## 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.

Before going through the test, to *refresh concepts* on any topic or to know *how to solve problems at a high speed*, you should refer to **our concept tutorials and articles** listed below.

### Concept tutorials and articles on Arithmetic

#### Number system, fractions and surds

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

**Factorization or finding out factors**

**Fractions and decimals, basic concepts part 1**

**How to solve surds part 1 rationalization**

**How to solve surds part 2 double square root surds and surd term factoring**

#### Ratio and proportion and mixing liquids

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

**How to solve arithmetic mixture problems in a few steps 1**

**How to solve arithmetic mixture problems in a few steps 2**

#### Percentage

**Basic and rich percentage concepts**

#### Componendo dividendo

**Componendo dividendo explained**

#### Simple interest and compound interest

**Basic and rich concepts on simple interest and compound interest**

#### Work time, work wages and pipes and cisterns

**How to solve arithmetic problems on work time, work wages and pipes and cisterns**

**How to solve time work problems in simpler steps type 1**

**How to solve time work problems in simpler steps type 2**

#### Speed time distance, train problems and boats in rivers

**Basic concepts on speed time distance, train running and boats and rivers**

**How to solve time distance problems in a few simple steps 1**

**How to solve time distance problems in a few simple steps 2**

#### Profit and loss

**How to solve in a few steps profit and loss problems 1**

**How to solve similar problems in a few seconds profit and loss problems 2**

**How to solve difficult profit and loss problems in a few steps 3**

**How to solve difficult profit and loss problems in a few steps 4**

### 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.

### Question and Solution sets on WBCS Main Arithmetic

**WBCS main level Arithmetic Solution set 8**

**WBCS main level Arithmetic Question set 8**

**WBCS Main level Arithmetic Solution Set 7**

**WBCS Main level Arithmetic Question Set 7**

**WBCS Main level Arithmetic Solution set 6**

**WBCS Main level Arithmetic Question set 6**

**WBCS Main level Arithmetic Solution set 5**

**WBCS Main level Arithmetic Question set 5**

**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**