 5 km, the two 5 km legs (one north, one south) cancel each other out entirely, leaving only the 3 km eastward leg. So the man ends up exactly 3 km east of his starting point.

7. Statement: "All the government schools in the city will be shut down due to lack of funding." Assumption: Government schools rely primarily on government funding to stay operational. Is this assumption implicit in the statement?

Yes, this is a valid implicit assumption. The statement claims that a lack of funding will cause the schools to shut down, which only makes logical sense if those schools genuinely depend on that funding to operate in the first place, if government schools had substantial independent funding sources, a funding shortfall alone wouldn't necessarily force a shutdown, statement-assumption questions like this test whether you can identify the unstated premise that the given statement's logic actually depends on.

8. Doctor is to Hospital as Teacher is to ?

This is a role-to-workplace analogy, a Doctor's primary workplace is a Hospital, so the matching answer for Teacher is School, the relationship being tested is simply "a person works primarily at this place."

9. Find the odd one out: Apple, Mango, Potato, Banana.

Apple, Mango, and Banana are all fruits, while Potato is a vegetable, making Potato the odd one out. Odd-one-out questions are testing whether you can spot the shared category quickly, the trap is usually one item that seems similar on the surface (all four are foods) but breaks the more specific pattern.

10. Find the missing term in the series: 3, 9, 27, 81, ?

Each term is exactly 3 times the previous one, 3×3=9, 9×3=27, 27×3=81, so the next term is 81×3=243.

11. A cube is painted red on all its faces and then cut into 27 equal smaller cubes. How many of the smaller cubes have exactly 2 faces painted?

Cutting a cube into 27 equal pieces means cutting it into a 3×3×3 grid. The smaller cubes with exactly 2 painted faces are the ones sitting on an edge of the larger cube, but not at a corner. A cube has 12 edges, and for a 3×3×3 split, each edge contributes exactly 1 such cube (the middle one along that edge, since the two ends of each edge are corner cubes with 3 painted faces). So the answer is 12 edges × 1 cube each = 12 cubes.

12. What is the value of x? Statement I: x² = 16. Statement II: x is a positive number.

Statement I alone gives x = 4 or x = −4, two possible values, so it's not sufficient alone. Statement II alone only tells you x is positive, with no specific value at all, also not sufficient alone. Combining both, x² = 16 and x is positive, narrows it down to exactly x = 4. So the correct answer is that both statements together are sufficient, but neither is sufficient alone, this is the standard format for data sufficiency questions, and the skill being tested is precision about what each statement does and doesn't tell you on its own.

13. In a class of 40 students, Raj ranks 12th from the top. What is his rank from the bottom?

The formula is: rank from bottom = (total students − rank from top) + 1. So Raj's rank from the bottom is (40 − 12) + 1 = 29.

14. If "A + B" means A is the mother of B, "A − B" means A is the brother of B, and "A × B" means A is the father of B, then in the expression "P + Q − R," how is P related to R?

Breaking down the expression, "P + Q" means P is the mother of Q, and "Q − R" means Q is the brother of R, which means Q and R are siblings. If P is the mother of Q, and R is Q's sibling, P must also be the mother of R. So P is the mother of R.

15. Six friends A, B, C, D, E, and F sit around a circular table facing the center. B is second to the right of A. D is second to the left of A. C is to the immediate right of D. F is to the immediate left of B. Where does E sit relative to A?

Number the six seats 1 through 6 going clockwise, and place A at seat 1. "Second to the right" (clockwise) of A lands on seat 3, so B is at seat 3. "Second to the left" (counter-clockwise) of A lands on seat 5, so D is at seat 5. C is immediate right of D (seat 5), which is seat 6. F is immediate left of B (seat 3), which is seat 2. That leaves seat 4 for E. Since seats 1 and 4 are directly opposite each other in a 6-seat circular arrangement, E sits directly opposite A.

16. Statement: "Should students be allowed to use calculators in school exams?" Argument I: "Yes, it saves time on calculations and lets them focus more on concepts." Argument II: "No, it will make students dependent and weaken their basic arithmetic skills." Which argument is strong?

