## Numerical Ability

#### Numerical Ability

1. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC =

1. For IMHO = JNIP
I + 1 = J
M + 1 = N
H + 1 = I
O + 1 = P
For
SO = TP
S + 1 = T
O + 1 = P
Similarly, for IDC = JED
I + 1 = J
D + 1 = E
C + 1 = D

##### Correct Option: B

For IMHO = JNIP
I + 1 = J
M + 1 = N
H + 1 = I
O + 1 = P
For
SO = TP
S + 1 = T
O + 1 = P
Similarly, for IDC = JED
I + 1 = J
D + 1 = E
C + 1 = D

1. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of X and Y. What is the minimum possible value of P?

1. Given product of three integers, X.Y.Z = 192
Given: Z = 4

 ∴ X.Y = 192 = 48 4

 ∵ P = X + Y 2

Now,
Possible value of (X, Y) are (48, 1), (24, 2), (16, 3), (12, 4), (8, 6)
 So, (P)min< 8 + 6 = 7 2

So, min value of P is 7.

##### Correct Option: C

Given product of three integers, X.Y.Z = 192
Given: Z = 4

 ∴ X.Y = 192 = 48 4

 ∵ P = X + Y 2

Now,
Possible value of (X, Y) are (48, 1), (24, 2), (16, 3), (12, 4), (8, 6)
 So, (P)min< 8 + 6 = 7 2

So, min value of P is 7.

1. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is

1. Let GDP in 2015 be x
Now, in 2016, GDP will be 1.
1x Fiscal deficit in 2015 = 0.04 × x
Fiscal deficit in 2016 = 0.05 × 1.1 x
Here percentage increase in the actual fiscal deficit

 = 0.05 × 1.1x - 0.04 × x × 100 = 37.5% 0.04x

##### Correct Option: B

Let GDP in 2015 be x
Now, in 2016, GDP will be 1.
1x Fiscal deficit in 2015 = 0.04 × x
Fiscal deficit in 2016 = 0.05 × 1.1 x
Here percentage increase in the actual fiscal deficit

 = 0.05 × 1.1x - 0.04 × x × 100 = 37.5% 0.04x

1. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed. The total time taken to fill the tank (in hours) is _____.

1. Here,

 In 1 hr, part of tank filled by P alone is = 1 6

 In 1 hr, part of tank filled by Q alone is = 1 9

 In 1 hr, part of tank emptied by R is = 1 12

Initially, P and R opened for 4 hr,
 So part of tank filled = 4 1 - 1 = (4 / 12) = (1 / 3) 6 12

After 4 hr, P is closed and for 6 more hr Q and R are opened.
 So part of tank filled = 6 1 - 1 = (1 / 6) 9 12

 So, total tank filled in 10 hr = 1 + 1 = 2 + 4 = 1 6 3 12 2

So, remaining 1/2 part of the tank is filled by Q alone
Now, Q will take 9/2 = 4.5 hr to fill remaining half of the tank.
Hence, total time taken = 4 + 6 + 4.5 = 14.5 hr

##### Correct Option: C

Here,

 In 1 hr, part of tank filled by P alone is = 1 6

 In 1 hr, part of tank filled by Q alone is = 1 9

 In 1 hr, part of tank emptied by R is = 1 12

Initially, P and R opened for 4 hr,
 So part of tank filled = 4 1 - 1 = (4 / 12) = (1 / 3) 6 12

After 4 hr, P is closed and for 6 more hr Q and R are opened.
 So part of tank filled = 6 1 - 1 = (1 / 6) 9 12

 So, total tank filled in 10 hr = 1 + 1 = 2 + 4 = 1 6 3 12 2

So, remaining 1/2 part of the tank is filled by Q alone
Now, Q will take 9/2 = 4.5 hr to fill remaining half of the tank.
Hence, total time taken = 4 + 6 + 4.5 = 14.5 hr

1. The Venn diagram shows the preference of the student population for leisure activities.

Play sports Read books Watch TV From the data given, the number of students who like to read books or play sports is

1. No. of person reading Books = 13 + 44 + 12
n(A) + 7 = 76
No. of person playing = 15 + 44 + 7 + 17
n(B) = 83
No. of person watch TV = 29 + 12 + 7 + 17
n(C) = 65
n(A ⋂ B) = 44 + 7 = 51
n(A ⋃ B)= n(A) + n(B) – n(A ⋂ B)
= 76 + 83 – 51 = 108

##### Correct Option: D

No. of person reading Books = 13 + 44 + 12
n(A) + 7 = 76
No. of person playing = 15 + 44 + 7 + 17
n(B) = 83
No. of person watch TV = 29 + 12 + 7 + 17
n(C) = 65
n(A ⋂ B) = 44 + 7 = 51
n(A ⋃ B)= n(A) + n(B) – n(A ⋂ B)
= 76 + 83 – 51 = 108