## Numerical Ability

#### Numerical Ability

1. S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency of others but for half as many days as E worked, S and M have 6 hour shifts in a day, whereas E and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the project?

1. M efficiency = 2 [efficiency of S, E and F]
Contribution of M in the project = x days × 6 hrs × 2
Contribution of E in the project = 2x days × 12 hrs × 1
Contribution of M: Contribution of E x × 6 × 2 : 2x × 12 × 1
1: 2

##### Correct Option: B

M efficiency = 2 [efficiency of S, E and F]
Contribution of M in the project = x days × 6 hrs × 2
Contribution of E in the project = 2x days × 12 hrs × 1
Contribution of M: Contribution of E x × 6 × 2 : 2x × 12 × 1
1: 2

1. The binary operation – is defined as a– b = ab + (a + b), where a and b are any two real numbers. The value of the identity element of this operation, defined as the numberx such that a– x = a, for any a, is ______.

1. The binary operation – is defined
⇒ a – b = ab + (a + b)
a – x = a
∴ From the equation ‘b’ is the variable
Option A: x = 0
a – o = a × 0 + (a + 0) = 0 + a = a
Option B: x = 1
a – 1 = a × 1 + (a + 1) = a + a + 1 = 2a + 1
Option C: x = 2
a – 2 ⇒ a × 2 + (a + 2) = 2a + a + 2 = 3a+ 2
Option D: x = 10
a – 10 ⇒ a × 10 + (a + 10) = 10a + a + 10 = 11a + 10
∴ Option ‘A’ only True.

##### Correct Option: A

The binary operation – is defined
⇒ a – b = ab + (a + b)
a – x = a
∴ From the equation ‘b’ is the variable
Option A: x = 0
a – o = a × 0 + (a + 0) = 0 + a = a
Option B: x = 1
a – 1 = a × 1 + (a + 1) = a + a + 1 = 2a + 1
Option C: x = 2
a – 2 ⇒ a × 2 + (a + 2) = 2a + a + 2 = 3a+ 2
Option D: x = 10
a – 10 ⇒ a × 10 + (a + 10) = 10a + a + 10 = 11a + 10
∴ Option ‘A’ only True.

1. Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun's place?

1. I = I live
AH = Ahmed lives
M = Michel lives
S = Susan lives
A = Arun lives

##### Correct Option: C I = I live
AH = Ahmed lives
M = Michel lives
S = Susan lives
A = Arun lives

1. Right triangle PQR is to be constructed in the xy– plane so that the right angle is at P and line PR is parallel to the-axis. The x and y coordinates of P, Q, and R are to be integers that satisfy the inequalities: -4 <, x < 5 and 6 < y < 16. How many different triangles could be constructed with these properties?

1. We have the rectangle with dimensions 10 ×11 (10 horizontal dots and 11 vertical). PQ is parallel to y-axis and PR is parallel to x-axis.
Choose the (x, y) coordinates for vertex P (right angle): 10C1 × 11C1
Choose the x coordinate for vertex R (as y coordinate is fixed by A): 9C1, (10 – 1 = 9 as 1 horizontal dot is already occupied by A)
Choose the y coordinate for vertex Q (as x coordinate is fixed by A): 10C1, (11 – 1 = 10 as 1 vertical dot is already occupied by A).
Hence, required number of triangles will be 10C1 × 11C1 × 9C1 × 10C1 = 9900.

##### Correct Option: C

We have the rectangle with dimensions 10 ×11 (10 horizontal dots and 11 vertical). PQ is parallel to y-axis and PR is parallel to x-axis.
Choose the (x, y) coordinates for vertex P (right angle): 10C1 × 11C1
Choose the x coordinate for vertex R (as y coordinate is fixed by A): 9C1, (10 – 1 = 9 as 1 horizontal dot is already occupied by A)
Choose the y coordinate for vertex Q (as x coordinate is fixed by A): 10C1, (11 – 1 = 10 as 1 vertical dot is already occupied by A).
Hence, required number of triangles will be 10C1 × 11C1 × 9C1 × 10C1 = 9900.

1. A coin is tossed thrice. Let X be the event that head occurs in each of the first two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occurs in three tosses. Based on the above information, which one of the following statements is TRUE?

1. x = {HHT, HHH}
y depends on x
z = {TTH, TTT}
∴ ‘d’ is the correct choice.

##### Correct Option: B

x = {HHT, HHH}
y depends on x
z = {TTH, TTT}
∴ ‘d’ is the correct choice.