eLitmus Sample Papers 2026: Quant, LR & Verbal Questions Solved

The eLitmus pH Test draws from a consistent question bank: number theory and combinatorics in Quantitative Ability, cryptarithmetic in Problem Solving, and inference-based comprehension in Verbal Ability.

This article sits alongside the FACE Prep eLitmus previous papers with solutions guide, which covers the 2026 IRT scoring model, section weightings, and a full prep plan. The focus here is different: section-by-section sample questions verified from first principles, plus pattern notes on how the pH Test has evolved since 2018.

eLitmus pH Test: Section Overview

Three sections, 20 questions each, with no mandatory time split per section. The full eLitmus pH Test syllabus and exam pattern guide covers eligibility, registration, and handicap-based negative marking in detail. The section-level summary:

Section	Questions	Core Question Types
Quantitative Ability	20	Number theory, combinatorics, algebra, work-rate, geometry
Problem Solving	20	Cryptarithmetic, logical puzzles, data sufficiency
Verbal Ability	20	Fill-in-the-blank, sentence arrangement, reading comprehension

The eLitmus official website lists current test dates, centre locations, and the job board where companies post their pH score cutoffs. A score stays valid for two years from the date of your test, so one sitting covers multiple hiring cycles.

Quantitative Ability: Worked Sample Questions

Quantitative Ability runs at above-standard campus difficulty. Number theory and combinatorics questions regularly involve multi-step logic rather than direct formula substitution. The five problems below represent the question types that have appeared consistently since 2018. Solutions are derived from first principles.

Combinatorics

• Q1. Find the number of ways to fill a 3x3 grid with 3 white marbles and 6 black marbles, given that all marbles of the same colour are identical.
  • a) 9C3
  • b) 6C3
  • c) 9C3 + 6C3
  • d) (9C3 + 6C3) divided by 6
• Answer: a) 9C3 = 84
• Step 1: 9 total grid positions. Choose 3 positions for the white marbles.
• Step 2: The remaining 6 positions automatically take black marbles.
• Step 3: Since all marbles of the same colour are identical, only the position-choice matters, not the order. Answer = 9C3 = (9 x 8 x 7) / (3 x 2 x 1) = 84 ways.

Quadratic Equations and Number Theory

• Q2. For how many values of c does the equation x-squared minus 5x plus c = 0 have integer roots?
  • a) 1
  • b) 3
  • c) 6
  • d) Infinite (no upper bound)
• Answer: d) Infinite
• Step 1: Roots are (5 plus or minus sqrt(25 - 4c)) / 2. For integer roots, (25 - 4c) must be a perfect square of an odd number, so that 5 plus or minus (odd) is even and divides cleanly by 2.
• Step 2: Let 25 - 4c = k-squared, where k is an odd integer. Then c = (25 - k-squared) / 4.
• Step 3: k = 1 gives c = 6 (roots 3 and 2). k = 3 gives c = 4 (roots 4 and 1). k = 5 gives c = 0 (roots 5 and 0). k = 7 gives c = -6 (roots 6 and -1).
• Step 4: Any odd integer k produces a valid integer value of c. Since there is no upper bound on odd integers, there are infinitely many valid c values.

Escalators and Relative Speed

• Q3. Einstein walks down an escalator at 5 steps per second and reaches the bottom in 10 seconds. Walking back up at the same pace, he takes 40 seconds. How many steps does the escalator have?
  • a) 40
  • b) 60
  • c) 120
  • d) 80
• Answer: d) 80
• Step 1: Let escalator speed = x steps/sec, total steps = L.
• Step 2: Going down (both move in the same direction): L / (5 + x) = 10, so L = 50 + 10x.
• Step 3: Going up (opposite directions): L / (5 - x) = 40, so L = 200 - 40x.
• Step 4: Setting equal: 50 + 10x = 200 - 40x gives 50x = 150, so x = 3.
• Step 5: L = 50 + 30 = 80 steps.

