Mathematical Reasoning & Aptitude: 150+ Questions with Solutions
This comprehensive set contains over 150 questions to practice mathematical reasoning and aptitude. Topics include reasoning, series, codes, fractions, percentages, ratios, profit & loss, time & distance, interest, averages, and mixed aptitude problems. Solutions are provided for each question.
Part I: Types of Reasoning (1–20)
- Verbal Reasoning: Identify the odd one: Apple, Banana, Carrot, Mango.
Answer: Carrot (vegetable; others are fruits) - Find the missing number: 2, 4, 8, 16, ?
Answer: 32 (×2 each term) - Which word does not belong? Dog, Cat, Lion, Chair.
Answer: Chair (others are animals) - Analogies: Brother is to Sister as Uncle is to ?
Answer: Aunt - If TABLE = 52, what is CHAIR?
Answer: 38 (sum of letter positions: C=3+H=8+…) - Find next letter: A, C, E, G, ?
Answer: I - Odd one: 3, 5, 9, 13, 16
Answer: 16 (not part of sequence +2,+4,+4,...) - Find next number: 1, 1, 2, 3, 5, ?
Answer: 8 (Fibonacci series) - Logical reasoning: All roses are flowers. Some flowers fade quickly. Can it be concluded that some roses fade quickly?
Answer: Cannot be concluded. - Which code is correct if CAT=3120? DOG=?
Answer: 4157 (sum of alphabetical positions) - Find the odd shape in series: ◼ ◻ ◼ ◻ ?
Answer: ◼ - If 5 + 3 = 28, 6 + 2 = 16, find 7 + 3 = ?
Answer: 40 (pattern: multiply sum by 4) - Find missing term: 2, 5, 10, 17, ?
Answer: 26 (+3,+5,+7,+9...) - Which is odd one out: Circle, Square, Triangle, Rectangle, Apple
Answer: Apple (not a shape) - Logical puzzle: If all cats are animals and some animals are black, can a cat be black?
Answer: Yes, possibly. - Find missing number: 9, 16, 25, 36, ?
Answer: 49 (perfect squares) - Letter pattern: B, E, H, K, ?
Answer: N (+3 each time) - Odd one: 2, 3, 5, 7, 9, 11
Answer: 9 (not prime) - Find missing in code: 2→4, 3→9, 4→16, 5→?
Answer: 25 (square) - Which pair does not match: Pen–Write, Knife–Cut, Plate–Drink, Spoon–Eat
Answer: Plate–Drink
Part II: Number Series & Letter Series (21–50)
- Series: 5, 10, 20, 40, ?
Answer: 80 - Series: 2, 4, 8, 14, 22, ?
Answer: 32 (+2,+4,+6,+8...) - Series: 1, 4, 9, 16, ?
Answer: 25 (squares) - Find missing letter: A, D, G, J, ?
Answer: M (+3) - Find next number: 1, 3, 6, 10, 15, ?
Answer: 21 (triangular numbers) - Series: 2, 6, 12, 20, ?
Answer: 30 (n^2+n pattern) - Letter pattern: Z, X, V, T, ?
Answer: R (-2) - Find missing: 3, 9, 27, ?
Answer: 81 (×3) - Series: 1, 2, 4, 8, 16, ?
Answer: 32 - Letter series: M, P, S, V, ?
Answer: Y (+3) - Series: 100, 95, 90, 85, ?
Answer: 80 (-5) - Find next number: 0, 1, 1, 2, 3, 5, ?
Answer: 8 (Fibonacci) - Letter series: C, F, I, L, ?
Answer: O (+3) - Series: 1, 4, 9, 16, 25, ?
Answer: 36 (square numbers) - Series: 2, 6, 12, 20, 30, ?
Answer: 42 (pattern: n(n+1)) - Letter pattern: P, R, T, V, ?
Answer: X (+2) - Series: 1, 8, 27, 64, ?
