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# Arithmetical Reasoning MCQ

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## 25 Questions MCQ Test | Arithmetical Reasoning MCQ

Arithmetical Reasoning MCQ for CLAT 2022 is part of CLAT preparation. The Arithmetical Reasoning MCQ questions and answers have been prepared according to the CLAT exam syllabus.The Arithmetical Reasoning MCQ MCQs are made for CLAT 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Arithmetical Reasoning MCQ below.
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Arithmetical Reasoning MCQ - Question 1

### A shepherd had 17 sheep. All but nine died. How many was he left with?

Detailed Solution for Arithmetical Reasoning MCQ - Question 1

'All but nine died' means 'All except nine died' i.e. 9 sheep remained alive.

Arithmetical Reasoning MCQ - Question 2

### A bird shooter was asked how many birds he had in the bag. He replied that there were all sparrows but six, all pigeons but six, and all ducks but six. How many birds he had in the bag in all?

Detailed Solution for Arithmetical Reasoning MCQ - Question 2

There were all sparrows but six' means that six birds were not sparrows but only pigeons and ducks.
Similarly, number of sparrows + number of ducks = 6 and number of sparrows + number of pigeons = 6.
This is possible when there are 3 sparrows, 3 pigeons and 3 ducks i.e. 9 birds in all.

Arithmetical Reasoning MCQ - Question 3

### What is the smallest number of ducks that could swim in this formation—two ducks in front of a duck, two ducks behind a duck and a duck between two ducks?

Detailed Solution for Arithmetical Reasoning MCQ - Question 3

Clearly, the smallest such number is 3. Three ducks can be arranged as shown above to satisfy all the three given conditions.

Arithmetical Reasoning MCQ - Question 4

The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner?

Detailed Solution for Arithmetical Reasoning MCQ - Question 4

Clearly, every member except one (i.e. the winner) must lose one game to decide the winner. Thus, minimum number of matches to be played = 30 - 1 = 29.

Arithmetical Reasoning MCQ - Question 5

A man wears socks of two colours—black and brown. He has altogether 20 black socks and 20 brown socks in a drawer. Supposing he has to take out the socks in the dark, how many must he take out to be sure that he has a matching pair?

Detailed Solution for Arithmetical Reasoning MCQ - Question 5

Since there are socks of only two colours, so two out of any three socks must always be of the same colour.

Arithmetical Reasoning MCQ - Question 6

What is the product of all the numbers in the dial of a telephone?

Detailed Solution for Arithmetical Reasoning MCQ - Question 6

Since one of the numbers on the dial of a telephone is zero, so the product of all the numbers on it is 0.

Arithmetical Reasoning MCQ - Question 7

A group of 1200 persons consisting of captains and soldiers is travelling in a train. For every 15 soldiers there is one captain. The number of captains in the group is

Detailed Solution for Arithmetical Reasoning MCQ - Question 7

Generally we may commit mistake of dividing 1200/15.
But out of 16 persons there is one captain.
so, it will be 1200/16 = 75

Arithmetical Reasoning MCQ - Question 8

Aruna cut a cake into two halves and cuts one half into smaller pieces of equal size. Each of the small pieces is twenty grams in weight. If she has seven pieces of the cake in all with her, how heavy was the original cake?

Detailed Solution for Arithmetical Reasoning MCQ - Question 8

Seven pieces of cakes means one half cake and six pieces of another half cake
Total weight of 6 small pieces =6 x 20 g=120g
∴ Weight of the half cake=120 g
Total weight of the cake=240 g.

Arithmetical Reasoning MCQ - Question 9

First bunch of bananas has 1/4 again as many bananas as a second bunch. If the second bunch has 3 bananas less than the first bunch, then the number of bananas in the-first bunch is

Detailed Solution for Arithmetical Reasoning MCQ - Question 9

Assuming the number of bananas in the second bunch to be x
No. of bananas in 1st is x + x/4 = 5x/4
So, 5x/4 - x = 3x/4 = 3
x = 12
No. of bananas in 1st = 5x/4 = 5 x 12/4 = 5 x 3 = 15

Arithmetical Reasoning MCQ - Question 10

A tailor had a number of shirt pieces to cut from a roll of fabric. He cut each roll of equal length into 10 pieces. He cut at the rate of 45 cuts a minute. How many rolls would be cut in 24 minutes ?

Detailed Solution for Arithmetical Reasoning MCQ - Question 10

It is quite clear that the number of cuts made to cut a roll into 10 pieces = 9.
So, required number of rolls = (45 x 24)/9 = 120 rolls
Hence, option (D) is the correct answer.

Arithmetical Reasoning MCQ - Question 11

In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If the number of boys participating in the sports is 15, then how many girls are there in the class?

Detailed Solution for Arithmetical Reasoning MCQ - Question 11

Let the number of boys and girls participating in sports be 3x and 2x respectively.
Then, 3x = 15 or x = 5.
So, number of girls participating in sports = 2x = 10.
Number of students not participating in sports = 60 - (15 + 10) = 35.
Let number of boys not participating in sports be y.
Then, number of girls not participating in sports = (35 -y).
Therefore (35 - y) = y + 5 <=> 2y<=>  30<=> y = 15.
So, number of girls not participating in sports = (35 - 15) = 20.
Hence, total number of girls in the class = (10 + 20) = 30.

Arithmetical Reasoning MCQ - Question 12

In a class, there are 18 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class?

Detailed Solution for Arithmetical Reasoning MCQ - Question 12

Let the number of boys be x.
Then, 3/4 x = 18
=> x = 24
If total number of students is y, then
2/3 y = 24
=> y = 36
Number of girls in class = y - x
= 36 - 24 = 12

Arithmetical Reasoning MCQ - Question 13

A student got twice as many sums wrong as he got right. If he attempted 48 sums in all, how many did he solve correctly?

