Mphasis Aptitude Questions: Syllabus, Pattern and Worked Solutions

The Mphasis aptitude round has 16 questions, runs for 16 minutes, and is delivered on the AMCAT platform: the same engine used by dozens of IT services firms that hire on AMCAT scores.

Understanding the test pattern and the specific topics Mphasis tests is the first step. The 10 worked examples in this article are solved from scratch, with every step written out, so you can follow the method rather than just memorise the answer.

For the full picture of how aptitude fits into the Mphasis selection pipeline, see the Mphasis recruitment process, test pattern, and eligibility guide.

Mphasis Aptitude Syllabus

Mphasis uses AMCAT as its assessment platform. The aptitude module within AMCAT draws from three difficulty tiers, each testing a distinct layer of mathematical ability.

Difficulty Tiers

Tier	What It Tests	Typical Topics
Basic Mathematics	Core arithmetic and number theory	HCF, LCM, divisibility, basic fractions, ratio and proportion
Applied Mathematics	Formulaic problem-solving	Profit and loss, time and work, time-speed-distance, permutations and combinations, probability
Engineering Mathematics	Conceptual reasoning applied to abstract problems	Logarithms, number-base conversions, advanced P&C, algebraic identities

Topic-by-Topic Breakdown

Topic	Tier	Weight (approx.)
Permutations and Combinations	Applied / Engineering	High
Number Systems (HCF, LCM, divisibility)	Basic	Medium
Logarithms	Engineering	Medium
Time and Work	Applied	Medium
Time, Speed and Distance (Boats and Streams)	Applied	Medium
Profit and Loss	Applied	Low-Medium
Probability	Applied	Low-Medium
Ratio and Proportion	Basic	Low

The AMCAT official syllabus has the full module-level breakdown if you want to cross-reference the exact sub-topics.

Mphasis Aptitude Test Pattern

The structural facts for the aptitude section:

Parameter	Value
Number of questions	16
Duration	16 minutes
Difficulty range	Easy to Intermediate
Platform	AMCAT
Negative marking	None (AMCAT standard; confirm with recruiter for current cycle)

Time Management Within the Round

With 16 questions in 16 minutes, the average is 60 seconds per question. In practice, the distribution should be tighter:

• Easy questions (Basic Mathematics tier): under 30 seconds each.
• Intermediate questions (Applied / Engineering tier): 45 to 60 seconds each.

Finishing easy questions quickly creates a buffer for the P&C and logarithm problems that require more steps. Going in without a per-question time budget is the most common reason students leave questions unanswered.

For the other sections of the Mphasis online test, the Mphasis online test pattern and syllabus guide covers the programming and verbal sections alongside aptitude.

Mphasis Aptitude Questions with Solutions

The 10 questions below are drawn from the Mphasis practice question set. Each answer is re-derived independently. Nothing is copied from older sources.

Permutations and Combinations

• Q1. In how many ways can the 7 letters A, B, C, D, E, F, G be arranged so that C and E are never together?

• Options: 5040 / 6480 / 3600 / 1440

• Answer: 3600

• Step 1: Total arrangements of 7 distinct letters = 7! = 5040

• Step 2: Arrangements where C and E ARE together: treat {C,E} as one unit, giving 6 units. These arrange in 6! = 720 ways. C and E can also swap internally: multiply by 2 = 1440.

• Step 3: C and E NEVER together = 5040 minus 1440 = 3600

• Q2. In how many ways can the letters of the word MANAGE be arranged?

• Options: 360 / 144 / 256 / 720

• Answer: 360

• Step 1: MANAGE has 6 letters: M, A, N, A, G, E. The letter A appears twice; all others once.

• Step 2: Arrangements = 6! divided by 2! = 720 divided by 2 = 360

• Q3. In how many ways can 6084 be written as a product of two different factors?

• Options: 27 / 13 / 14 / 26

• Answer: 13

• Step 1: Factorise 6084: 6084 = 4 × 1521 = 2² × 39² = 2² × 3² × 13²

• Step 2: Total divisors = (2+1)(2+1)(2+1) = 27

• Step 3: 6084 is a perfect square (square root = 78), so unordered pairs = (27 + 1) / 2 = 14

• Step 4: Subtract the pair (78, 78) where both factors are equal: 14 minus 1 = 13

Number Systems and Divisibility

• Q4. The HCF of two numbers is 30 and the other two factors of their LCM are 10 and 12. What is the larger of the two numbers?

• Options: 310 / 320 / 360 / 345

• Answer: 360

• Step 1: The two numbers share HCF = 30. Their remaining factors are 10 and 12.

• Step 2: The numbers are 30 × 10 = 300 and 30 × 12 = 360.

• Step 3: Larger number = 360

• Q5. If a number is exactly divisible by 85, what is the remainder when the same number is divided by 17?

• Options: 3 / 4 / 1 / 0

• Answer: 0

• Step 1: 85 = 5 × 17. So 17 divides 85 evenly.

• Step 2: Any multiple of 85 is also a multiple of 17 (since 85 = 17 × 5).

