Analytical Ability

Question: What is the angle between the hour and minute hand of a clock when it is 4 : 40 pm?

সমাধান:
4টা 40 মিনিট = 4 + (40/60) ঘন্টা
= 4 + 2/3 = 14/3 ঘন্টা

আমরা জানি,
ঘণ্টার কাঁটা 12 ঘণ্টায় 360° ঘোরে।
∴ 1 ঘণ্টায় ঘোরে = 360°/12 = 30°
∴ 14/3 ঘণ্টায় ঘোরে = (30° × 14)/3
= 140°

আবার,
মিনিটের কাঁটা 60 মিনিটে 360° ঘোরে।
∴ 1 মিনিটে ঘোরে = 360°/60 = 6°
∴ 40 মিনিটে ঘোরে = 40 × 6° = 240°

ঘড়ির কাঁটা দুটির মধ্যবর্তী কোণ = |240° - 140°| = 100°

Question: If the day before yesterday was Thursday, when will Sunday be?

Solution:
Day before yesterday = Thursday
Yesterday = Friday
Today = Saturday
Tomorrow = Sunday

Therefore, Sunday will be tomorrow.

Question: Robin is 28th from left end of a row of 50 students and Siam is 27th from right end of the row. How many students are sitting between them?

Solution:



Siam's position from left = 50 - 27 + 1 = 24

So,
Robin's position from left = 28
Siam's position from left = 24

∴ Number of students are sitting between them = (28 - 24) - 1 
= 4 - 1
= 3

Question: How many degrees are between the hands of a clock at  3:30?
Solution:
Value of angle = {(11 × 30) - (60 × 3)}/2
= (330 - 180)/2
= 150/2
= 75°

Question: If ‘A’ stands for ‘÷’, ‘B’ stands for ‘+’, ‘C’ stands for ‘×’ and ‘D’ stands for ‘-’, then what will come in place of the question mark (?) 
7 C 11 B 12 A 6 D 18 = ?

Solution: 
দেওয়া আছে 
A = ÷
B = +
C = × এবং 
D = -

প্রদত্ত শর্ত অনুসারে পাই 
7 C 11 B 12 A 6 D 18 = 7 × 11 + 12 ÷ 6 - 18
= 7 × 11 + 2 - 18
= 77 + 2 - 18
= 79 - 18
= 61

Question: It was Sunday on January 1, 2012. What was the day of the week on January 1, 2013?

Solution:
2012 সাল একটি লিপ ইয়ার (Leap Year), কারণ 2012 ÷ 4 = 503 (অতএব 4 দ্বারা বিভাজ্য)।

লিপ ইয়ারে মোট দিন = 366 দিন
আমরা জানি, 366 = 52 সপ্তাহ + 2 দিন

অর্থাৎ পরের বছরের একই তারিখে দিন 2 দিন এগিয়ে যাবে।

দেওয়া আছে, 1 Jan 2012 = Sunday
∴ 1 Jan 2013 = Sunday + 2 দিন = Tuesday

সঠিক উত্তর: খ) Tuesday

Question: Today is Thursday. After 44 days, it will be-

Solution:
We know that each day of the week is repeated after 7 days.

44 ÷ 7 = 6 (remainder 2)

So, after (7 × 6) = 42 days it will be Thursday.
∴ after 44 days it will be (Thursday + 2 days) = Saturday

Question: What is the angle between the hour and minute hands of a clock when it is 3:15 pm?

Solution:
3টা 15 মিনিট = 3 + (15/60) ঘন্টা = 3 + 1/4 = 13/4 ঘন্টা

আমরা জানি, ঘণ্টার কাঁটা 12 ঘণ্টায় 360° ঘোরে।
∴ 1 ঘণ্টায় ঘোরে = 360°/12 = 30°
∴ 13/4 ঘণ্টায় ঘোরে = (30° × 13)/4
= 390°/4
= 97.5°

আবার, মিনিটের কাঁটা 60 মিনিটে 360° ঘোরে।
∴ 1 মিনিটে ঘোরে = 360°/60 = 6°
∴ 15 মিনিটে ঘোরে = 15 × 6° = 90°

∴ ঘড়ির কাঁটা দুটির মধ্যবর্তী কোণ = |97.5° - 90°|
= 7.5°

Question: What will be the number in the question mark?
2, 5, 11, 20, 32, ?

