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NTS MCQs

National Testing Service — Complete MCQ Bank

1,081 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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761
Mathematics Medium

The product of two numbers is 48 and their HCF is 4. What is their LCM?

  • A12
  • B16
  • C24
  • D48
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Correct Answer: Option A — 12
Explanation: LCM × HCF = Product of the two numbers. LCM = 48 ÷ 4 = 12. This important formula is frequently tested in competitive exams. It allows rapid calculation of LCM or HCF when the product and one factor are known making it a key shortcut for number theory problems in timed exam conditions.
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762
Mathematics Medium

If 5 workers finish a job in 8 days how many days will 10 workers take?

  • A2 days
  • B4 days
  • C6 days
  • D8 days
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Correct Answer: Option B — 4 days
Explanation: Total work = 5×8 = 40 worker-days. With 10 workers: days = 40÷10 = 4 days. Work and time problems rely on the inverse relationship between number of workers and time. They are among the most common question types in competitive exams requiring understanding of work rate as a fundamental concept.
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763
Mathematics Medium

A man walks 4 km North then 3 km East. How far is he from the start?

  • A5 km
  • B6 km
  • C7 km
  • D8 km
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Correct Answer: Option A — 5 km
Explanation: This forms a right triangle with legs 4 and 3. Distance = √(4²+3²) = √(16+9) = √25 = 5 km. The 3-4-5 Pythagorean triple is the most commonly used in competitive exams. The Pythagorean theorem a²+b²=c² is applied in distance navigation construction and coordinate geometry problems.
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764
Mathematics Medium

In a right triangle if one angle is 30° what is the other acute angle?

  • A45°
  • B50°
  • C60°
  • D70°
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Correct Answer: Option C — 60°
Explanation: Sum of angles = 180°. With 90° and 30° the third angle = 180°-90°-30° = 60°. The 30-60-90 triangle has side ratios 1:√3:2 and is one of the most important special triangles in mathematics. It appears extensively in trigonometry geometry and physics problems in all levels of competitive examinations.
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765
Mathematics Medium

If 3x - 7 = 2x + 5 what is x?

  • A10
  • B12
  • C14
  • D16
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Correct Answer: Option B — 12
Explanation: Subtract 2x: x - 7 = 5. Add 7: x = 12. Solving linear equations with variables on both sides is a core algebraic skill. Such equations frequently appear in word problems about ages work rates and number relationships in competitive exams. The key step is collecting like terms on each side methodically.
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766
Mathematics Medium

What is the compound interest on Rs 1000 for 2 years at 10% per annum?

  • ARs 200
  • BRs 210
  • CRs 220
  • DRs 100
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Correct Answer: Option B — Rs 210
Explanation: CI = P(1+r/100)ⁿ - P = 1000(1.1)² - 1000 = 1210 - 1000 = Rs 210. Compound interest exceeds simple interest because interest is earned on previously accumulated interest. CI problems appear in banking and finance sections of competitive exams and require correct application of the compound interest formula.
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767
Mathematics Medium

Two numbers are in ratio 5:3 and their sum is 40. What is the larger number?

  • A20
  • B25
  • C30
  • D35
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Correct Answer: Option B — 25
Explanation: Let numbers be 5x and 3x. Sum = 8x = 40 so x = 5. Larger = 5×5 = 25. Ratio problems requiring algebraic substitution are consistent in competitive exams. Using a common multiplier x to represent ratio parts then solving with the given total sum or difference is the most reliable standard method.
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768
Mathematics Medium

If the simple interest on Rs 1000 for 2 years is Rs 100 what is the rate?

  • A4%
  • B5%
  • C6%
  • D8%
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Correct Answer: Option B — 5%
Explanation: SI = (P×R×T)/100 → 100 = (1000×R×2)/100 → 100 = 20R → R = 5%. Simple interest problems are standard in competitive exams. The ability to rearrange the SI formula to find principal rate or time is a key skill. Always identify which variable is unknown and rearrange accordingly before substituting values.
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769
Mathematics Medium

Simplify: (a² - b²) divided by (a - b)

  • Aa + b
  • Ba - b
  • Ca² + b²
  • Dab
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Correct Answer: Option A — a + b
Explanation: a² - b² factors as (a+b)(a-b) using the difference of squares identity. Dividing by (a-b) cancels that factor leaving (a+b). Recognizing algebraic identities including difference of squares perfect square trinomials and sum or difference of cubes is essential for quickly simplifying expressions in competitive exam algebra sections.
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770
Mathematics Easy

What is the value of 3 factorial?

  • A3
  • B6
  • C9
  • D12
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Correct Answer: Option B — 6
Explanation: 3! = 3 × 2 × 1 = 6. Factorial of n is the product of all positive integers from 1 to n. Factorials appear in permutations combinations probability and the binomial theorem. Key values to memorize are: 0!=1 1!=1 2!=2 3!=6 4!=24 5!=120 6!=720 for competitive exam speed and accuracy.
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