Both arguments are strong here. Argument I raises a genuine, relevant benefit (freeing up time to focus on conceptual understanding), and Argument II raises a genuine, relevant concern (dependency weakening fundamental skills), neither is vague, irrelevant, or purely emotional, which is exactly the bar for a "strong" argument in this question format. A lot of candidates assume these questions always have one clearly "correct" side, but plenty of well-known statement-argument questions are specifically designed so that both sides hold up, testing whether you can evaluate relevance rather than just picking a side you personally agree with.

17. In a certain code, MADRAS is written as NBESBT. How would BOMBAY be written in the same code?

Compare each letter of MADRAS to the corresponding letter of NBESBT, M→N, A→B, D→E, R→S, A→B, S→T, every letter has simply been shifted forward by one position in the alphabet. Applying that same +1 shift to BOMBAY, B→C, O→P, M→N, B→C, A→B, Y→Z, gives the code CPNCBZ.

18. Find the missing number: Row 1: 4, 6, 8. Row 2: 5, 7, 9. Row 3: 6, 8, ?

Within each row, the numbers increase by 2 (4→6→8, 5→7→9). Across rows, the starting number increases by 1 each time (4, then 5, then 6). Following both patterns, row 3 should be 6, 8, 10, so the missing number is 10.

19. Point A is 4 km east of point B. Point C is 3 km north of point A. What is the straight-line distance between B and C?

Plotting this out, B to A is a 4 km horizontal leg, and A to C is a 3 km vertical leg, forming a right angle at A. The straight-line distance from B to C is the hypotenuse of that right triangle, calculated using the Pythagorean theorem, √(4² + 3²) = √(16 + 9) = √25 = 5 km. This is a direct application of the well-known 3-4-5 right triangle, worth recognizing on sight to save calculation time.

20. A is B's brother. C is B's mother. D is C's father. E is D's mother. How is A related to D?

Since C is B's mother, and A is B's brother, C is also A's mother. D is C's father, which makes D the father of A's mother, meaning D is A's maternal grandfather. So A is D's grandchild.

Verbal Ability

1. Choose the word most nearly opposite in meaning to "Ephemeral."

"Ephemeral" means lasting for a very short time. The correct antonym would be a word like "Permanent" or "Everlasting," since it describes something that lasts indefinitely, the opposite of something fleeting or short-lived.

2. Identify the error in the sentence: "Neither of the students have completed their assignment."

The error is in subject-verb agreement, "neither" is a singular subject (it means "not one of the two"), so it requires a singular verb, "has," not "have." The corrected sentence reads, "Neither of the students has completed their assignment." This specific "neither/either" singular-subject rule is one of the most frequently tested grammar patterns in verbal ability sections.

3. Arrange the following sentences into a coherent paragraph: (A) This process is called photosynthesis. (B) Plants use sunlight to convert carbon dioxide and water into glucose. (C) They also release oxygen as a byproduct of this process. (D) Without it, most life on Earth as we know it would not be possible.

The logical order is B, A, C, D. B introduces the core process first (plants converting CO2 and water using sunlight), A names that process, C adds the additional detail about oxygen being released as a byproduct, and D closes with the broader significance of the process. Para jumble questions are solved by finding the sentence that introduces the topic first, then tracing which sentences logically reference or build on each other.

4. Read the passage and answer: "The rise of remote work has fundamentally changed how companies evaluate productivity. Traditional metrics based on hours spent in an office no longer apply, forcing managers to shift toward outcome-based evaluation instead." What is the main idea of this passage?

The main idea is that remote work has forced a shift in how productivity is measured, from tracking time spent physically present in an office to evaluating actual outcomes and results instead. Reading comprehension questions are testing whether you can identify the passage's central claim, not just recall an isolated detail mentioned somewhere within it.

5. Choose the correct one-word substitution for: "A person who is unable to read or write."

The correct word is "Illiterate." One-word substitution questions test vocabulary breadth directly, and they're worth building a small, memorized list for, since they show up constantly and there's no real "reasoning" shortcut, you either know the specific word or you don't.