Answer: 125 (cubes) - Find next: 7, 14, 28, 56, ?
Answer: 112 (×2) - Letter series: D, G, J, M, ?
Answer: P (+3) - Series: 10, 20, 40, 80, ?
Answer: 160
Part III: Fractions, Ratios & Proportions (51–80)
- Simplify: 2/3 + 3/4
Answer: 17/12 = 1 5/12 - Subtract: 7/8 - 1/3
Answer: 13/24 - Multiply: 3/5 × 10/7
Answer: 6/7 - Divide: 9/10 ÷ 3/5
Answer: 3/2 - Ratio: 15:25
Answer: 3:5 - Ratio & proportion: a:b = 2:3, b:c = 4:5 → a:b:c=?
Answer: 8:12:15 - Fractions: Find 2/5 of 50
Answer: 20 - Ratio problem: A:B=3:4, total=28 → find A & B
Answer: A=12, B=16 - Proportion: 4/5 = ?/25
Answer: 20/25 - Mixing: Milk & water 3:2 → total 25L → milk & water quantity?
Answer: Milk=15L, Water=10L - Percentage: 20% of 150
Answer: 30 - Percentage increase: 200→250 → ?%
Answer: 25% - Discount: Item 500, 10% off → selling price?
Answer: 450 - Profit & loss: CP=400, SP=500 → profit%?
Answer: 25% - Profit & loss: SP=900, profit=10% → CP?
Answer: 818.18 - Simple interest: P=2000, R=5%, T=3 → SI?
Answer: 300 - Compound interest: P=1000, R=10%, T=2 → A?
Answer: 1210 - Averages: 5 numbers average 20, one number 30 → remaining 4?
Answer: 17.5 - Average marks: 50 students, avg=60, one scored 90 → remaining 49?
Answer: 59.39 - Time & distance: Speed 60 km/h, time 2.5h → distance?
Answer: 150 km
Part IV: Miscellaneous Aptitude (81–150+)
- Two trains 60 km apart, move towards each other at 40 km/h & 20 km/h → time to meet?
Answer: Distance/(speed sum)=60/60=1 hour - Work problem: A can do a job in 12 days, B in 8 days. Together?
Answer: 1/12+1/8=5/24 → 24/5=4.8 days - Pipe filling tank: Pipe A 10h, B 15h → both together?
Answer: 1/10+1/15=1/6 → 6h - Speed & distance: Car 180 km, 4h → speed?
Answer: 45 km/h - Simple interest: P=5000, R=6%, T=4 → SI?
Answer: 1200 - CI: P=2000, R=5%, T=3 → A?
Answer: 2315.25 - Percentage: 35% of 80
Answer: 28 - Profit & loss: CP=150, SP=180 → profit?
Answer: 30, profit%=20% - Discount: MP=1000, 10% discount → SP?
Answer: 900 - Mixture: 60L water & milk 1:2 → milk quantity?
Answer: 40L - Time & work: 3 men 6h → 5 men?
Answer: Work=3×6=18 man‑hours → 5 men → 18/5=3.6h - Number series: 7, 14, 28, 56, ?
Answer: 112 - Letter series: D, G, J, M, ?
Answer: P - Number pattern: 1, 4, 9, 16, 25, ?
Answer: 36 - Ratio problem: A:B:C = 2:3:5 → total 50 → A,B,C?
Answer: 10,15,25 - Fraction: 7/8 × 16/21
Answer: 8/21 - Number series: 2, 6, 12, 20, 30, ?
Answer: 42 - Logical reasoning: All birds can fly. Penguins are birds. Can penguins fly?
Answer: No, exception exists - Time & distance: 120 km in 3h → speed?
Answer: 40 km/h - Work: 8 men in 12 days → 4 men?
Answer: 24 days - CI: P=5000, R=8%, T=2 → A?
Answer: 5832 - Profit & loss: CP=250, SP=300 → profit?