Combinatorics and Divisibility

• Q4. How many 6-digit numbers can be formed using digits 1 to 6 (without repetition) such that the number is divisible by the digit at the units place?
  • a) 402
  • b) 528
  • c) 648
  • d) 720
• Answer: c) 648
• Step 1: Units digit = 1. Any arrangement of the remaining 5 digits gives a multiple of 1. Count = 5 x 4 x 3 x 2 x 1 = 120.
• Step 2: Units digit = 2. The number ends in 2 so it is even, hence divisible by 2. Count = 120.
• Step 3: Units digit = 3. Digit sum = 1 + 2 + 3 + 4 + 5 + 6 = 21, which is divisible by 3. Any arrangement works. Count = 120.
• Step 4: Units digit = 4. The last two digits must form a number divisible by 4. From the set 6 at the tens place, only the endings 24 and 64 are divisible by 4. Each allows 4 x 3 x 2 x 1 = 24 arrangements for the remaining digits. Count = 2 x 24 = 48.
• Step 5: Units digit = 5. Numbers ending in 5 are divisible by 5. Count = 120.
• Step 6: Units digit = 6. Ending in 6 is even, and digit sum 21 is divisible by 3, so the number is divisible by 6. Count = 120.
• Step 7: Total = 120 + 120 + 120 + 48 + 120 + 120 = 648.

Working Backwards

• Q5. A thief steals some diamonds. On the way out he meets 3 watchmen one by one. To each watchman he gives half his current diamonds plus 2 more. He escapes with 1 diamond. How many did he steal originally?
  • a) 40
  • b) 36
  • c) 32
  • d) 38
• Answer: b) 36
• Step 1: After giving the 3rd watchman: if the thief had x diamonds before, he retains x/2 - 2 = 1, so x = 6.
• Step 2: Before the 2nd watchman: x/2 - 2 = 6, so x = 16.
• Step 3: Before the 1st watchman: x/2 - 2 = 16, so x = 36 diamonds stolen originally.

Problem Solving: Worked Sample Questions

Cryptarithmetic is the question type that most clearly separates pH Test preparation from standard aptitude prep. Each letter represents a unique digit; no leading zeros. The cryptarithmetic guide for eLitmus and Infosys covers the full column-analysis method. The two examples below show how to apply it on pH Test-style puzzles.

Letter Addition Puzzles

• Q6. XZY + XYZ = YZX. Find X, Y, and Z.

  • a) X=9, Y=5, Z=4
  • b) X=5, Y=4, Z=9
  • c) X=4, Y=5, Z=9
  • d) X=4, Y=9, Z=5

• Answer: d) X = 4, Y = 9, Z = 5

• Step 1: Column 2 (tens place): Z + Y produces a carry to column 1. So Z + Y = 10 + Z, giving Y = 9.

• Step 2: Column 1 (hundreds place): X + X + carry = Y, so 2X + 1 = 9, giving X = 4.

• Step 3: The remaining digit is Z = 5.

• Step 4: Verify: 459 + 495 = 954. Units: 9 + 5 = 14 (write 4, carry 1). Tens: 5 + 9 + 1 = 15 (write 5, carry 1). Hundreds: 4 + 4 + 1 = 9. Result YZX = 954. Confirmed.

• Q7. MAC + MAAR = JOCKO. Find the value of 3A + 2M + 2C.

  • a) 31
  • b) 36
  • c) 33
  • d) 38

• Answer: a) 31

• Step 1: JOCKO is a 5-digit result from a 3-digit plus 4-digit addition. The leading J must be a carry of 1, so J = 1 and O = 0.

• Step 2: Leftmost column (M + M): produces the carry giving J = 1. With O = 0 and carry out = 1, we get M = 9.

• Step 3: Units column (C + R): must end in O = 0 with carry 1 out. So C + R = 10. Try C = 2, R = 8.

• Step 4: Hundreds column (M + A): 9 + A = C with a carry in from tens (carry = 1), so 9 + A = 12, giving A = 3, carry out = 1.

• Step 5: Tens column (A + A + carry in): 3 + 3 + 1 = 7, so K = 7.

• Step 6: Verify: MAC = 932, MAAR = 9338. 932 + 9338 = 10270. JOCKO with J=1, O=0, C=2, K=7, O=0 gives 10270. Confirmed.

