Top 10 - Part 1

1. Number Series

Find the missing number:

2,  6,  12,  20,  30,  ?

A) 36 B) 40 C) 42 D) 44

Answer: C) 42

Explanation:

Look at the difference between consecutive numbers:

2 → 6    = +4
6 → 12   = +6
12 → 20  = +8
20 → 30  = +10

The differences increase by 2 each time:

+4, +6, +8, +10, +12

Therefore:

30 + 12 = 42

So the missing number is 42.

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2. Coding-Decoding

If MANGO is coded as NBOPH, then how is APPLE coded?

The coding pattern is:

M → N
A → B
N → O
G → H
O → P

MANGO → NBOPH

Each letter is moved one position forward in the alphabet.

Using the same pattern:

A → B
P → Q
P → Q
L → M
E → F

Therefore:

APPLE → BQQMF

A) BQQMF B) BQQMG C) BPQMF D) BQPMF

Answer: A) BQQMF

Explanation:

Every letter is shifted by +1.

A + 1 = B
P + 1 = Q
P + 1 = Q
L + 1 = M
E + 1 = F

Therefore:

APPLE → BQQMF

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3. Blood Relation

P’s mother is Q’s father’s only sister. How is P related to Q?

Relationship:

             Grandparents
                 |
        +--------+--------+
        |                 |
   Q's Father          P's Mother
        |                 |
        Q                 P

Here, P’s mother and Q’s father are brother and sister.

Therefore, P and Q are children of siblings.

A) Brother B) Cousin C) Uncle D) Nephew

Answer: B) Cousin

Explanation:

P’s mother is the sister of Q’s father.

Therefore:

P's Mother ↔ Q's Father
  Sister       Brother

Their children are:

P ↔ Q

Children of siblings are cousins.

Therefore, P is Q’s cousin.

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4. Direction Sense

A person walks 5 km towards North. He then turns right and walks 3 km. He turns right again and walks 5 km.

Where is he from his starting point?

                    North
                      ↑
                      |
                      | 5 km
                      |
Starting Point ●------+
                      |
                      |
                      +------→ 3 km
                             East

After the second right turn:

                 North
                   ↑
                   |
                   | 5 km
                   |
Starting ●─────────+
          3 km →   |
                   |
                   ↓
                 South

Complete path:

                 B
                 ●
                 |
                 | 5 km
                 |
Starting ●-------+
          3 km →
                 |
                 | 5 km
                 |
                 ● C

He ends up 3 km East of his starting point.

A) 3 km East B) 3 km West C) 5 km East D) 5 km West

Answer: A) 3 km East

Explanation:

The person moves:

5 km North
↓
3 km East
↓
5 km South

The north and south movements cancel:

5 km North - 5 km South = 0

Only the 3 km eastward movement remains.

Therefore, he is 3 km East of the starting point.

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5. Syllogism

Statements

• All engineers are graduates.
• Some graduates are managers.

Represent the first statement:

      GRADUATES
   ┌───────────────┐
   │               │
   │   ENGINEERS   │
   │    ┌─────┐    │
   │    │     │    │
   │    └─────┘    │
   │               │
   └───────────────┘

Some graduates are managers:

        GRADUATES
   ┌─────────────────┐
   │      ┌──────┐   │
   │      │      │   │
   │      │      │   │
   │      └──────┘   │
   │     MANAGERS    │
   └─────────────────┘

But we cannot conclude that engineers and managers overlap.

Conclusions

I. Some engineers are managers. II. All engineers are graduates.

A) Only I follows B) Only II follows C) Both I and II follow D) Neither I nor II follows

Answer: B) Only II follows

Explanation:

The first statement directly tells us:

Engineers → Graduates

Therefore, Conclusion II is definitely true.

However:

Some Graduates → Managers

does not mean:

Some Engineers → Managers

There is no information proving that engineers are managers.

Therefore:

Only Conclusion II follows.

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6. Seating Arrangement

Five people P, Q, R, S and T are sitting in a row facing North.

Rules:

• P is immediately left of Q.
• R is immediately right of Q.
• S is immediately left of P.
• T is at the right end.

Let’s construct the arrangement:

Position:   1    2    3    4    5
           +----+----+----+----+----+
Person:    | S  | P  | Q  | R  | T  |
           +----+----+----+----+----+

Therefore, who is sitting in the middle?

