Arithmetic Questions and Answers

Q1 :

Which one of the following number is exactly divisible by 11 ?

A

315624

B

245642

C

415624

D

235641

View Answer

Correct Answer: C

415624

Description:

Q2 :

The product of two numbers is forty five and their difference is four. The sum squares of the 2 numbers is

A

135

B

240

C

73

D

106

View Answer

Correct Answer: D

106

No Description

Q3 :

The value of expression

$1 div Biggl{ frac{1}{2} + frac{1}{3} + frac{1}{6} div bigg(frac{3}{4}-frac{1}{3}bigg) Biggr}$ is:

A

$frac{5}{12}$

B

$frac{1}{12}$

C

$frac{30}{37}$

D

1

View Answer

Correct Answer: C

$frac{30}{37}$

Description:

$=1div Biggl{ frac{1}{2} + frac{1}{3} + frac{1}{6} div bigg(frac{3}{4}-frac{1}{3}bigg) Biggr}$

$=1div Biggl{ frac{1}{2} + frac{1}{3} + frac{1}{6} div frac{5}{12} Biggr}$

$=1div Bigg{ frac{1}{2} + frac{1}{3} + frac{1}{6} times frac{12}{5} Bigg}$

$=1div Bigg{ frac{1}{2} + frac{1}{3} + frac{2}{5} Bigg} = frac{30}{37}$

Q4 :

Find the square root of 20.8849

A

.457

B

4.57

C

45.7

D

457

View Answer

Correct Answer: B

4.57

Description:

= 4.57*4.57
= 20.8849

Q5 :

Find the value of $sqrt{frac{36.1}{102.4}}$

A

$frac{19}{34}$

B

$frac{19}{31}$

C

$frac{6.1}{34}$

D

$frac{19}{32}$

View Answer

Correct Answer: D

$frac{19}{32}$

Description:

$=sqrt{frac{36.1}{102.4}} = sqrt{frac{361}{1024}} = frac{19}{32}$

Q6 :

The decimal number $0.overline{32}$ is equal to the rational number

A

$frac{32}{100}$

B

$frac{32}{99}$

C

$frac{30}{100}$

D

$frac{31}{99}$

View Answer

Correct Answer: B

$frac{32}{99}$

Description:

$text{ Let } x = 0.overline{32} = 0.323232...$

$therefore 100x = 32.323232...$

$= 32.overline{32} Rightarrow 99x = 32$

$therefore x = frac{32}{99}$

Q7 :

Which one of the following measures of central tendency gives greater importance to smaller and lesser importance to bigger items of a series?

A

Arithmetic mean

B

Geometric mean

C

Median

D

Mode

View Answer

Correct Answer: B

Geometric mean

Description:

Geometric mean gives the greater importance to smaller and lesser importance to bigger items of a series.

Q8 :

The mean of 5 observations $x, x+ 2, x + 4, x + 6 text{ and } x + 8$ is 11. Then the mean of last 3 observations is

A

11

B

13

C

15

D

17

View Answer

Correct Answer: B

13

Description:

Mean of the given observations

$= x + 4 = 11 Rightarrow x = 7$

Required mean of the last three observations

$= x + 6 = 13$

Q9 :

The arithmetic mean of $n$ number is $overline{x}$ . The sum of the first $(n - 1)$ numbers is $k$ . The $n$ th number is

A

$n overline{x} - 2k$

B

$n overline{x} - k$

C

$n overline{x} + k$

D

$n overline{x} + 2k$

View Answer

Correct Answer: B

$n overline{x} - k$

Description:

The sum of $n$ number $= n ; overline { x}$ ,
any given sum of $(n - 1)text{th no. } = k$
$therefore text{ nth number } = n ; overline{x} - k$

Q10 :

If $frac{3}{4}$ of an estate is worth Rs. 90,000/-, then the value of $frac{2}{3}$ of the same will be

A

Rs. 60,000

B

Rs. 65,000

C

Rs. 70,000

D

Rs. 80,000

View Answer

Correct Answer: D

Rs. 80,000

Description:

The value of $frac{2}{3}$ rd estate is $= frac{90,000 times 4 times 2}{3 times 3}$

= Rs. 80,000/-

Q11 :

Let $n[text{X}]$ denote the number of elements in the set $text{X}$ . If for two sets A and B, $n$ [A] = 12, $n$ [B] = 30, $n$ [A $cap$ B] = 25, then $n$ [A $cup$ B] is equal to

A

25

B

19

C

17

D

15

View Answer

Correct Answer: C

17

Description:

