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100+ Free BCS Written Math & Mental Ability Practice Questions

Pass your BCS Written Compulsory: Mathematical Reasoning & Mental Ability exam on the first try — instant access, no signup required.

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2026 Statistics

Key Facts: BCS Written Math & Mental Ability Exam

100

Total Marks

BPSC Syllabus

50

Math Marks

BPSC Syllabus

50

Mental Ability MCQs

BPSC Syllabus

0.5

Negative Mark per MCQ

BPSC Exam Rules

Cycle-wise

Qualifying Standard

BPSC Rules

The BCS Written Compulsory Math & Mental Ability component evaluates secondary-level mathematics and cognitive/logical reasoning. It forms a key part of the 900-mark written stage for general cadres.

Sample BCS Written Math & Mental Ability Practice Questions

Try these sample questions to test your BCS Written Math & Mental Ability exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1If the price of sugar increases by 25%, by what percentage must a household reduce its sugar consumption so that its expenditure on sugar remains unchanged?
A.20%
B.25%
C.15%
D.30%
Explanation: Let the original price of sugar be P and consumption be C. Original expenditure = P * C. New price = 1.25 * P. Let the new consumption be C'. To keep expenditure same, 1.25 * P * C' = P * C. Therefore, C' = C / 1.25 = 0.8 * C. This represents a reduction of (1 - 0.8) * 100 = 20% in consumption. Alternatively, reduction percentage = [r / (100 + r)] * 100 = [25 / 125] * 100 = 20%.
2The average weight of 8 men is increased by 1.5 kg when a new man replaces one of them who weighs 65 kg. What is the weight of the new man?
A.70 kg
B.73 kg
C.75 kg
D.77 kg
Explanation: Total weight increase for the 8 men = 8 * 1.5 kg = 12 kg. Since this increase is caused by replacing a man weighing 65 kg with a new man, the new man must weigh 65 kg + 12 kg = 77 kg.
3A sum of 12,000 BDT is to be divided among A, B, and C in the ratio 2 : 3 : 5. How much more money will C receive compared to B?
A.2,400 BDT
B.3,600 BDT
C.6,000 BDT
D.1,200 BDT
Explanation: The ratio is 2 : 3 : 5, which means the sum of parts = 2 + 3 + 5 = 10. Total sum = 12,000 BDT. One part = 12,000 / 10 = 1,200 BDT. B's share = 3 parts = 3 * 1,200 = 3,600 BDT. C's share = 5 parts = 5 * 1,200 = 6,000 BDT. The difference between C's share and B's share = 6,000 - 3,600 = 2,400 BDT (or directly: 5 - 3 = 2 parts = 2 * 1,200 = 2,400 BDT).
4By selling a watch for 1,440 BDT, a shopkeeper incurs a loss of 10%. At what price must he sell the watch to gain 10%?
A.1,600 BDT
B.1,760 BDT
C.1,800 BDT
D.1,680 BDT
Explanation: Let the Cost Price (CP) be x BDT. A loss of 10% means Selling Price (SP) is 90% of CP. So, 0.9 * x = 1,440 BDT => x = 1,440 / 0.9 = 1,600 BDT. To gain 10%, the new SP must be 110% of CP. New SP = 1.1 * 1,600 = 1,760 BDT.
5A sum of money doubles itself in 8 years at a certain rate of simple interest. In how many years will it triple itself at the same rate of interest?
A.12 years
B.16 years
C.24 years
D.10 years
Explanation: Under simple interest, the interest earned is constant for equal intervals of time. Let the principal sum be P. If it doubles in 8 years, the interest earned is P. To triple itself, the total amount must be 3P, meaning the total interest earned must be 2P. Since P interest is earned in 8 years, 2P interest will require 8 * 2 = 16 years.
6If $x + y = 7$ and $xy = 12$, what is the value of $x^2 + y^2$?
A.25
B.13
C.49
D.37
Explanation: Using the algebraic identity: $(x + y)^2 = x^2 + 2xy + y^2$. Rearranging, we get $x^2 + y^2 = (x + y)^2 - 2xy$. Substituting the given values: $x^2 + y^2 = 7^2 - 2(12) = 49 - 24 = 25$. Alternatively, by inspection, the numbers are 3 and 4 (since 3 + 4 = 7 and 3 * 4 = 12). Thus, $3^2 + 4^2 = 9 + 16 = 25$.
7Solve the exponential equation for $x$: $2^{x+3} + 2^x = 9$.
A.$x = 0$
B.$x = 1$
C.$x = 2$
D.$x = -1$
Explanation: We can rewrite $2^{x+3}$ as $2^x * 2^3$. So the equation becomes: $2^x * 8 + 2^x = 9 \implies 2^x(8 + 1) = 9 \implies 2^x * 9 = 9 \implies 2^x = 1$. Since $2^0 = 1$, we must have $x = 0$.
8In a group of 100 students, 60 study English, 45 study mathematics, and 20 study both. How many students study neither English nor mathematics?
A.15
B.25
C.5
D.35
Explanation: Let E be the set of students studying English and M be the set of students studying mathematics. We are given: n(Total) = 100, n(E) = 60, n(M) = 45, and n(E ∩ M) = 20. The number of students studying at least one of the subjects is n(E ∪ M) = n(E) + n(M) - n(E ∩ M) = 60 + 45 - 20 = 85. The number of students studying neither is n(Total) - n(E ∪ M) = 100 - 85 = 15.
9A father's age is 4 times that of his son. Six years ago, the father was 7 times as old as his son. What is the father's current age?
A.40 years
B.48 years
C.36 years
D.44 years
Explanation: Let the son's current age be s. The father's current age is 4s. Six years ago, the son's age was s - 6 and the father's age was 4s - 6. We are given: $4s - 6 = 7(s - 6) \implies 4s - 6 = 7s - 42 \implies 3s = 36 \implies s = 12$. The father's current age is 4 * 12 = 48 years.
10What is the 12th term of the arithmetic progression: 5, 9, 13, 17, ...?
A.45
B.49
C.53
D.41
Explanation: The first term (a) = 5. The common difference (d) = 9 - 5 = 4. The formula for the nth term of an arithmetic progression is $a_n = a + (n - 1)d$. For the 12th term (n = 12): $a_{12} = 5 + (12 - 1) * 4 = 5 + 11 * 4 = 5 + 44 = 49$.

