## Numerical Ability

#### Numerical Ability

1. The statistics of runs scored in a series by four batsmen are provided in the following table. Who is the most consistent batsman of these four?

 Batsman Average Standard Deviation K 31.2 5.21 L 46.0 6.35 M 54.4 6.22 N 17.9 5.90

1. Most consistent player is the one with least dispersion in the scores. For this, Coefficient of Variance is used to measure relative measure of dispersion between two sets.

 Coefficient of Variance(CV) = Standard Deviation Mean

Calculating it for all the four players.
K's CV = 0.167
L's CV = 0.138
M's CV = 0.114
N's CV = 0.329
Larger the value of CV, less consistent is the player. So the most consistent player is M.

##### Correct Option: B

Most consistent player is the one with least dispersion in the scores. For this, Coefficient of Variance is used to measure relative measure of dispersion between two sets.

 Coefficient of Variance(CV) = Standard Deviation Mean

Calculating it for all the four players.
K's CV = 0.167
L's CV = 0.138
M's CV = 0.114
N's CV = 0.329
Larger the value of CV, less consistent is the player. So the most consistent player is M.

1. Forty students watched films, A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films?

1. 13 + 16 + 19 = 48 > 40
Hence, 4 students would have watched all three due to which there is a double counting of 4 × 2 = 8.

##### Correct Option: C

13 + 16 + 19 = 48 > 40
Hence, 4 students would have watched all three due to which there is a double counting of 4 × 2 = 8.

1. A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

1. Let two digit number be xy.
Now sum of digit is 9
∴ x + y = 9 ....(i)
and when ‘45’ is subtracted from number then digit gets interchanged
∴ 10x + y – 45 = 10y + x
∴ x – 5 = y
x – y = 5 ....(ii)
Now solving equation (i) and (ii) we get
x = 7 and y = 2
Hence the number is 72.

##### Correct Option: B

Let two digit number be xy.
Now sum of digit is 9
∴ x + y = 9 ....(i)
and when ‘45’ is subtracted from number then digit gets interchanged
∴ 10x + y – 45 = 10y + x
∴ x – 5 = y
x – y = 5 ....(ii)
Now solving equation (i) and (ii) we get
x = 7 and y = 2
Hence the number is 72.

1. Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

1.  Machine × time = M1 × t1 Number of toys T1

 = M2 × t2 T2

 ∴ 7 × 7 = 100 × t2 7 100

∴ t2 = 7 min

##### Correct Option: B

 Machine × time = M1 × t1 Number of toys T1

 = M2 × t2 T2

 ∴ 7 × 7 = 100 × t2 7 100

∴ t2 = 7 min

1. Which of the following functions describe the graph shown in the below figure.

1. Here from graph for x = 1, y = – 1
Checking the same from options.
From option (a)
for x = 1
y = ||1| + 1| - 2
= 2 - 2 = 0
∴ Option (a) is wrong
From option (c)
for x = 1
y = ||x| + 1| - 1
=|1 + 1| - 1 = 1
∴ Option (c) is wrong.

##### Correct Option: B

Here from graph for x = 1, y = – 1
Checking the same from options.
From option (a)
for x = 1
y = ||1| + 1| - 2
= 2 - 2 = 0
∴ Option (a) is wrong
From option (c)
for x = 1
y = ||x| + 1| - 1
=|1 + 1| - 1 = 1
∴ Option (c) is wrong.