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NTS MCQs

National Testing Service — Complete MCQ Bank

61 Questions
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How to prepare for NTS

NTS tests evaluate aptitude, analytical reasoning, quantitative ability, English and subject knowledge for admissions, scholarships and recruitment.

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11
Mathematics Medium

What is 30% of 40% of 500?

  • A50
  • B60
  • C70
  • D80
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Correct Answer: Option B — 60
Explanation: 40% of 500 = 200. 30% of 200 = 60. Successive percentages require applying one percentage to the result of another. This type appears in successive discount problems population growth and data interpretation. Never add the percentages directly as 70% of 500 gives the wrong answer of 350.
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12
Mathematics Medium

The average of 5 consecutive even numbers is 20. What is the largest number?

  • A22
  • B24
  • C26
  • D28
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Correct Answer: Option B — 24
Explanation: Consecutive even numbers: n n+2 n+4 n+6 n+8. Average = n+4 = 20 so n=16. Largest = 16+8 = 24. Consecutive number problems are common in competitive exams. Setting up the correct algebraic representation and using the average formula is the standard approach for solving such sequence problems efficiently.
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13
Mathematics Medium

What is the surface area of a sphere with radius 7 cm using π = 22/7?

  • A616 cm²
  • B600 cm²
  • C588 cm²
  • D624 cm²
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Correct Answer: Option A — 616 cm²
Explanation: Surface area = 4πr² = 4 × (22/7) × 49 = 4 × 22 × 7 = 616 cm². Sphere formulas for both surface area and volume (4/3)πr³ are standard geometry questions. Understanding which formula to apply and correctly substituting values including the radius is the key challenge in competitive exam geometry problems.
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14
Mathematics Medium

Two dice are rolled. What is the probability of getting a sum of 7?

  • A1/6
  • B5/36
  • C6/36
  • D7/36
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Correct Answer: Option C — 6/36
Explanation: Total outcomes = 36. Pairs giving sum 7: (1+6 2+5 3+4 4+3 5+2 6+1) = 6 pairs. Probability = 6/36 = 1/6. Dice probability requires careful enumeration of favorable outcomes from the total sample space. Such problems test systematic counting skills and are extremely common in competitive exam probability sections.
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15
Mathematics Medium

If sin θ = 3/5 what is cos θ for an acute angle?

  • A3/4
  • B4/5
  • C5/3
  • D3/5
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Correct Answer: Option B — 4/5
Explanation: Using Pythagorean theorem: opposite=3 hypotenuse=5 so adjacent = √(25-9) = 4. cos θ = 4/5. The 3-4-5 triple is the most used in trigonometry problems. Finding one trigonometric ratio from another using the Pythagorean identity is a standard and frequently tested competitive exam skill.
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16
Mathematics Medium

What is 40% of three-quarters of 200?

  • A45
  • B50
  • C55
  • D60
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Correct Answer: Option D — 60
Explanation: 3/4 of 200 = 150. 40% of 150 = 0.4×150 = 60. Multi-step percentage problems require sequential operations. Always complete the inner fraction first then apply the percentage. These chained calculations appear throughout competitive exams in discount problems population calculations and data interpretation questions.
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17
Mathematics Medium

A and B together do a job in 12 days. A alone takes 18 days. How long does B take alone?

  • A36 days
  • B30 days
  • C28 days
  • D24 days
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Correct Answer: Option A — 36 days
Explanation: B's rate = 1/12 - 1/18 = 3/36 - 2/36 = 1/36. B alone takes 36 days. This work problem requires subtracting individual rates from combined rates. Mastery of work-rate subtraction is essential as such problems appear in almost every competitive exam quantitative aptitude section often in more complex multi-worker forms.
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18
Mathematics Medium

What is the sum of arithmetic series: first term 1 last term 100 with 100 terms?

  • A5050
  • B4950
  • C5000
  • D5100
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Correct Answer: Option A — 5050
Explanation: Sum = n/2 × (first + last) = 100/2 × (1+100) = 50×101 = 5050. This famous result was demonstrated by Gauss. Arithmetic series formulas are fundamental for sequences and series questions and appear in problems involving salary increments equal installments and staircase patterns in competitive exams.
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19
Mathematics Medium

What is the discriminant of x² - 5x + 6 = 0?

  • A1
  • B4
  • C5
  • D6
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Correct Answer: Option A — 1
Explanation: Discriminant D = b²-4ac = (-5)²-4(1)(6) = 25-24 = 1. Since D > 0 there are two distinct real roots. The discriminant determines nature of roots: D>0 (two real roots) D=0 (one repeated root) D<0 (complex roots). This concept is fundamental in quadratic equations tested across all competitive exam levels.
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20
Mathematics Medium

The slope of a line through points (2 3) and (4 7) is?

  • A1
  • B2
  • C3
  • D4
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Correct Answer: Option B — 2
Explanation: Slope = (y₂-y₁)/(x₂-x₁) = (7-3)/(4-2) = 4/2 = 2. The slope formula measures the steepness and direction of a line. Positive slope rises left to right. Slope is fundamental in coordinate geometry forming the basis for line equations parallel lines perpendicular lines and linear modeling.
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