Data Sufficiency

At a glance 10 rules

1. 1Decide, never solveSufficient means exactly one answer is fixed. Stop the moment you know it is fixed; never work it out fully.
2. 2Order of testingTest I alone, then II alone with I covered up. If I works, II decides 'I alone' or 'each alone'; if both fail alone, try them together.
3. 3Value or yes/noA value question needs one value. A yes/no question needs always yes or always no, and a definite no is sufficient.
4. 4Two casesTwo cases that fit a statement but give different answers prove it is not sufficient. One clean case each way is enough.
5. 5Average and total$\text{total} = \text{average} \times \text{count}$$\text{every value} \le m \Rightarrow \text{average} \le m$
6. 6Ratio needs an anchorA ratio or a percentage alone fixes shares, never counts or rupees. One actual number (a total, a part or a gap) turns it into counts.
7. 7Combined average$\bar{a} = \dfrac{n_1 a_1 + n_2 a_2}{n_1 + n_2}$$n = \text{size},\ a = \text{mean};\ \text{only } n_1 : n_2 \text{ matters}$
8. 8Same percent changeIf every part changes by the same percent, the total changes by that percent. Unequal changes need the parts' sizes.
9. 9Equations and unknownsn unknowns need n different equations ($3x + 2y = 130$ and $6x + 4y = 260$ count as one). Whole-number counts can make a single equation enough.
10. 10Group rates misleadEvery group's rate can rise while the overall rate falls, if the group sizes shift. An overall rate needs the group sizes too.