## First question set for WBCS Main level Arithmetic

Compulsory paper VI of WBCS Main is on Arithmetic and Test of Reasoning. It has 200 questions to be answered in 180 minutes. In this first question set here on Arithmetic, 10 representative questions are included. The time recommended is 10 minutes.

### How to prepare before you answer the question set

To prepare for Arithmetic, you need to build the **base of Arithmetic concepts ***step by step* on: * Number system*,

*,*

**Factorization***,*

**HCF and LCM***, Indices,*

**Fractions surds and decimals***, Average and*

**Ratio and Proportion***. You may learn concepts from corresponding Tutorials in this website, and NCERT books.*

**Percentage**Together with concept reading, **you have to practice solving a lot of sums on these base topics** from NCERT books or good online resources. Unless you give enough dedicated time on this phase of building the base, you will fall short in next steps.

After building the base, preparation should start on the **Applications of Arithmetic**—topics on Time and Work, Work and wages, Speed time distance, Boats in rivers, Profit and loss, Simple interest and Compound interest and so on.

Following same method, you should do concept reading and then problem solving on each topic. Worked out sums from NCERT books, and concept tutorials from this website should quickly give you confidence to start solving problems yourself.

### Important to remember—One: Understand concepts first

Without understanding worked out sums or going through concept reading you shouldn't start to practice solving sums.

### Important to remember—two: Ability in maths builds step by step

**Don't skip any step**. For example, without giving sufficient time on say, visualization of factors in multiples, or building Arithmetic base, you should not try to conquer Arithmetic applications.

### Important to remember—three: Don't be impatient with maths preparation

Compared to any other subject in competitive exams, building Maths excellence takes maximum time. Be patient, work systematically and hard in a planned manner.

After you covered these three, the last and **most important item confronts you**.

In competitive math MCQ tests, you can't think of solving sums procedurally step by step, you must practice solving such problems in mind, wholly based on concepts, but in mind applying analytical reasoning. With as little writing as possible. This is what we call

Efficient Math Problem solving.

After answering this question set, scoring yourself (+2 correct, -0.5 incorrect) and measuring time, if you go through the **companion solution** (link given at the end), you might get an idea on what we mean by efficient math problem solving.

Now let us get down to solving the question set with your time watch on.

### 1st WBCS main level Arithmetic: time 10 mins

#### Problem 1

If A and B complete a job working together in 20 days, B and C together in 15 days and C and A in 12 days, all three working together will be able to complete the same job in,

- 9 days
- 10 days
- 10.5 days
- 6 days

#### Problem 2

If $x$ is a prime number, the LCM of $x$ and $(x+1)$ is,

- $x^2$
- $(x+1)^2$
- $\displaystyle\frac{x(x+1)}{2}$
- $x(x+1)$

#### Problem 3

$\left(2-\displaystyle\frac{1}{3}\right)\left(2-\displaystyle\frac{3}{5}\right)\left(2-\displaystyle\frac{5}{7}\right)...\left(2-\displaystyle\frac{999}{1001}\right)$ is equal to,

- $\displaystyle\frac{1003}{3}$
- $\displaystyle\frac{999}{1001}$
- $\displaystyle\frac{1001}{3}$
- None of these

#### Problem 4

The value of $\displaystyle\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}$ is,

- 2
- 4
- $\sqrt{2}$
- 8

#### Problem 5

The difference between the squares of two consecutive even integers is always divisible by,

- 3
- 4
- 6
- 7

#### Problem 6

The least number which when divided by 15, 27, 35, and 42 leaves a remainder of 7 in each division is,

- 1883
- 2007
- 1897
- 1987

#### Problem 7

$\left(\displaystyle\frac{243}{32}\right)^{-\displaystyle\frac{4}{5}}$ is equal to,

- $\displaystyle\frac{81}{16}$
- $\displaystyle\frac{16}{81}$
- $\displaystyle\frac{2}{9}$
- $\displaystyle\frac{9}{2}$

#### Problem 8

$\sqrt{248 +\sqrt{52 + \sqrt{144}}}$ is equal to,

- 16.6
- 16
- 14
- 18.8

#### Problem 9

The ratio of cost price to sale price is 20 : 23. What is the profit percentage?

- 20%
- 15%
- 5%
- 6%

#### Problem 10

$\sqrt[3]{0.000216}$ is equal to,

- 0.6
- 0.006
- 0.06
- 0.0006

Solutions to these problems with conceptual explanation, and how to solve the problems easily and quickly, are available in companion solution set,

* WBCS Main level Arithmetic solution set 1*.

### Answers to the questions

**Problem 1. Answer:** Option b: 10 days.

**Problem 2. Answer:** Option d: $x(x+1)$.

**Problem 3.** **Answer:** Option a: $\displaystyle\frac{1003}{3}$.

**Problem 4. Answer:** Option a: 2.

**Problem 5.** **Answer:** Option b: 4.

**Problem 6.** **Answer:** Option c: 1897.

**Problem 7.** **Answer:** Option b: $\displaystyle\frac{16}{81}$.

**Problem 8.** **Answer:** Option b: 16.

**Problem 9.** **Answer:** Option b: 15%.

**Problem 10.** **Answer:** Option c: 0.06.

### Important tutorials on Arithmetic topics

**Numbers, Number systems and basic arithmetic operations**

**Fractions and decimals basic concepts part 1**

**Arithmetic problems on mixing liquids and based on ages**

**How to solve Arithmetic problems on Work time, Work wages and Pipes and cisterns**

**Basic concepts on problems on speed time distance, Train running and Boats in rivers**

**Basic and rich concepts on Simple interest and Compound interest**

**Basic and rich percentage concepts**

### Question and Solution sets on WBCS Main Aritmetic

**WBCS Main level Arithmetic Solution set 4**

**WBCS Main level Arithmetic Question set 4**

**WBCS Main level Arithmetic Solution set 3**

**WBCS Main level Arithmetic Question set 3**

**WBCS Main level Arithmetic Solution set 2**

**WBCS Main level Arithmetic Question set 2**

**WBCS Main level Arithmetic Solution set 1**

**WBCS Main level Arithmetic Question set 1**