29. Data Sufficiency discipline
AD/BCE elimination grid. Two-scenario rule: two possible answers = insufficient. Beware over-crediting statements.
Core ideas
- Run the AD/BCE grid: test Statement 1 alone first. If it works, the answer is A or D; if not, B, C, or E. Never let one statement's info leak into your test of the other.
- Two-scenario rule: if you can build two different answers that both satisfy a statement, that statement is insufficient. Stop hunting for more cases; two is enough.
- Value questions need exactly ONE value. "x = 7 or x = -7" is insufficient even though you know a lot about x.
- A ratio alone never gives counts. Without-replacement probability changes with total size, so a ratio without a total is insufficient.
Worked example 1
What is the value of x?
(1) x^2 = 49
(2) x < 0
Show solution
Test (1) alone: x could be 7 or x could be -7. Two possible values for a value question means insufficient, so cross off A and D. Test (2) alone: x could be -1, -50, anything negative, so insufficient; cross off B. Together: x^2 = 49 and x < 0 forces x = -7, one value. Answer: C.
Worked example 2
A jar contains only red and blue marbles. If two marbles are drawn at random without replacement, what is the probability that both are red?
(1) The ratio of red to blue marbles is 3 to 2.
(2) The jar contains 15 marbles in total.
Show solution
Test (1) alone: with 3 red and 2 blue, P = (3/5)(2/4) = 3/10; with 6 red and 4 blue, P = (6/10)(5/9) = 1/3. Two different answers from the same ratio, so (1) is insufficient; the ratio alone cannot fix the counts. Test (2) alone: 15 marbles with unknown split gives many probabilities, insufficient. Together: 3:2 ratio of 15 total means 9 red and 6 blue, so P = (9/15)(8/14) = 12/35, one value. Answer: C.
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