Apply $n(A cup B) = n(text{A}) + n(text{B}) - n(text{A} cap text{B})$

Q12 :

The value of $frac{(.05 times .05 times .05) + (.04 times .04 times .04)}{(.05 times .05) - (.05 times .04) + (.04 times .04)}$ is

A

0.0009

B

0.01

C

0.09

D

0.41

View Answer

Correct Answer: C

0.09

Description:

Apply the formula $frac{a^3 + b^3}{a^2 - ab + b^2} = (a + b)$

where $a = 0.05 text{ and } b = 0.04$

Q13 :

If A and B are two sets, then $text{A} cap (text{A} cup text{B})$ is equal to

A

B

C

$phi$

D

A $cap$ B

View Answer

Correct Answer: C

$phi$

Description:

$text{A} cap (text{A} cup text{B})text{'} = text{A} cap (text{A'} cap text{B'})$

$= (text{A} cap text{A'}) cap text{B'} = phi cap text{B'} = phi$

Q14 :

Let N be the set of all natural numbers, E be the universal set, $phi$ be the null set and B be the unit set containing 0, i.e. B = {0}. If A is the subset of every set X, then A is equal to

A

N

B

C

$phi$

D

E

View Answer

Correct Answer: C

$phi$

Description:

Empty set is a subset of every set.

Q15 :

If $n$ is any whole number, $n^2 (n^2 - 1)$ is always divisible by:

A

12

B

24

C

36

D

9

View Answer

Correct Answer: A

12

Description:

Here we can apply least value of whole no. in the place $n^2 (n^2 - 1)$ except 0 and 1.

$n^2 (n^2 - 1) = 2^2 (2^2 - 1 ) = 12$

Q16 :

Simplify: $sqrt{75} + sqrt{48} - sqrt{243}$

A

0

B

$2sqrt{3}$

C

$3sqrt{3}$

D

$4sqrt{3}$

View Answer

Correct Answer: A

0

Description:

$sqrt{75} + sqrt{48} - sqrt{243}$

$=5sqrt{3} + 4sqrt{3} - 9sqrt{3}$

$=sqrt{3}(5 + 4 -9)$

$=sqrt{3} times 0$

$=0$

Q17 :

Solve the following—
$sqrt{0.0625} + sqrt{0.250} = text{ ?}$

A

.005

B

0.5

C

5

D

None of the Above

View Answer

Correct Answer: D None of the Above

Description:

$begin{aligned} sqrt{0.0625} + sqrt{0.250} Rightarrow .25 + .5 = .75 end{aligned}$

Q18 :

Solve the following equation:

$8461 div 11.99 - 24.01 div frac{5}{10} = ?$

A

225

B

625

C

400

D

25

View Answer

Correct Answer: A

225

Description:

$8461 div 11.99 - 24.01 div frac{5}{10}$

$approx 705 - 24 times 20$

$approx 705 - 480$

$approx 225$

Q19 :

If in a grouped data median is 50 and each frequency is multiplied by 3, then the new median is—

A

300

B

150

C

50

D

None of the above

View Answer

Correct Answer: C

50

No Description

Q20 :

If $23 times 5 = 26$ and $13 times 8 = 19$ , then $39 times 7$ =

A

42

B

43

C

44

D

40

View Answer

Correct Answer: C

44

Description:

$begin{aligned} because quad & 23+5-2 = 26 & 13+8-2 = 19 therefore quad & 39+7-2 = 44 end{aligned}$

Q21 :

What is the value of $x$ for which $x, x + 1, x + 3$ are all prime numbers?

A

0

B

1

C

2

D

101

View Answer

Correct Answer: C

2

Description:

If $x = 2$ , then, $x, x + 1$ and $x + 3$ are all prime numbers.

Q22 :

Which of the following statements about the number 222222 is correct?

A

It is divisible by 3 but not divisible by 7

B

It is divisible by 3 and 7 but not divisible by 11

C

It is divisible by 2 and 7 but not divisible by 11

D

It is divisible by 3, 7 and 11

View Answer

Correct Answer: D

It is divisible by 3, 7 and 11

Description:

Given, number is 222222.

Here, sum of digits
= 2 + 2 + 2 + 2 + 2 + 2 = 12,
which is divisible by 3. So, given number
is divisible by 3.

Now, sum of odd terms of digits − Sum
of even terms of digits = 6 − 6 = 0,
it is divisible by 11.

Also, in a number if a digit is repeated
six times, then the number is divisible by
7, 11 and 13.

Hence, the given number is divisible by
3, 7 and 11.