What the exam asks
A question is followed by two statements, I and II. You do not have to find the answer - you only decide whether the statements give enough data to find a single definite answer. Target: 40 to 50 seconds.
Standard options
| Option | Meaning |
|---|---|
| 1 | Statement I alone is sufficient, II alone is not |
| 2 | Statement II alone is sufficient, I alone is not |
| 3 | Either I alone or II alone is sufficient |
| 4 | Both together are sufficient, neither alone is |
| 5 | Even both together are not sufficient |
Method (always in this order)
- Decide what exactly is asked (a value? a yes/no?).
- Test Statement I alone. Ignore II completely.
- Test Statement II alone. Ignore I completely.
- Only if both fail, combine them.
Equation counting: n unknowns need n independent equations. If a statement adds an equation with a new unknown, it does not help. Two ratios of the same pair (4 : 3 and 3 : 2 for A : B) are not independent of each other unless one gives an actual value.
Quick checks by topic
- SI / CI: need P, R and T (or enough to get them). For CI the compounding period matters.
- Profit and loss: CP cannot be found without either profit % with SP, or a direct cost.
- Trains: a train crossing a pole gives L = vt; crossing a platform gives L + P = vt. Both together fix v if P is known.
- Time and work: combined time plus one individual time gives the other individual time.
- Ages: a ratio plus a difference (or sum) gives the ages.
- Two-digit numbers: digit sum plus digit difference fixes the number.
Worked example
What is the speed of the train? I. It crosses a 300 m platform in 25 s. II. It crosses a pole in 10 s.
I alone: (L + 300)/25 = v - two unknowns. II alone: L = 10v - two unknowns. Together: 10v + 300 = 25v, v = 20 m/s. Answer: both together are needed.
Worked example 2
What is the principal? I. SI at 10% for 2 years is Rs. 1,000. II. CI at 10% for 2 years is Rs. 1,050.
I: 0.2P = 1,000, P = 5,000. II: 0.21P = 1,050, P = 5,000. Answer: either statement alone.
Common traps
- Solving fully - waste of time. Stop as soon as you know a unique answer exists.
- Assuming information not given (for example that a number is an integer, or that a rate is compounded annually when the statement does not say so).
- Choosing "both" when one statement alone was already enough - always check each alone first.
- Two roots: x² = 49 alone gives 7 or -7, which is not unique unless another statement says x > 0.
- Yes/no questions: a definite "no" is also a sufficient answer.
Time target: 45 seconds. DS rewards logic over arithmetic - write unknowns, count equations, decide.