Arithmetical reasoning - Reasoning

Arithmetical reasoning

In arithmetical reasoning, questions are based on calculations on problems, data based, ages, Venn-diagrams. This is to test the ability of candidate and the candidate is required to select the appropriate answer for the given questions.

Arithmetical reasoning questions are divided into four types. They are:

1. Calculations based on problems.

2. Data based questions.

3. Problems on ages.

4. Venn diagram based questions.

1. The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago ?

A.        71 years                 B. 72 years                 C. 74 years                 D. 77 years

Answer: Option A

Explanation:

Required sum = (80 - 3 x 3) years = (80 - 9) years = 71 years.

2. Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A ?

A.        Rs. 4, Rs. 23                  B.     Rs. 13, Rs. 17             C.        Rs. 15, Rs. 14             D.        Rs. 17, Rs. 13

Answer: Option B

Explanation:

Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A.

Then, 2x + 3y = 77 ...(i) and

3x + 2y = 73 ...(ii)

Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y = 85 or y = 17.

Putting y = 17 in (i), we get: x = 13.

           

3.A is 3 years older to B and 3 years younger to C, while B and D are twins. How many years older is C to D?

A.        2                   B.           3               C.   6                  D.            12

Answer: Option C

Explanation:

Since B and D are twins, so B = D.

Now, A = B + 3 and A = C - 3.

Thus, B + 3 = C - 3   D + 3 = C-3   C - D = 6.

           

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 ?

A.        15                B.            29            C.    61                D.            None of these

Answer: Option B

Explanation:

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.

           

5.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

A.        20 m                 B.       22 m                 C.       24 m                    D.    26 m

Answer: Option C

Explanation:

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.

6.A bus starts from city X. The number of women in the bus is half of the number of men. In city

Y, 10 men leave the bus and five women enter. Now, number of men and women is equal. In

the beginning, how many passengers entered the bus ?

A. 15                        B. 30                             C. 36                        D. 45

Answer: Option D

Explanation:

Originally, let number of women = x. Then, number of men = 2x.

So, in city Y, we have : (2x - 10) = (x + 5) or x - 15.

Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 45.

           

7.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 ?

A.        12              B.  16                C.            18               D. 24

Answer: Option B

Explanation:

Suppose the boy got x sums right and 2x sums wrong.

Then, x + 2x = 48  3x = 48  x = 16.

           

8.David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?

A.        19                   B.         28                 C.           30                 D.           37

Answer: Option C

Explanation:

         

  

9.I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?

A.        25                   B.         37                 C.           54                D.            65

Answer: Option A

Explanation:

Clearly, the required number would be such that it leaves a remainder of 1 when divided by 2, 3 or 4 and no remainder when divided by 5. Such a number is 25.

10.If a clock takes seven seconds to strike seven, how long will it take to strike ten ?

A.        7 seconds                    B.        9 seconds                      C.      10 seconds                        D.  None of these

Answer: Option D

Explanation:

11.In a group of cows and hens, the number of legs are 14 more than twice the number of heads. The number of cows is

A.        5                  B.            7                       C.       10                         D.   12

Answer: Option B

Explanation:

Let the number of cows be x and the number of hens be y.

Then, 4x + 2y = 2 (x + y) + 14  4x + 2y = 2x + 2y + 14   2x = 14  x = 7.