• Step 3: Remainder = 0

• Q6. A rectangular courtyard 3.78 m long and 5.25 m wide is to be paved exactly with square tiles of the same size. What is the largest tile size that works?

• Options: 14 cm / 42 cm / 21 cm / None

• Answer: 21 cm

• Step 1: Convert to centimetres: 3.78 m = 378 cm, 5.25 m = 525 cm

• Step 2: Factorise: 378 = 2 × 3³ × 7; 525 = 3 × 5² × 7

• Step 3: HCF(378, 525) = 3 × 7 = 21 cm

Logarithms

• Q7. If log(a/b) + log(b/a) = log(a + b), find the value of a + b.
• Options: a + b = 1 / a minus b = 1 / a = b / a² minus b² = 1
• Answer: a + b = 1
• Step 1: log(a/b) + log(b/a) = log((a/b) × (b/a)) = log(1) = 0
• Step 2: If log(a + b) = 0, then a + b = 10 to the power of 0 = 1

Time and Work

• Q8. A can do a piece of work in 8 days and B in 6 days. Together with C, they complete it in 3 days for Rs. 3200. How much does C get paid?
• Options: Rs. 500 / Rs. 700 / Rs. 650 / Rs. 400
• Answer: Rs. 400
• Step 1: A’s daily rate = 1/8; B’s daily rate = 1/6
• Step 2: Combined daily rate of A and B = 1/8 + 1/6 = 3/24 + 4/24 = 7/24
• Step 3: (A + B + C) combined rate = 1/3 (finish in 3 days)
• Step 4: C’s daily rate = 1/3 minus 7/24 = 8/24 minus 7/24 = 1/24
• Step 5: Ratio A : B : C = 1/8 : 1/6 : 1/24 = 3 : 4 : 1 (multiply each by 24)
• Step 6: Total parts = 8. C’s share = (1/8) × Rs. 3200 = Rs. 400

Time, Speed and Distance

• Q9. A boat travels at 13 km/hr in still water. The stream speed is 4 km/hr. How long does it take to travel 68 km downstream?
• Options: 2 hours / 3 hours / 4 hours / 5 hours
• Answer: 4 hours
• Step 1: Downstream speed = boat speed + stream speed = 13 + 4 = 17 km/hr
• Step 2: Time = Distance divided by Speed = 68 divided by 17 = 4 hours

Profit and Loss

• Q10. An article sold for Rs. 2770 would yield 10% additional gain if sold for Rs. 3000 instead. What is the cost price?
• Options: Rs. 2300 / Rs. 2360 / Rs. 1950 / Rs. 1150
• Answer: Rs. 2300
• Step 1: Difference in selling prices = Rs. 3000 minus Rs. 2770 = Rs. 230
• Step 2: This Rs. 230 represents 10% of the cost price (the stated “additional gain of 10%”)
• Step 3: CP = Rs. 230 divided by 0.10 = Rs. 2300

Preparation Strategy

Three days is enough to cover the full Mphasis aptitude syllabus, assuming you’re already comfortable with secondary-school arithmetic.

Three-Day Topic Plan

Day	Topics	Target
Day 1	Number systems (HCF, LCM, divisibility), Profit and Loss, Ratio and Proportion	10 to 20 questions per topic
Day 2	Permutations and Combinations, Probability	15 to 20 questions per topic; focus on arrangement vs. selection distinction
Day 3	Logarithms, Time and Work, Time-Speed-Distance (boats and streams)	10 to 15 questions per topic

What to Focus on Within Each Topic

• P&C: The two sub-skills — arrangement (permutations) and selection (combinations) — behave differently. Work out which formula applies before solving.
• Logarithms: The product, quotient, and power rules cover 90% of AMCAT-level problems. Memorise them; don’t re-derive on-test.
• Time-and-Work: The unitary method (convert all rates to “fraction of work done per day”) is faster than formula memorisation.
• Number systems: Learn divisibility rules for 2, 3, 4, 5, 7, 9, 11, and 13. Questions like Q6 above (HCF for tile size) are solved in one step once you can prime-factorise quickly.

For the logical reasoning and verbal sections that sit alongside aptitude in the same test, the Mphasis logical reasoning questions and syllabus guide is the companion resource.

What Comes After the Aptitude Round

The 10 problems above cover the core aptitude syllabus. Clear the AMCAT round and you move to the programming and HR sections. The programming section tests basic coding concepts; the HR round is where articulation counts more than technical depth.

If you’re targeting Mphasis or similar IT services firms, clearing aptitude is table stakes. The students who stand out at the offer stage typically have a project or two that shows they’ve applied their skills, not just studied them. The 10 worked problems in this article each called for a specific method: rate-ratio for work problems, product rule for logarithms. That same logic applies to building with AI tools. Working through a real problem beats watching five tutorials.

TinkerLLM is a structured environment to build your first AI-powered projects for ₹499, the kind of thing you can reference in a Mphasis technical interview when asked what you’ve built outside coursework. If the aptitude round is where you’re focused right now, come back to this after you’ve cleared it.