6. Choose the meaning of the idiom "to let the cat out of the bag."

It means to reveal a secret, usually unintentionally. Idiom questions are pure vocabulary recall, there's no way to logically derive the meaning from the individual words, so they're worth building a small, memorized list of common idioms for specifically.

7. Change the following sentence to passive voice: "The manager approved the proposal."

In passive voice, the object of the original sentence becomes the subject, and the original subject moves after "by." The passive version is, "The proposal was approved by the manager." The general pattern, object + a form of "be" + past participle + "by" + original subject.

8. Change the following sentence to indirect (reported) speech: She said, "I am going to the market."

When converting to reported speech, pronouns and tenses typically shift back one step, "I" becomes "she," and the present continuous "am going" shifts to the past continuous "was going." The correct indirect form is, "She said that she was going to the market."

9. Fill in the blank with the correct word: "She has been working here _ 2015."

The correct word is "since." "Since" is used with a specific starting point in time (a year, a date, an event), while "for" is used with a duration or span of time (for 5 years, for two months), this since-versus-for distinction is one of the most frequently tested preposition rules.

10. Choose the word closest in meaning to "Meticulous."

The closest synonym is "Careful" or "Precise," meticulous describes someone who shows great attention to detail and is extremely thorough and careful about small details.

11. Choose the word that best completes the sentence: "Despite his ____, he managed to finish the marathon."

"Fatigue" fits best, "despite" signals a contrast, so the blank needs to describe something that would normally have prevented him from finishing, fatigue (tiredness) creates exactly that contrast with actually completing the marathon.

12. Identify the error in the sentence: "He don't like playing cricket in the evening."

The error is again subject-verb agreement, "He" is a third-person singular subject, which requires "doesn't," not "don't." The corrected sentence reads, "He doesn't like playing cricket in the evening."

13. Read the passage and answer: "Automation is reshaping manufacturing industries worldwide, reducing the need for repetitive manual labor while increasing demand for workers skilled in operating and maintaining automated systems." According to the passage, what is one effect of automation on the workforce?

According to the passage, automation reduces the need for repetitive manual labor while simultaneously increasing demand for workers who can operate and maintain the automated systems themselves, it's shifting the type of labor needed, not simply eliminating jobs outright, which is exactly the nuance a good reading comprehension answer should reflect rather than an oversimplified "it removes jobs."

14. Choose the pair that best expresses a relationship similar to "Author : Book."

"Sculptor : Statue" is the best match, both original pairs express a creator-to-creation relationship, an Author creates a Book, a Sculptor creates a Statue, verbal analogy questions are testing whether you can identify the type of relationship, not just find another pair of related words.

15. Choose the word most nearly opposite in meaning to "Verbose."

The correct antonym is "Concise." "Verbose" describes using far more words than necessary, so its opposite describes being brief and to the point.

Data Interpretation

1. The table below shows the number of units sold by four salespersons across two quarters. Based on this, answer the following.

a) Who had the highest percentage increase in sales from Q1 to Q2?

Calculate the percentage change for each: A increased from 120 to 150, a rise of 30, which is 30/120 = 25%. B decreased, so it's not a candidate. C increased from 90 to 140, a rise of 50, which is 50/90 ≈ 55.6%. D stayed flat at 0% change. C had the highest percentage increase, at roughly 55.6%, notice that C had the highest percentage increase even though A and B both had higher absolute unit totals, DI questions frequently test this exact distinction between absolute and percentage change.

b) What was the overall percentage change in total units sold (all four salespeople combined) from Q1 to Q2?

Total Q1 units: 120 + 200 + 90 + 160 = 570. Total Q2 units: 150 + 180 + 140 + 160 = 630. The increase is 630 − 570 = 60. Percentage change is 60/570 ≈ 10.5%.

2. The table below shows the number of cars sold by a dealership over 5 months. Based on this, answer the following.

a) What is the average number of cars sold per month?