About the BCS Written Math & Mental Ability Exam

The Mathematical Reasoning & Mental Ability exam is a compulsory component of the Bangladesh Civil Service (BCS) Written Examination. It consists of two parts: a 50-mark Mathematical Reasoning section (usually subjective/written in the real exam, requiring candidates to show detailed calculations) and a 50-mark Mental Ability section (which is conducted as a 50-question MCQ test with negative marking of 0.5 marks per wrong answer). This practice bank consolidates both areas into 100 high-quality MCQ questions to facilitate comprehensive preparation, covering algebra, arithmetic, geometry, logical reasoning, numerical series, spatial ability, and verbal reasoning.

Assessment

100 multiple-choice questions (Practice Bank Format)

Time Limit

3 hours

Passing Score

BPSC sets minimum qualifying standards per cycle; merit ranking, not a fixed percentage, determines written qualification

Exam Fee

Tk 200 (Bangladesh Public Service Commission (BPSC))

BCS Written Math & Mental Ability Exam Content Outline

50%

Mathematical Reasoning

Covers arithmetic, algebraic identities, linear & quadratic equations, inequalities, progressions, sets, logarithms, geometry, trigonometry, and statistics/probability.

50%

Mental Ability

Covers logical reasoning, analogies, coding-decoding, blood relations, calendar & clocks, number & letter series, mirror & water images, direction sense, and spatial puzzles.

How to Pass the BCS Written Math & Mental Ability Exam

What You Need to Know

  • Passing score: BPSC sets minimum qualifying standards per cycle; merit ranking, not a fixed percentage, determines written qualification
  • Assessment: 100 multiple-choice questions (Practice Bank Format)
  • Time limit: 3 hours
  • Exam fee: Tk 200

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

BCS Written Math & Mental Ability Study Tips from Top Performers

1Practice basic algebraic equations and identities, as they form the foundation of many Mathematical Reasoning questions.
2Memorize key geometry formulas for areas, volumes, and properties of triangles, circles, and quadrilaterals.
3Work on numerical series and coding-decoding questions daily to increase speed and recognize patterns quickly for the Mental Ability section.
4Understand direction tests and spatial orientation (e.g., mirror images and folding patterns) which are common spatial ability items.
5Be careful with negative marking in the Mental Ability section; skip questions if you are unsure of the answer.

Frequently Asked Questions

What is the breakdown of marks for Math and Mental Ability in the BCS Written Exam?

The Written Compulsory Math & Mental Ability paper carries 100 marks in total. Mathematical Reasoning carries 50 marks, and Mental Ability carries 50 marks. In the actual BPSC exam, the Mental Ability section is MCQ-based, while the Mathematical Reasoning section is subjective.

Is there negative marking in the BCS Written Mental Ability section?

Yes, in the official BPSC written exam, the Mental Ability section has 50 MCQs, and 0.5 marks are deducted for each wrong answer, making it highly critical to avoid guessing.

What is the standard of math tested in the BCS Written Exam?

The math questions are based on secondary school levels (Class 9-10 General Math and Higher Math). Topics include arithmetic, algebra, geometry, sets, logarithms, and basic probability.

Are calculators allowed in the BCS Written Exam?

Calculators are generally not allowed in the Preliminary exam, but non-programmable calculators are permitted during the written subjective Mathematical Reasoning exam.