Bank Math Master

Question: In a code PREMIER is written as XOILSIO, ANTAGONAISE is written as MQNMZBQMSWI, then how can PROMISE be written in the same code?

Solution:
PREMIER is written as XOILSIO
P ⇒ X
R ⇒ O
E ⇒ I
M ⇒ L
I ⇒ S
E ⇒ I
R ⇒ O

ANTAGONAISE is written as MQNMZBQMSWI
A ⇒ M
N ⇒ Q
T ⇒ N
A ⇒ M
G ⇒ Z
O ⇒ B
N ⇒ Q
A ⇒ M
I ⇒ S
S ⇒ W
E ⇒ I

PROMISE
P ⇒ X
R ⇒ O
O ⇒ B
M ⇒ L
I ⇒ S
S ⇒ W
E ⇒ I
∴ PROMISE is written as XOBLSWI.

Question: Which number will complete the series:
155, 151, 147, 143, 139, ........?

Solution:
The pattern is followed by
155 - 4 = 151
151 - 4 = 147
147 - 4 = 143
143 - 4 = 139
139 - 4 = 135

Hence the number= 135.

Question: If x = 7 -  4√3, then √x + 1/√x =?

Solution:
Given that,
x = 7 -  4√3
⇒ x = 4 - 4√3 + 3
⇒ x = (2)² - 2 . 2 . √3 + (√3)²
⇒ x = (2 - √3)²
∴  √x = 2 - √3

∴ 1/√x = 1/(2 - √3)
= {1(2 + √3)}/{(2 - √3)(2 + √3)}
= (2 + √3)/{2² - (√3)²}
= (2 + √3)/(4 - 3)
= 2 + √3

∴ √x + 1/√x = 2 - √3 + 2 + √3
= 4

Question: If in a certain language PRIVATE is coded 1234567 and RISK is coded as 2398. How is KITE coded in the language?

Solution:
PRIVATE is coded 1234567
P = 1
R = 2
I = 3
V = 4
A = 5
T = 6
E = 7 
RISK is coded as 2398
R = 2
I = 3
S = 9
K = 8 

∴ KITE = 8367

Question: Which number will complete the series:
1, 3, 7, 15, 31, 63, 127, __?

Solution:
3 - 1 = 2
7 - 3 = 4 = 2 × 2
15 - 7 = 8 = 4 × 2
31 - 15 = 16 = 8 × 2
63 - 31 = 32 = 16 × 2
127 - 63 = 64 = 32 × 2

∴ The next number of 127 will be 127 + 64 × 2
= 127 + 128
= 255

Question: What number will replace the '?' mark?

Solution:
নিচের ১ম সংখ্যা + নিচের দুই সংখ্যার পার্থক্য = উপরের সংখ্যা।

১ম চিত্রে, 30 + (30 - 15) = 45
তৃতীয় চিত্রে, 28 + (28 - 21) = 35

∴ দ্বিতীয় চিত্রে, 25 + (25 - 19) = 31

Question: If 4x² - px + 25 is a square number, then p =?

Solution:
4x² - px + 25
= (2x)² - 2. 2x. 5 + 5² - px + 20x
= (2x - 5)² - px + 20x 

Now,
- px + 20x = 0 [The expression is a square number]
⇒ px = 20x
∴ p = 20

Question: If Z = 52 and BAT = 46, then BALL will be equal to-

Solution:

Here,
The Position number of Z is 26 which is re-write as 26 × 2 = 52.
Now,
BAT = (2 × 2) + (1 × 2) + (20 × 2) 
= 4 + 2 + 40
= 46

Similarly,
BALL = (2 × 2) + (1 × 2) + (12 × 2) + (12 × 2)
= 4 + 2 + 24 + 24
= 54 

Question: In a certain language PENSION is coded as NEISNOP, how is COLLEGE coded in that code?

Solution: 
PENSION ⇔ NEISNOP
P ⇒ E ⇒ N ⇒ S ⇒ I ⇒ O ⇒ N 
1 ⇒ 2 ⇒ 3 ⇒ 4 ⇒ 5 ⇒ 6 ⇒ 7
N ⇒ E ⇒ I ⇒ S ⇒ N⇒ O ⇒ P
Here,
Letters of 1st and 7th position inter-change their position.
Letters of 3rd and 5th position also inter-change their position.
And the letters of even number position remain same.

