In Data Sufficiency questions, you are not asked to solve the entire problem immediately. Instead, determine whether the given statement(s) provide enough information to answer the question.

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Standard Answer Options

Most exams use one of these options:

A. Statement I alone is sufficient.

B. Statement II alone is sufficient.

C. Both Statements I and II together are sufficient,
   but neither alone is sufficient.

D. Even both statements together are not sufficient.

E. Either Statement I or Statement II alone is sufficient.

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How to Solve

             Read the Question
                    │
                    ▼
         Check Statement I Alone
                    │
        ┌───────────┴───────────┐
        │                       │
   Sufficient?             Not Sufficient
        │                       │
      Answer A           Check Statement II
                                │
                      ┌─────────┴─────────┐
                      │                   │
                Sufficient?         Not Sufficient
                      │                   │
                   Answer B      Combine I + II
                                         │
                          ┌──────────────┴──────────────┐
                          │                             │
                    Unique Answer?                 Still Multiple?
                          │                             │
                     Answer C                     Answer D

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1. Statement I Alone

Example 1

Question

What is the value of x?

Statement I

x + 5 = 10

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Solution

Subtract 5 from both sides.

x + 5 = 10

x = 5

There is only one possible value.

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Diagram

x + 5 = 10
    │
    ▼
 x = 5
    │
Unique Answer
    │
 Statement I is Sufficient

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Final Answer

✅ Statement I alone is sufficient.

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Example 2

Question

What is the value of x?

Statement I

x > 3

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Solution

Possible values are

4
5
6
7
100
...

Many values satisfy the condition.

---

Diagram

x > 3

4
5
6
7
8
9
...

Many Answers

---

Final Answer

❌ Statement I alone is not sufficient.

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2. Both Statements Together

Example

Question

Find the area of a rectangle.

Statement I

Length = 8 cm

Statement II

Perimeter = 24 cm

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Solution

Statement I Alone

Area = Length × Width

Length = 8

Width = ?

Cannot calculate area.

❌ Not sufficient.

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Statement II Alone

Perimeter = 24

2(L + W) = 24

L + W = 12

Many possibilities.

L = 7  W = 5

L = 8  W = 4

L = 9  W = 3

Different areas.

❌ Not sufficient.

---

Combine Both

Statement I gives

Length = 8

Statement II

2(8 + W) = 24

8 + W = 12

W = 4

Area

8 × 4 = 32 cm²

Unique answer.

---

Diagram

Statement I

Length = 8
      │

Statement II

Length + Width = 12
      │
      ▼

Width = 4
      │
      ▼

Area = 32

---

Final Answer

✅ Both statements together are sufficient.

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3. Even Both Are Not Enough

Example

Question

Is n even?

Statement I

n is a multiple of 3

Statement II

10 < n < 20

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Solution

Using both statements,

Possible values are

12
15
18

Now check parity.

12 → Even

15 → Odd

18 → Even

Both Yes and No are possible.

---

Diagram

Multiples of 3

3 6 9 12 15 18 ...

          │
          ▼

Between 10 and 20

12
15
18

Even?
✔
✘
✔

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Final Answer

❌ Even together, the statements are not sufficient.

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4. Data Sufficiency in Different Topics

The same idea applies to every subject.

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Example

Question

What is the probability of selecting a red ball?

Statement I

5 red balls
10 blue balls

Statement II

Total balls = 15

---

Solution

Statement I Alone

Since

5 red
10 blue

Total balls are already known.

5 + 10 = 15

Probability

5 / 15

= 1/3

Unique answer.

---

Statement II Alone

Total = 15

But

Red = ?

Cannot calculate probability.

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Diagram

        Bag

   🔴 🔴 🔴 🔴 🔴

   🔵 🔵 🔵 🔵 🔵
   🔵 🔵 🔵 🔵 🔵

Red = 5

Total = 15

Probability

5 / 15 = 1/3

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Final Answer

✅ Statement I alone is sufficient.