## Numerical Ability

#### Numerical Ability

1. What will be the maximum sum of 44, 42, 40, ........, 2, 0?

1.  Sn = n [ 2a + (n - 1)d ] 2

44, 42, 40, ------ 2, 0
Here , a = 44 , d = -2 , n = 22 terms
 S22 = 22 [ 2 × 44 + (22 - 1)(-2) ] 2

 S22 = 22 [ 88 - 42 ] 2

 S22 = 22 × [ 46 ] 2

S22 = 11 × 46 = 506

##### Correct Option: C

 Sn = n [ 2a + (n - 1)d ] 2

44, 42, 40, ------ 2, 0
Here , a = 44 , d = -2 , n = 22 terms
 S22 = 22 [ 2 × 44 + (22 - 1)(-2) ] 2

 S22 = 22 [ 88 - 42 ] 2

 S22 = 22 × [ 46 ] 2

S22 = 11 × 46 = 506

1. What will be the maximum sum of 44, 42, 40, ........, 2, 0?

1.  Sn = n [ 2a + (n - 1)d ] 2

44, 42, 40, ------ 2, 0
Here , a = 44 , d = -2 , n = 22 terms
 S22 = 22 [ 2 × 44 + (22 - 1)(-2) ] 2

 S22 = 22 [ 88 - 42 ] 2

 S22 = 22 × [ 46 ] 2

S22 = 11 × 46 = 506

##### Correct Option: C

 Sn = n [ 2a + (n - 1)d ] 2

44, 42, 40, ------ 2, 0
Here , a = 44 , d = -2 , n = 22 terms
 S22 = 22 [ 2 × 44 + (22 - 1)(-2) ] 2

 S22 = 22 [ 88 - 42 ] 2

 S22 = 22 × [ 46 ] 2

S22 = 11 × 46 = 506

1. Which of the following assertions are CORRECT?
P : Adding 7 to each entry in a list adds 7 to the mean of the list
Q : Adding 7 to each entry in a list adds 7 to the standard deviation of the list
R : Doubling each entry in a list doubles the mean of the list
S : Doubling each entry in a list leaves the standard deviation of the list unchanged

1. P and R always holds true
Else consider a sample set {1, 2, 3, 4} and check accordingly.

##### Correct Option: C

P and R always holds true
Else consider a sample set {1, 2, 3, 4} and check accordingly.

1. An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and V supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of X's shock absorbers, 96% are reliable. Of Y's shock absorbers, 72% are reliable. The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is

1.  X Y Supply 60% 40% Reliable 96% 72% Overall 0.576 0.228

 ∴ P(X) = 0.288 = 0.334 0.576 + 0.288

##### Correct Option: B

 X Y Supply 60% 40% Reliable 96% 72% Overall 0.576 0.228

 ∴ P(X) = 0.288 = 0.334 0.576 + 0.288

1. A political party orders an arch for the entrance to the ground in which the annual conventions is being held. The profile of the arch follows the equation y = 2x – 0.1x2 where y is the height of the arch in meters. The maximum possible height of the arch is

1. y = 2x – 0.1x2

 dy = 2 – 0.2x dx

 d2y < 0 dx2

Hence maximises at 2 – 0.2x = 0
⇒ x = 10
∴ y = 20 – 10 = 10 m

##### Correct Option: B

y = 2x – 0.1x2

 dy = 2 – 0.2x dx

 d2y < 0 dx2

Hence maximises at 2 – 0.2x = 0
⇒ x = 10
∴ y = 20 – 10 = 10 m