Data Sufficiency made clear.
Your job is to decide whether the information determines an answer, not necessarily to calculate that answer. Test each statement independently before combining them.
Key concepts in Data Sufficiency
Alone means alone
When testing statement I, do not borrow information from statement II.
Unique determination
A statement is sufficient if every allowed case gives the same answer to the question.
Yes/no questions
A definite “no” is just as sufficient as a definite “yes”. A mix of yes and no cases is insufficient.
Answer convention
This lesson names the outcome in words. Actual exams use different letter mappings, so read their code carefully.
Sufficiency decision path
| I alone | II alone | Next decision |
|---|---|---|
| Sufficient | Insufficient | I only |
| Insufficient | Sufficient | II only |
| Sufficient | Sufficient | Each alone |
| Insufficient | Insufficient | Test both together |
A reliable solving method
- Identify exactly what is being asked and the variable domain.
- Test statement I alone with at least two possible cases if needed.
- Reset, then test statement II alone.
- Only if neither suffices, test the two together.
Step-by-step solved examples
Find x. I: x+3=8. II: 2x=10.
- I alone gives x=5.
- II alone independently gives x=5.
- Each statement alone is sufficient.
Find positive x. I: x+y=10. II: y=4.
- I alone permits several values of x.
- II alone says nothing about x.
- Together x=6, so both together are sufficient.
Is integer n even? I: n=2k+1 for integer k. II: n>10.
- I always makes n odd, giving a definite “no”.
- II permits 11 and 12, giving different answers.
- Only I is sufficient.
Data Sufficiency: practice questions
Choose one answer before opening the explanation. Write down your reasoning as well as the option; a correct guess is different from a method you can repeat.
Find x. I: x=7. II: x>0.
Show answer and explanation — question 1
Answer A: I only
I fixes x, while II allows many positive values.
Find x. I: x<10. II: x=4.
Show answer and explanation — question 2
Answer B: II only
Only II determines the exact number.
Find positive x. I: x²=9. II: x+1=4.
Show answer and explanation — question 3
Answer C: Each alone
Positivity selects 3 in I; II also gives 3.
Find x. I: x+y=8. II: y=3.
Show answer and explanation — question 4
Answer C: Together only
Neither alone fixes x; together x=5.
Find x. I: x>2. II: x<8.
Show answer and explanation — question 5
Answer D: Together insufficient
Even together, many values between 2 and 8 remain.
Is n positive? I: n<0. II: n is an integer.
Show answer and explanation — question 6
Answer A: I only
I gives a definite no; being an integer alone does not decide sign.
Frequently asked questions
Do I need to fully solve every sufficient case?
No. Showing that exactly one answer is forced is enough.
Why can x²=9 be insufficient?
Without a positive-domain restriction, x could be 3 or −3, so the numerical value is not unique.
Identify exactly what is being asked and the variable domain. Only if neither suffices, test the two together.