Solution:
প্রদত্ত ধারাটি হলো: 2, 5, 11, 20, 32, ?
ধারার সংখ্যাগুলোর মধ্যে পার্থক্য নির্ণয় করি:
5 - 2 = 3
11 - 5 = 6
20 - 11 = 9
32 - 20 = 12

এখানে, প্রতিবার পার্থক্য 3 করে বৃদ্ধি পাচ্ছে।
∴ পরবর্তী পার্থক্য হবে = 12 + 3 = 15
∴ পরবর্তী সংখ্যাটি হবে = 32 + 15 = 47
অতএব, প্রশ্নবোধক স্থানে 47 বসবে।

Shortcut: 2 (+3)→ 5 (+6)→ 11 (+9)→ 20 (+12)→ 32 (+15) → 47.

Question: What is the angle between the hour and minute hands of a clock when it is 20 minutes past 9?

Solution:
20 minutes past 9 অর্থাৎ, 9টা 20 মিনিট।
= 9 + (20/60) ঘন্টা
= 9 + 1/3
= 28/3 ঘন্টা

আমরা জানি,
ঘণ্টার কাঁটা 12 ঘণ্টায় 360° ঘোরে।
∴ 1 ঘণ্টায় ঘোরে = 360°/12 = 30°
∴ 28/3 ঘন্টায় ঘোরে = (30° × 28)/3 = 280°

আবার,
মিনিটের কাঁটা 60 মিনিটে 360° ঘোরে।
∴ 1 মিনিটে ঘোরে = 360°/60 = 6°
∴ 20 মিনিটে ঘোরে = 20 × 6° = 120°

∴ ঘড়ির কাঁটা দুটির মধ্যবর্তী কোণ = | 280° - 120° | = 160°

Question: Which number replaces the question mark?


Solution:
এখানে,
বাম হাতের উপাদানগুলোর পার্থক্য × ডান হাতের উপাদানগুলোর পার্থক্য = উপরের সংখ্যা।

অতএব, ১ম চিত্রে,
(14 - 9) × (13 - 7) = 5 × 6 = 30

২য় চিত্রে,
(12 - 9) × (17 - 11) = 3 × 6 = 18

∴ প্রশ্নবোধক স্থানে সংখ্যাটি হবে 18

Question: The clock showed 10 : 30 in the mirror. What is the actual time?

Solution:
আমরা জানি,
প্রকৃতপক্ষে সময়
= 11 : 60 - আয়নায় দেখা সময়
= 11 : 60 - 10 : 30
= 1 : 30

Question: If LATER = 13579 and CHAIR = 20349, then CHEAT = ?

Solution:
Given that,
L    A   T   E    R
↓    ↓   ↓    ↓    ↓
1    3   5   7    9

and
C   H   A   I    R
↓    ↓   ↓    ↓    ↓
2   0    3   4    9

So
C   H   E    A   T
↓    ↓   ↓    ↓    ↓
2   0    7   3    5

Question: What number should come next in the series:
3, 7, 15, 31, 63, .......?

Solution: দেওয়া আছে,
সিরিজটি হলো: 3, 7, 15, 31, 63, .......

প্রতিটি পার্থক্য আগের পার্থক্যের 2 গুণ।

3 থেকে 7 পর্যন্ত পার্থক্য: 4
7 থেকে 15 পর্যন্ত পার্থক্য: 8 (4 × 2)
15 থেকে 31 পর্যন্ত পার্থক্য: 16 (8 × 2)
31 থেকে 63 পর্যন্ত পার্থক্য: 32 (16 × 2)
সুতরাং, পরবর্তী পার্থক্যটি হবে: 32 × 2 = 64

পরবর্তী সংখ্যাটি হবে শেষ সংখ্যা এবং এই পার্থক্যের যোগফল: 63 + 64 = 127

অতএব, পরবর্তী সংখ্যাটি হলো 127

Question: A clock is started at noon. By 20 minutes past 4, through how many degrees has the hour hand turned?

From noon (12.00 pm) to 4 pm = 4 hours
and 20 minutes = 20/60 hours = 1/3 hours

Total time = (4 + 1/3) = 13/3 hours

We know,
Angle traced by hour hand in 12 hours =  360°

∴ Angle in 13/3 hours,
= (360/12) × (13/3)
= 130°

Question: Today is Monday. After 59 days, it will be-

Solution:
We know that each day of the week is repeated after 7 days.