Detailed Solution for Arithmetical Reasoning MCQ - Question 13

Let us suppose right sums are x then according to question wrong sums will be 2x and we know if we sum up right ones with the wrong then we will get no of questions attempted ' 2x+x = 48 then we will get value of x= 16

Arithmetical Reasoning MCQ - Question 14

The number of boys in a class is three times the number of girls. Which one of the following numbers cannot represent the total number of children in the class?

Detailed Solution for Arithmetical Reasoning MCQ - Question 14

Let number of girls = x and number of boys = 3x.
Then, 3x + x = 4x = total number of students.
Thus, to find exact value of x, the total number of students must be divisible by 4. 42 is not divisible by 4.

Arithmetical Reasoning MCQ - Question 15

A placed three sheets with two carbons to get two extra copies of the original. Then he decided to get more carbon copies and folded the paper in such a way that the upper half of the sheets were on top of the lower half. Then he typed. How many carbon copies did he get?

Detailed Solution for Arithmetical Reasoning MCQ - Question 15

Since the number of carbons is 2, only two copies can be obtained.

Arithmetical Reasoning MCQ - Question 16

A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle?

Detailed Solution for Arithmetical Reasoning MCQ - Question 16

Total number of routes from Bristol to Carlisle =(4×3×2)=24.

Arithmetical Reasoning MCQ - Question 17

A pineapple costs Rs. 7 each. A watermelon costs Rs. 5 each. X spends Rs. 38 on these fruits. The number of pineapples purchased is

Detailed Solution for Arithmetical Reasoning MCQ - Question 17

Let the number of pineapples and watermelons be x and y respectively.
Then, 7x+5y=38 or 5y=(38−7x)
or y= 5
38−7x
​Clearly, y is a whole number, only when (38−7x) is divisible by 5.
This happens when x=4.

Arithmetical Reasoning MCQ - Question 18

If you write down all the numbers from 1 to 100, then how many times do you write 3?

Detailed Solution for Arithmetical Reasoning MCQ - Question 18

Clearly, from 1 to 100, there are ten numbers with 3 as the unit's digit- 3, 13, 23, 33, 43, 53, 63, 73, 83, 93; and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.

So, required number = 10 + 10 = 20.

Arithmetical Reasoning MCQ - Question 19

The total number of digits used in numbering the pages of a book having 366 pages is

Detailed Solution for Arithmetical Reasoning MCQ - Question 19

Total number of digits
= (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)
= (1 x 9 + 2 x 90 + 3 x 267) = (9 + 180 + 801) = 990.

Arithmetical Reasoning MCQ - Question 20

A printer numbers the pages of a book starting with 1 and uses 3189 digits in all. How many pages does the book have?

Detailed Solution for Arithmetical Reasoning MCQ - Question 20

No. of digits in 1-digit page nos. = 1x9 = 9.
No. of digits in 2-digit page nos. = 2 x 90 = 180.
No. of digits in 3-digit page nos. = 3 x 900 = 2700.
No. of digits in 4-digit page nos. = 3189 - (9 + 180 + 2700) = 3189 - 2889 = 300.
Therefore No. of pages with 4-digit page nos. = (300/4) = 75.
Hence, total number of pages = (999 + 75) = 1074.

Arithmetical Reasoning MCQ - Question 21

In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is

Detailed Solution for Arithmetical Reasoning MCQ - Question 21

Each row contains 12 plants.

There are 11 gapes between the two corner trees (11 x 2) metres and 1 metre on each side is left.

Therefore Length = (22 + 2) m = 24 m.

Arithmetical Reasoning MCQ - Question 22

A farmer built a fence around his square plot. He used 27 fence poles on each side of the square. How many poles did he need altogether?

Detailed Solution for Arithmetical Reasoning MCQ - Question 22

Since each pole at the corner of the plot is common to its two sides, so we have :

Total number of poles needed = 27 x 4 - 4 = 108 - 4 = 104.

Arithmetical Reasoning MCQ - Question 23

An enterprising businessman earns an income of Re. 1 on the first day of his business. On every subsequent day, he earns an income which is just double of that made on the previous day. One the 10th day of business, his income is

Detailed Solution for Arithmetical Reasoning MCQ - Question 23

Income on the first day = Re. 1.
Income on the 2nd day =
Rs. (1×2)= Rs. 21
Income on the 3rd day =
Rs. (21×2)= Rs.22
and so on. Thus, Income on the rth day = Rs. 2n−1
.Therefore Income on the 10th day = Rs. 29
.

Arithmetical Reasoning MCQ - Question 24

In a family, the father took 1/4  of the cake and he had 3 times as much as each of the other members had. The total number of family members is

Detailed Solution for Arithmetical Reasoning MCQ - Question 24

Let the family members b x.
Father ate 1/4 of the cake;
Rest members got 3/4x,
the father had 3 times more than other members share i.e 3/4,
Now,
3(3/4x) = 1/4,
3/4x = 1/12,
36 = 4x,
X = 9,
9 + 1(father) = 10 total family member.

Arithmetical Reasoning MCQ - Question 25

A waiter’s salary consists of his salary and tips. During one week his tips were 5/4  of his salary. What fraction of his income came from tips?

Detailed Solution for Arithmetical Reasoning MCQ - Question 25

Let Salary = Rs. x. Then tips = Rs. ((5/4)x).
Total income = Rs. ∴ Required fraction = Use Code STAYHOME200 and get INR 200 additional OFF Use Coupon Code
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