Total cars sold across the 5 months: 40 + 55 + 45 + 60 + 50 = 250. Average is total divided by number of months, 250/5 = 50 cars per month.

b) What is the percentage increase in sales from March to April?

The increase from March (45) to April (60) is 60 − 45 = 15. Percentage increase is (increase/original value) × 100, (15/45) × 100 ≈ 33.3%.

3. A company's annual budget of ₹50,00,000 is allocated across departments as follows: Marketing 25%, R&D 30%, Operations 20%, Salaries 15%, Miscellaneous 10%. Based on this, answer the following.

a) How much of the budget is allocated to R&D in rupees?

R&D gets 30% of ₹50,00,000, which is 0.30 × 50,00,000 = ₹15,00,000.

b) How much more is allocated to R&D than to Salaries?

Salaries get 15% of ₹50,00,000 = ₹7,50,000. R&D gets ₹15,00,000 (calculated above). The difference is 15,00,000 − 7,50,000 = ₹7,50,000, R&D receives exactly double what Salaries receives, since 30% is exactly double 15%, a pattern worth spotting quickly rather than computing both figures from scratch.

Time Management and Test-Taking Strategy

A genuinely common failure pattern isn't lack of knowledge, it's running out of time on a section you could have finished if you'd paced yourself better. A few concrete habits that help:

• Skip and return: If a question isn't clicking within roughly 30 to 45 seconds, mark it and move on, don't let one hard question eat time you need for three easier ones later, assuming the test format allows returning to skipped questions.
• Know your section's per-question budget going in: If a section has 20 questions in 20 minutes, you have roughly 1 minute per question on average, know that number before you start, not while you're already behind.
• Do the fast questions first if the format allows it: Ratio, averages, and simple percentage questions are usually faster to solve than multi-step time-and-work or probability questions, banking the quick, easy points first protects you if you run low on time later.
• Watch for negative marking: If wrong answers cost you marks, a pure guess on a question you have no idea about can actually hurt your score, know the specific test's negative marking rules before deciding whether to guess or skip.

Common Mistakes Candidates Make

• Skipping verbal and reasoning to over-prepare quant: A lot of engineering students assume math is the only section that matters and under-prepare verbal ability specifically, which is often the section where marks are lost simply due to unfamiliarity with grammar rules, not difficulty.
• Not practicing under actual timed conditions: Solving problems untimed at home builds the wrong instinct, real practice needs a visible timer and the same pressure you'll actually face in the test.
• Re-deriving basic formulas mid-test: Things like percentage-to-ratio conversions, standard time-speed-distance conversion factors, and common squares/cubes should be memorized cold, working them out from scratch during the actual test wastes time you don't have.
• Ignoring the specific company's actual format: TCS NQT, Wipro, and Infosys don't test in exactly the same way, practicing generically without checking the specific format, sectional cutoffs, and negative marking rules of the company you're actually applying to leaves you unprepared for format-specific surprises.

A Practical Preparation Plan

Cramming everything the night before genuinely doesn't work for aptitude the way it might for a single technical topic, since speed comes from repetition, not last-minute review. A reasonable structure over roughly 3 to 4 weeks:

• Week 1: Cover the core quantitative topics one at a time (percentages, profit/loss, time and work, time-speed-distance, ratios), solving problems untimed first to build the underlying concept, then timed once you're comfortable with the method.
• Week 2: Move to logical reasoning (series, syllogisms, blood relations, seating arrangements, direction sense) and start layering in verbal ability practice (grammar rules, one-word substitutions, and a reading comprehension passage or two daily).
• Week 3: Add data interpretation practice and start taking full-length, timed mock tests that combine all sections together, this is where you actually discover which specific section is eating too much of your time.
• Week 4: Focus specifically on your weakest section from the mocks, and take at least 2 to 3 more full, timed mock tests in the actual format of the company you're applying to, reviewing every mistake to understand exactly why it happened, a wrong answer due to a careless mistake needs a different fix than one due to not knowing a concept at all.

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