59 ÷ 7 = 8 (remainder 3)

So, after (7 × 8) = 56 days, it will be Monday.
∴ After 59 days, it will be (Monday + 3 days) = Thursday

Question: Play : Actor :: Concert : ?

Solution:
সঠিক উত্তর: খ) Musician

- Play (নাটক) এর মূল ব্যক্তি বা পারফর্মার হলো Actor (যে অভিনয় করে)
- ঠিক একইভাবে Concert (সঙ্গীতানুষ্ঠান) এর মূল ব্যক্তি বা পারফর্মার হলো Musician (যে সঙ্গীত পরিবেশন করে)

অতএব, Play : Actor :: Concert : Musician

Question: If the word PSYCHOLOGY is viewed in a mirror, what will be its reflected image?

Solution: 
PSYCHOLOGY -এর আয়নায় প্রতিফলিত রূপটি হবে:

Question: One morning after sunrise, Sakib was standing facing a pole. The shadow of the pole fell exactly to his left. Which direction was Sakib facing?

Solution:
1. In the morning, the sun is in the east, so all shadows fall toward the west.
2. If the shadow (west) is to Sakib's left, he must be facing north.If he were facing south, the shadow would be to his right

Question: What word can be formed by arranging the letters of 'AEEHLPTN'?

Solution:
By rearranging the letters 'AEEHLPNT', the name of an animal (ELEPHANT ⇒ Elephant) can be formed.

Question: 5, 8, 14, 26, 50, 98, ..... What number should come next?

Solution: Given series: 5, 8, 14, 26, 50, 98...

First number: 5
Now, 
5 + 3 = 8
8 + 6 = 14
14 + 12 = 26
26 + 24 = 50
50 + 48 = 98

∴ Next number = 98 + 96 = 194

Question: An accurate clock shows 2:00 PM. Through how many degrees will the hour hand rotate by the time the clock shows 8:00 PM?

Solution:
We know,
A clock is a full circle = 360°
There are 12 hours on the clock face
So the hour hand moves = 360° ÷ 12 = 30° per hour

From 2 : 00 PM to 8 : 00 PM is exactly 6 hours later.
Therefore, the hour hand rotates,
6 hours × 30° per hour = 180°

So the hour hand will rotate through 180°.

Question: Runa is shorter than Shila but taller than Tuli. Fahim is taller than Runa. Shila is the second-tallest person among them. Akash is shorter than Tuli. Who is the third-tallest person among them?

Solution:
First statement: Shila > Runa > Tuli

Second statement: Fahim > Runa

Third statement: Shila is the second-tallest, meaning one person is taller than Shila. Since Fahim is taller than Runa and Shila is taller than Runa, Fahim must be taller than Shila.
Therefore, Fahim > Shila > Runa

Fourth statement: Tuli > Akash

Putting everyone together: Fahim > Shila > Runa > Tuli > Akash

∴ The third-tallest person is Runa.

Question: Which year is not a leap year?

Solution:
A leap year is divisible by 4.

Here, 
1996 ÷ 4 = 499, divisible by 4 , so leap year.
1994 ÷ 4 = 498.5, not divisible by 4 , not a leap year.
2000 ÷ 4 = 500, divisible by 4 , so leap year.
2004 ÷ 4 = 501, divisible by 4, so leap year.
1988 ÷ 4 = 497, divisible by 4, so leap year.

Question: What is the angle between the hour and minute hands of a clock when it is 8: 20?

Solution:
We know, the angle between the hour and minute hands is,
Angle = |11M - 60H|/2
= |(11 × 20) - (60 × 8)|/2
= |220 - 480|/2
= |- 260|/2
= 260/2
= 130°

∴ The angle between the hour and minute hands at 8: 20 is 130°.

Question: What is the angle between the hour and minute hands of a clock when it is 4 : 20 pm?

