# Data Sufficiency — Decide If You Can Answer, Without Solving

Source: https://skills101.in/learn/reasoning/data-sufficiency — Skills101 free tutorial (Logical Reasoning). Updated 2026-11-09.

A data sufficiency (DS) question gives a question and two statements. You don't find the answer — you decide **whether the statements give enough information** to find it.

## 1. The method

![Flow: test statement I alone, then statement II alone, then both together. A table maps the result to the answer: I alone, II alone, either, both together, or not sufficient](https://skills101.in/learn-img/reasoning/ds-flow.svg)

The five standard options (the wording varies):

1. **I alone** is sufficient, II alone is not.
2. **II alone** is sufficient, I alone is not.
3. **Either** I alone or II alone is sufficient.
4. **Both together** are needed (neither alone works).
5. **Not sufficient** even together.

> When you test statement II alone, **forget everything statement I told you**. This is the most common mistake.

## 2. Solved examples

### Example 1
*What is the value of x?*
*I. 2x + 3 = 11*
*II. x² = 16*

- I alone: x = 4 ✓ (one value)
- II alone: x = 4 or −4 ✗ (two values)
- Answer: **I alone**.

### Example 2
*Is A taller than B?*
*I. A is taller than C.*
*II. C is taller than B.*

- I alone: nothing about B ✗. II alone: nothing about A ✗.
- Together: A > C > B → yes ✓.
- Answer: **Both together**.

### Example 3
*What is Ravi's age?*
*I. Ravi is 5 years older than Sunil.*
*II. The sum of their ages is 45.*

- Each alone ✗. Together: R − S = 5, R + S = 45 → R = 25 ✓.
- Answer: **Both together**.

### Example 4
*How many students are in the class?*
*I. Riya is 10th from the top and 21st from the bottom.*
*II. There are 18 boys and the girls are 12.*

- I alone: 10 + 21 − 1 = 30 ✓.
- II alone: 18 + 12 = 30 ✓.
- Answer: **Either** statement alone.

### Example 5 — a yes/no question
*Is n an even number?*
*I. n is divisible by 4.*
*II. n is a multiple of 3.*

- I: every multiple of 4 is even → definitely **yes** ✓.
- II: 6 is even, 9 is odd → could be either ✗.
- Answer: **I alone**.

> For yes/no questions, a statement is sufficient if it gives a **definite** yes **or** a definite no. "Definitely no" also counts as sufficient!

## Traps

- **Don't solve fully.** Once you know there's exactly one answer, stop.
- **Two values are not sufficient** (like x² = 16).
- **Don't assume** things that aren't stated (e.g. that x is positive or a whole number).

## Quick recap

- Test I alone, II alone (forget I), then both.
- Map the result to one of the five options.
- A definite "no" is sufficient.
- Watch for hidden second values and unstated assumptions.


Practice quiz and free certificate: https://skills101.in/learn/reasoning/data-sufficiency