• Step 7: 3A + 2M + 2C = 3(3) + 2(9) + 2(2) = 9 + 18 + 4 = 31.

Verbal Ability: Sample Questions

Verbal Ability mixes vocabulary fill-in-the-blank, sentence arrangement, and reading comprehension. The first two question types require logical coherence and contextual reasoning, not just vocabulary recall.

Fill in the Blank

• Q8. “Corruption is ____ in our society; the integrity of even senior officials is ____.”
  • a) rife, suspect
  • b) growing, unquestioned
  • c) endangered, disputed
  • d) pervasive, intact
• Answer: a) rife, suspect
• Explanation: The semicolon signals that the second clause expands on the first. If corruption is rife (widespread), the integrity of officials falls under suspicion (suspect). Option (d) fails internal logic: pervasive corruption alongside intact integrity is contradictory.

Sentence Arrangement

• Q9. Opening sentence: “Good literary magazines have always been good because of their editors.” Arrange A, B, C, D into a coherent paragraph.
  • A: “Furthermore, to edit by committee would prevent any magazine from finding its own identity.”
  • B: “The more quirky and idiosyncratic the editors, the better the magazine, as a general rule. But the number of editors should also match the number of contributions.”
  • C: “To have four editors for seven contributions is a bit silly to start with.”
  • D: “However, in spite of this anomaly, the magazine does acquire merit in its attempt to give a broad view.”
  • Choices: a) ABCD b) BCDA c) ABDC d) CBAD
• Answer: b) BCDA
• Explanation:
  • B states the general rule (quirkier editors = better magazine) then introduces the constraint (editor count should match contribution count).
  • C gives the concrete example of the constraint being violated (4 editors, 7 contributions).
  • D concedes that despite this anomaly, the magazine has merit.
  • A closes with the further point that committee editing prevents a magazine from building its own identity.

Pattern Shifts: 2018 to 2026

The questions above come from the 2018 paper bank and represent question types that have remained consistent across every pH Test cohort since. The format and difficulty have stayed broadly stable. Two things have shifted in the period from 2020 to 2026.

What Has Stayed Constant

• Combinatorics and number theory in Quantitative Ability, at above-standard campus difficulty.
• Cryptarithmetic as a core question type in Problem Solving, always requiring column-by-column carry analysis.
• Sentence arrangement and vocabulary fill-in-the-blank in Verbal Ability.
• Negative marking in all three sections, penalising inaccuracy over guessing.

What Has Shifted Since 2018

• Data sufficiency questions now appear more frequently in Problem Solving alongside cryptarithmetic, adding a second question type to master in that section.
• Verbal Ability has added inference-based comprehension passages alongside the standalone vocabulary questions common in earlier papers. Candidates who prepared only from vocabulary lists in 2018 would find the 2026 section slightly broader in scope.
• The scoring model uses IRT (Item Response Theory), meaning a correct answer to a harder question carries more weight than a correct answer to an easy one. This shifts the optimal strategy: attempting fewer hard questions correctly is often worth more than rushing to attempt all 20 in a section.

For more worked problems including IRT-aware scoring strategy, the eLitmus previous papers with solutions guide has the full 2026 problem set.

Practicing with Sample Papers

Working through sample papers without a system produces diminishing returns. A structured three-pass method gives better results in the same amount of time.

• First pass: Attempt every question without a timer. Focus on understanding the solution method, not the answer. Note which question types you had no approach for at all.
• Second pass: Set a section-level timer. Identify which question types consistently run you out of time. For most students this is cryptarithmetic in Problem Solving and multi-step combinatorics in Quantitative Ability.
• Third pass: Targeted practice on your two weakest question types only. Sample papers are most useful once you know which specific types cost you the most marks, not as a general drilling tool.
• After each mock: Calculate your attempt accuracy per section. eLitmus’s negative marking system penalises inaccuracy more than it rewards raw volume. If you’re attempting 18 of 20 questions and answering 10 correctly, the maths often favours attempting 12 with 11 correct.

The eLitmus help centre has guidance on score interpretation, retake eligibility, and the minimum pH scores companies post for each opening. Cross-referencing your mock scores with those cutoffs gives a concrete improvement target rather than a vague aim.

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