Solution:
4টা 20 মিনিট = 4 + (20/60) ঘন্টা
= 4 + 1/3 = 13/3 ঘন্টা

আমরা জানি,
ঘণ্টার কাঁটা 12 ঘণ্টায় 360° ঘোরে।
∴ 1 ঘণ্টায় ঘোরে = 360°/12 = 30°
∴ 13/3 ঘণ্টায় ঘোরে = (30° × 13)/3
= 390°/3 = 130°

আবার,
মিনিটের কাঁটা 60 মিনিটে 360° ঘোরে।
∴ 1 মিনিটে ঘোরে = 360°/60 = 6°
∴ 20 মিনিটে ঘোরে = 20 × 6° = 120°

∴ ঘড়ির কাঁটা দুটির মধ্যবর্তী কোণ = |130° - 120°| = 10°

Question: Four girls are sitting on a bench to be photographed. Where Nila is to the right of Sara. Maya is to the left of Sara. And Rima is between Sara and Nila. Who would be second from the left in the photograph?
 
Solution:
Nila is to the right of Sara
∴ Sara — Nila

Maya is to the left of Sara
∴ Maya — Sara

Rima is between Sara and Nila
∴ Sara — Rima — Nila

Now place all four together:
∴ Maya — Sara — Rima — Nila

∴ the second from the left is Sara.

Question: What will come at the place of the question mark?
7, 13, 25, 49, ?
 
Solution:
Here,
First term = 7

Second term = (7 × 2 - 1) = 13
Third term = (13 × 2 - 1) = 25
Fourth term = (25 × 2 - 1) = 49

So,
Fifth term = (49 × 2 - 1) = 97

Question: ACZ, CEY, EGX, GIW, _——, KMU.

Solution:
There are two independent alphabetical series here.

First series (first two letters as a pair):
Each pair advances by +2 in the alphabet for each letter :
A (+2) → C (+2) → E (+2) → G (+2) → I (+2) → K
C (+2) → E (+2) → G (+2) → I (+2) → K (+2) → M
∴ (AC, CE, EG, GI, IK, and KM).

Second series (third letter):
This is a reverse alphabetical sequence (decreasing by 1).
Z (-1) → Y (-1) → X (-1) → W (-1) → V (-1) → U
∴ Z, Y, X, W, V, U.

So the missing term after GIW is IKV.

Question: What is the angle between the hour and minute hand of a clock when it is 2 : 30 pm?

Solution:
2টা 30 মিনিট = 2 + (30/60) ঘন্টা
= 2 + 1/2 = 5/2 ঘন্টা

আমরা জানি,
ঘণ্টার কাঁটা 12 ঘণ্টায় 360° ঘোরে।
∴ 1 ঘণ্টায় ঘোরে = 360°/12 = 30°
∴ 5/2 ঘণ্টায় ঘোরে = (30° × 5)/2
= 75°

আবার,
মিনিটের কাঁটা 60 মিনিটে 360° ঘোরে।
∴ 1 মিনিটে ঘোরে = 360°/60 = 6°
∴ 30 মিনিটে ঘোরে = 30 × 6° = 180°

∴ ঘড়ির কাঁটা দুটির মধ্যবর্তী কোণ = |180° - 75°| = 105°

Question: In a certain code, AXIOM is written as ZWHNL. How is WAXED written in that code?

সমাধান:
এই কোডিং প্যাটার্নটি হলো প্রতিটি অক্ষরের পূর্ববর্তী অক্ষর ব্যবহার করা।
A ⇒ Z
X ⇒ W
I ⇒ H
O ⇒ N
M ⇒ L
এই নিয়ম অনুযায়ী, WAXED শব্দটির কোড হবে:
W ⇒ V
A ⇒ Z
X ⇒ W
E ⇒ D
D ⇒ C

সুতরাং, WAXED এর কোড হবে: VZWDC

Question: Mahi was facing east. he walked 7 km forward and then after turning to his right walked 5 km. Again he turned to his right and walked 7 km. After this he turned back. Which direction was he facing at that time?

Solution: 
Mahi's Movement-



∴ If Mahi turned back from final position he must be facing in the direction of East.

Question: If A = 3, B = 6, C = 9, and so on, what is the meaning of the following numbers 36, 27, 45, 42?

Solution:
Given,
A = 3, B = 6, C = 9, ......

∴ প্রতিটি কোড = অক্ষরের অবস্থান × 3

So,
36 ÷ 3 = 12 → L
27 ÷ 3 = 9 → I
45 ÷ 3 = 15 → O
42 ÷ 3 = 14 → N

∴ The meaning of the following number = LION