C ⇒ O ⇒ L ⇒ L ⇒ E ⇒ G ⇒ E 
1 ⇒ 2 ⇒ 3 ⇒ 4 ⇒ 5 ⇒ 6 ⇒ 7
E ⇒ O ⇒ E ⇒ L ⇒ L ⇒ G ⇒ C

∴ COLLEGE ⇔ EOELLGC

Question: Raitul walked 25 metres towards South. Then he turned to his left and walked 20 metres. He then turned to his left and walked 25 metres. He again turned to his right and walked 15 metres. At what distance is he from the starting point and in which direction?

Solution:
 
The movements of Raitul are as shown in figure.
Raitul's distance from starting point A to end point E = AE = (AD + DE) = (BC + DE) = (20 + 15) m = 35 m.
Also, E is to the East of A.

Question: If x - 1/x = - √3, then x⁴ + 1/x⁴ =?

Solution:
Given that,
x - 1/x = - √3
 ⇒ (x - 1/x)² = (- √3)²
⇒ x² + 1/x² - 2.x.(1/x) = 3
⇒ x² + 1/x² = 3 + 2
⇒ (x² + 1/x²)² = 5
⇒ (x²)² + (1/x²)² + 2.x².(1/x²) = 25
⇒ x⁴ + 1/x⁴ = 25 - 2
∴ x⁴ + 1/x⁴ = 23

Question: Which one will complete the series:
BKS, DJT, FIU, HHV, JGW, ___ ?

Solution:
প্রতিটি অংশে ৩ টি বর্ণ আছে। 

১ম বর্ণ গুলোয় একটি বর্ণটি বাদ দিয়ে পরের বর্ণটি বসে। 
B এর এক বর্ণ পর D , D এর পর একটি বর্ণ বাদ দিয়ে F, অতএব শূন্য স্থানে প্রথম বর্ণটি হবে J এর এক বর্ণ পরের বর্ণ L 

২য় বর্ণগুলোয় ক্রমান্বয়ে পূর্বের বর্ণটি বসে।
k এর আগের বর্ণ J, J এর আগের বর্ণ I, অতএব শূন্যস্থানে ২য় বর্ণটি হবে F 

৩য় বর্ণগুলোয় ক্রমান্বয়ে পরের বর্ণটি বসে।
S এর পরের বর্ণ T, T এর পরের বর্ণ U, অতএব শূন্যস্থানে ৩য় বর্ণটি হবে X

শূন্যস্থানে বসবে LFX 

Question: If SINGLE = 66, Then DOUBLE =? 

Solution:

S + I + N + G + L + E 
19 + 9 + 14 + 7 + 12 + 5
= 66

Now,
D + O + U + B + L + E
4 + 15 + 21 + 2 + 12 + 5
= 59

Question: A monkey climbs a 12 meters-high slippery pillar. In his first minute, he climbs 2 meters, and in the next minute, he slip one meter down. In this way, how much time will he take to reach the top of the pillar?

Solution: 
On first minute monkey climb = 2 m
On the second minute it slips = 1 m
For every two minute, it climbs 1 m
So, average speed = 1 m/2 min For 10 m,
time is taken = 20 min

For the last 2 m jump add 1 min
So time taken = 20 + 1 = 21 min

∴ Monkey takes 21 minutes to reach the top of the pole.

Question: If 19x + 12y = 23 and 14x - 5y = 363, then find the value of (2x + y).

Solution:
19x + 12y = 23 ................(1)
14x - 5y = 363 ................(2)

(1) × 5 ⇒ 95x + 60y = 115 ...............(3)
(2) × 12 ⇒ 168x - 60y = 4356 ...............(4)

from (3) + (4) we get,
263x = 4471
⇒ x = 17

Substituting x = 17 in (1)
19 × 17 + 12y = 23
⇒ 323 + 12y = 23
⇒ 12y = - 300
∴ y = - 25

Now,
(2x + y)
= 2 × 17 + (- 25)
= 34 - 25
= 9