Answer: 50, profit%=20% - Percentage: Increase 200→240 → %?
Answer: 20% - Number series: 1, 3, 6, 10, 15, ?
Answer: 21 - Letter series: A, C, F, J, ?
Answer: O - Odd one: 5, 7, 11, 13, 16
Answer: 16 - Misc fraction: 3/4 ÷ 9/8
Answer: 2/3 - Average: 6, 10, 12, 8, 14 → mean?
Answer: 10 - Speed: Train 120 km in 1.5 h → speed?
Answer: 80 km/h - Discount: MP 800, SP 700 → discount%?
Answer: 12.5% - Profit & loss: SP 600, CP 500 → profit?
Answer: 100, 20% - Fraction: 7/10 + 2/5
Answer: 11/10 = 1 1/10 - Time & work: 6 men 8 days → 4 men?
Answer: 12 days - Number series: 2, 5, 10, 17, ?
Answer: 26 - Letter series: Z, X, V, T, ?
Answer: R - CI: P=1500, R=10%, T=2 → A?
Answer: 1815 - Profit & loss: CP=400, SP=480 → profit?
Answer: 80, 20% - Fraction: 5/6 - 2/3
Answer: 1/6 - Number pattern: 3, 9, 27, 81, ?
Answer: 243 - Ratio: 3:5 → total 64 → numbers?
Answer: 24 & 40 - Percentage: 30% of 250
Answer: 75 - Time & distance: Speed 50 km/h, distance 200 km → time?
Answer: 4h - Work: 12 men 15 days → 6 men?
Answer: 30 days - Number series: 1, 2, 6, 24, 120, ?
Answer: 720 (factorial) - Letter series: B, D, H, P, ?
Answer: X (×2, ×2 pattern) - CI: P=2500, R=5%, T=3 → A?
Answer: 2881.25 - Profit & loss: CP=600, SP=720 → profit?
Answer: 120, 20% - Discount: MP 1500, 20% → SP?
Answer: 1200 - Percentage: Decrease 500→400 → ?%
Answer: 20% - Fraction: 7/8 × 16/21
Answer: 8/21 - Average: 10, 12, 14, 16, 18 → mean?
Answer: 14 - Speed: 120 km in 3h → speed?
Answer: 40 km/h - Time & work: A=10d, B=15d → together?
Answer: 6d - Number series: 1, 4, 9, 16, 25, ?
Answer: 36 - Letter series: C, F, I, L, ?
Answer: O - Profit & loss: CP=500, SP=625 → profit?
Answer: 125, 25% - CI: P=1000, R=8%, T=2 → A?
Answer: 1166.4 - Fraction: 5/6 ÷ 10/9
Answer: 3/4 - Number series: 2, 6, 12, 20, 30, ?
Answer: 42 - Ratio problem: 7:3 → total 50 → numbers?
Answer: 35 & 15 - Average: 7, 9, 11, 13, 15 → mean?
Answer: 11 - Time & distance: 90 km in 1.5h → speed?
Answer: 60 km/h - Discount: MP 1200, SP 1020 → discount?
Answer: 15% - Profit & loss: CP=450, SP=540 → profit?
Answer: 90, 20% - CI: P=2000, R=10%, T=2 → A?
Answer: 2420 - Number series: 3, 5, 9, 17, 33, ?
Answer: 65 (+2,+4,+8,+16,+32) - Letter series: F, I, L, O, ?
Answer: R (+3) - Fraction: 9/10 - 2/5
Answer: 1/2 - Average: 6, 12, 18, 24, 30 → mean?
Answer: 18 - Speed: 150 km in 3h → speed?
Answer: 50 km/h - Time & work: 5 men 10d → 10 men?
Answer: 5 days
Conclusion: Practicing these 150+ questions regularly builds speed, accuracy, and analytical reasoning skills. This material is ideal for exams and aptitude development.
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