Practice Questions
BODMAS Order
Brackets, Orders (powers/roots), Division & Multiplication (left to right), Addition & Subtraction (left to right).
Fraction Shortcuts
Cancel common factors before multiplying. Convert mixed fractions to improper fractions first.
Placement Focus
Quick mental math, percentage-fraction conversion, and nested arithmetic appear frequently in placement aptitude papers.
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Q1 EasyIf 2994 ÷ 14.5 = 172, then 29.94 ÷ 1.45 = ?ExplanationBoth numerator and denominator are divided by 10, so the quotient remains 172 ÷ 10 = 17.2.
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Q2 EasyWhat is the value of the expression 48 ÷ 6 × 2 + 8 when simplified using the BODMAS rule?ExplanationDivision and multiplication are done left to right: 48 ÷ 6 = 8, 8 × 2 = 16, then 16 + 8 = 24.
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Q3 EasySimplify the following expression completely: (3 + 5) × 4 − 6 ÷ 2.ExplanationBrackets first: (3 + 5) = 8. Then 8 × 4 = 32 and 6 ÷ 2 = 3. Finally 32 − 3 = 29.
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Q4 EasyWhat is the result when two-thirds is added to one-sixth of a whole?ExplanationConvert to a common denominator: 4/6 + 1/6 = 5/6.
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Q5 EasyA student needs to find 15 percent of 240; what is the correct value?Explanation15% of 240 = 240 × 0.15 = 36.
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Q6 EasyWhat is the simplified value of the square root of 144 plus the square root of 81 minus the square root of 49?Explanation√144 = 12, √81 = 9, and √49 = 7. Therefore 12 + 9 − 7 = 14.
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Q7 EasySimplify the nested arithmetic expression 2 + 3 × 4 − 4 ÷ 2 using the correct order of operations.ExplanationMultiply and divide before add/subtract: 3 × 4 = 12 and 4 ÷ 2 = 2. Then 2 + 12 − 2 = 12.
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Q8 MediumEvaluate: (2.39)² − (1.61)² / (2.39 − 1.61) = ?ExplanationUse a² − b² = (a + b)(a − b). The fraction simplifies to (2.39 + 1.61) = 4.
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Q9 MediumThe value of (0.96)³ − (0.1)³ / ((0.96)² + 0.096 + (0.1)²) is:ExplanationUse a³ − b³ = (a − b)(a² + ab + b²). The denominator cancels, leaving 0.96 − 0.1 = 0.86.
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Q10 Medium(112 × 5⁴) = ?Explanation112 × 5⁴ = 112 × (10/2)⁴ = (112 × 10⁴) / 16 = 1120000 / 16 = 70000.
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Q11 MediumWhen the expression (5/6 − 1/3) is multiplied by 12, what single number do you get?Explanation5/6 − 1/3 = 5/6 − 2/6 = 1/2. Then (1/2) × 12 = 6.
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Q12 MediumWhat is the value obtained when 125 percent of 64 is calculated and rounded to a whole number?Explanation125% of 64 = 64 × 1.25 = 80.
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Q13 HardThe value of (0.1 × 0.1 × 0.1 + 0.02 × 0.02 × 0.02) / (0.2 × 0.2 × 0.2 + 0.04 × 0.04 × 0.04) is:ExplanationNumerator = (0.1)³ + (0.02)³. Denominator = 2³[(0.1)³ + (0.02)³]. Cancel the common bracket and divide by 8 to get 0.125.
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Q14 Hard1397 × 1397 = ?Explanation(1397)² = (1400 − 3)² = 1960000 + 9 − 8400 = 1951609.
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DS1 Easy
What is the simplified value of the expression 3x + 5 when x is a real number?
Statement IThe value of x is an integer.
Statement IIThe value of x is equal to 5.
ExplanationSubstituting x = 5 gives 3(5) + 5 = 20. Statement I alone only tells us x is integral, not its value. -
DS2 Easy
What is fifteen percent of the positive integer N?
Statement IThe integer N is equal to 240.
Statement IIThe integer N is divisible by 12.
ExplanationIf N = 240, then 15% of N = 36. Divisibility by 12 alone does not fix N (e.g. 12, 24, 36…).
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DS3 Medium
What is the value of (a + b) if both a and b are positive integers?
Statement IThe sum a + b is equal to 20.
Statement IIThe difference a − b is equal to 4.
ExplanationTogether, a + b = 20 and a − b = 4 give a = 12 and b = 8, so a + b = 20. Neither statement alone identifies both numbers. -
DS4 Medium
What is the numerical value of the expression 2³ × 3²?
Statement IThe expression evaluates to 72.
Statement IIThe sum of the digits of the result is 9.
ExplanationStatement I directly gives 72. Many numbers have digit sum 9 (18, 27, 72), so Statement II alone is insufficient.