Bank Math Master

Question: If 6 > x > 1 and 3 < x < 10 which of the following best describes x?

Solution:
Here,
6 > x > 1
⇒ {2, 3, 4, 5}

and
3 < x < 10
⇒ {4, 5, 6, 7, 8, 9}

∴ 6 > x > 1 and 3 < x < 10
⇒ {4, 5}

∴ 3 < x < 6

Question: If 2x + y = 10 and x - y = 2, then x + y = ?

Solution:
Given,
2x + y = 10.............(1)
and x - y = 2.........(2)

from, (1) + (2) we get
2x + y + x - y = 10 + 2
⇒ 3x = 12
∴ x = 4

Now,
4 - y = 2
⇒ 4 - 2 = y
∴ y = 2

∴ x + y = 4 + 2 = 6

Question: Rafiq is shorter than Sajid, but taller than Farah. Lina is shorter than Rafiq. Nasir is shorter than Sajid but taller than Rafiq. Who is the tallest in terms of height?

Solution:
Rafiq is shorter than Sajid, but taller than Farah.
∴ Sajid > Rafiq > Farah

Lina is shorter than Rafiq
∴ Rafiq > Lina

Nasir is shorter than Sajid but taller than Rafiq
∴ Sajid > Nasir > Rafiq
From all of these relational statement we can say that, Sajid is the tallest in terms of height.

Question: Find the median of the following numbers: 11, 25, 15, 21, 12, 17, 18, 22, 27, 29, 16, 20.

Solution:
The numbers if arranged in ascending order will be: 11, 12, 15, 16, 17, 18, 20, 21, 22, 25, 27, 29
Here the number of data is even, i.e. n = 12

We know,
Median = {Value of sum of (12/2)^th and (12/2 + 1)^th terms}/2
= (value of sum of 6^th and 7^th terms)/2
= (18 + 20)/2
= 38/2
= 19

So, the median is 19.

Question: What is the sum of first 20 terms of the series 7 + 12 + 17 +.............. ?

Solution:
Given series: 7 + 12 + 17 +................

Here,
First term of the series a = 7
common difference d = 12 - 7 = 5
and number of terms n = 20

∴ It is an arithmetic series.

We know
the sum of first n-terms of an arithmetic series, S_n = (n/2){2a + (n - 1)d}

∴ So, the sum of 20 terms S₂₀ = (20/2){2 × 7 + (20 - 1)5}
= 10(14 + 19 × 5)
= 10(14 + 95)
= 10 × 109
= 1090

Question: If 9x² - px + 25 is a square number, then p/2 = ?

Solution:
9x² - px + 25
= (3x)² - 2. 3x. 5 + 5² - px + 30x
= (3x)² - 30x + 5² + 30x - px
= (3x - 5)²+ 30x - px

Then,
30x - px = 0
⇒ 30x = px
⇒ p = 30

∴ p/2 = 30/2 = 15

Question: If WORLD is written as 34526 and EARTH is written as 78519, then ALERT is written as-

Solution:
WORLD is written as 34526
W = 3
O = 4
R = 5
L = 2
D= 6

EARTH is written as 78519
E = 7
A = 8
R = 5
T = 1
H = 9

So, ALERT will be
A = 8
L = 2
E = 7
R = 5
T = 1

∴ ALERT will be = 82751

Qyestion: Insert the missing number in the given series: 8, 7, 11, 12, 14, 17, 17, 22, ....

Solution:
These are two series
1^st series odd positions terms = 8, 11, 14, 17, 20 increasing by 3.

and
2^nd even positions terms = 7, 12, 17, 22 increasing by 5.

The 9th term is in an odd position, so it follows the first pattern = 17 + 3 = 20

Question: Solve: |4x - 2| ≤ 6

Solution:
|4x - 2| ≤ 6
⇒ - 6 ≤ 4x - 2 ≤ 6
⇒ - 6 + 2 ≤ 4x - 2 + 2 ≤ 6 + 2
⇒ - 4 ≤ 4x ≤ 8
⇒ - 4/4 ≤ 4x/4 ≤ 8/4
∴ - 1 ≤ x ≤ 2

Question: If P = {x : x is a factor of 12 } and Q = {x : x is a multiple of 3 and x ≤ 12} then determine P - Q:

Solution:
Given,
P = {x : x is a factor of 12 }
∴ P = {1, 2, 3, 4, 6, 12}

Q = {x : x is a multiple of 3 and x ≤ 12}
∴ Q = {3, 6, 9, 12}

∴ P - Q = {1, 2, 3, 4, 6, 12} - {3, 6, 9, 12}
= {1, 2, 4}

Question: If 3x² + x - 10 is divided by (x + 2), the result is-

Solution:
Here,
3x² + x - 10
= 3x² + 6x - 5x - 10
= 3x(x + 2) - 5(x + 2)
= (x + 2)(3x - 5)

So, If (x + 2)(3x - 5) is devided by (x + 2) then the result is (3x - 5)

Question: If - 2x + 5 < 19, then the value of x:

Solution: 
Here,
- 2x + 5 < 19
⇒ - 2x + 5 - 5 < 19 - 5
⇒ - 2x < 14
⇒ 2x > - 14
⇒ x > - 14/2
∴ x > - 7

Question: If x + 1/x = 5 , then x³ + 1/x³ = ?

Solution:
x³ + 1/x³
=(x + 1/x)³ - 3. x. (1/x)(x + 1/x)
= 5³ - (3 × 5)
= 125 - 15
= 110

Question: What is the 8^th term of the series: 2 + 4 + 8 + 16 +..........

Solution:
Given,
a = 2
r = 4/2
= 2 > 1 
The given series is a geometric series.

We know,
the n^th term of a geometric series = ar^{(n - 1)}

8^th term of the series = 2 × 2^{(8 - 1)} = 2 × 2⁷ = 256

Question: If A = {3, 4, 5} and B = {4, 5, 6, 8} determine (A ∩ B)

Solution:
Given,
A = {3, 4, 5}
and B = {4, 5, 6, 8}

∴ A ∩ B ={3, 4, 5} ∩ {4, 5, 6, 8}
= {4, 5}

The set to be determined is: {4, 5}

Question: Average of 40 numbers are 52. When 5 more numbers are included, the average of 45 numbers become 55. Find the average of 5 numbers.

Solution:
Total of 40 numbers = 40 × 52 = 2080
Now, total of 45 numbers = 45 × 55 = 2475

Hence, sum of 5 numbers = 2475 - 2080 = 395

∴ Average of five numbers = 395/5
= 79

Question: Arrange the words given below in a meaningful sequence.
1. Boil, 2. Serve, 3. Wash, 4. Chop, 5. Cook

Solution:
Wash ⇒ Chop ⇒ Boil ⇒ Cook ⇒ Serve
3 ⇒ 4 ⇒ 1 ⇒ 5 ⇒ 2

Question: One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card?

Solution:
Total card = 52
Total face card = (4 + 4 + 4) = 12

∴ Probability = Number of face cards​/Total number of cards = 12/52 = 3/13

Question: A clock seen through a mirror reads a quarter to nine. What is the actual time?

Solution:
The quarter to nine = 8 : 45

So the actual time = (11 : 60 - 8 : 45)
= 3 : 15