A) P B) Q C) R D) S

Answer: B) Q

Explanation:

From the conditions:

S is immediately left of P

S → P

P is immediately left of Q:

S → P → Q

R is immediately right of Q:

S → P → Q → R

T is at the right end:

S → P → Q → R → T

There are five positions, so the middle position is position 3.

Therefore, Q is in the middle.

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7. Ranking

In a class, Rahul is 7th from the top and 18th from the bottom.

Top
 ↓

1
2
3
4
5
6
7  ← Rahul
8
9
...
...
...
...
18 ← Rahul's position counted from bottom

↑
Bottom

How many students are there in the class?

A) 24 B) 25 C) 26 D) 23

Answer: A) 24

Explanation:

Use the formula:

Total students
= Rank from top + Rank from bottom - 1

Therefore:

= 7 + 18 - 1
= 24

The -1 is necessary because Rahul is counted from both directions.

Therefore, there are 24 students.

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8. Logical Puzzle — 3 Switches and 3 Bulbs

There are 3 switches outside a room and 3 bulbs inside the room.

Each switch controls exactly one bulb.

You cannot see the bulbs while standing outside.

You can enter the room only once.

Outside the room

       ROOM
     ┌─────────┐
     │         │
S1 ──┤         │
S2 ──┤         │
S3 ──┤         │
     │         │
     └─────────┘

Inside the room

     ┌──────────────┐
     │              │
     │   (Bulb 1)   │
     │              │
     │   (Bulb 2)   │
     │              │
     │   (Bulb 3)   │
     │              │
     └──────────────┘

Each of these:

S1 → ?
S2 → ?
S3 → ?

controls exactly one bulb.

You may manipulate the switches before entering the room, but once you enter, you cannot return outside.

How can you determine which switch controls which bulb?

A) Turn all switches on and enter B) Use the switches in a sequence involving ON/OFF and check the bulbs C) It is impossible D) Turn all switches off and enter

Answer: B) Use the switches in a sequence involving ON/OFF and check the bulbs

Explanation:

Use both light and heat.

Step 1

Turn S1 ON and leave it on for several minutes.

S1 → ON

The bulb controlled by S1 becomes warm.

Step 2

Turn S1 OFF.

S1 → OFF

Step 3

Turn S2 ON and leave S3 OFF.

S1 → OFF
S2 → ON
S3 → OFF

Step 4

Enter the room.

You will find:

Bulb ON + warm
      ↓
     S1

Bulb ON + not warm
      ↓
     S2

Bulb OFF + cold
      ↓
     S3

Therefore, all three switch-bulb relationships can be identified.

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9. Data Sufficiency

What is the value of X?

Statement I

X + Y = 15

Statement II

Y = 7

Individually:

Statement I:

X + Y = 15
       ↓
Cannot determine X alone

Statement II:

Y = 7
       ↓
Cannot determine X alone

Together:

X + Y = 15
Y = 7

Therefore:

X + 7 = 15

X = 8

Can the value of X be determined?

A) Statement I alone is sufficient B) Statement II alone is sufficient C) Both statements together are sufficient D) Even both statements together are insufficient

Answer: C) Both statements together are sufficient

Explanation:

Statement I alone:

X + Y = 15

We don’t know Y, so X cannot be determined.

Statement II alone:

Y = 7

There is no equation involving X, so X cannot be determined.

Together:

X + Y = 15
Y = 7

X + 7 = 15

X = 8

Therefore, both statements together are sufficient.

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10. Statement and Assumption

Statement

“Use our company’s antivirus software to protect your computer from security threats.”

Assumption I

Computers can be affected by security threats.

Assumption II

Every computer currently has a virus.

Think about the logic:

Computer
   |
   ↓
May face security threats
   |
   ↓
Antivirus can provide protection

The statement does not say:

Every computer
      |
      ↓
Already has a virus

Therefore, determine which assumption is implicit.

A) Only I is implicit B) Only II is implicit C) Both I and II are implicit D) Neither I nor II is implicit

Answer: A) Only I is implicit

Explanation:

The recommendation to use antivirus software assumes that computers can be exposed to security threats.

However, it does not assume that every computer already has a virus.

The distinction is:

Security threat
      ≠
Already infected with a virus

Therefore:

• Assumption I → Implicit
• Assumption II → Not implicit

So the correct answer is A) Only I is implicit.

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