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ABHYAS PREP: REASONING PUZZLES · DATA SUFFICIENCY

Data sufficiency (two statements, five fixed options)

Judge statement I alone, then statement II alone, and only then both together. A statement is sufficient only if it leaves exactly one possible answer; you never need to find the answer itself.

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Worked examples

Example 1 · level 1

Tenzin is thinking of a two-digit number. What is the number? I. It is odd. II. The sum of its digits is 3.

  1. Statement I alone is sufficient, but statement II alone is not.
  2. Statement II alone is sufficient, but statement I alone is not.
  3. Either statement I alone or statement II alone is sufficient.
  4. Both statements together are sufficient, but neither alone is.
  5. Even both statements together are not sufficient.
Show solution
  1. Statement I alone still allows 11 or 13 (and more).
  2. Statement II alone still allows 12 or 21 (and more).
  3. Both together fix the answer at 21.
  4. So: Both statements together are sufficient, but neither alone is.

Answer: Both statements together are sufficient, but neither alone is.

Example 2 · level 2

Isha is thinking of a two-digit number. What is the number? I. Reversing its digits gives a number 27 smaller than it. II. The sum of its digits is 11.

  1. Statement I alone is sufficient, but statement II alone is not.
  2. Statement II alone is sufficient, but statement I alone is not.
  3. Either statement I alone or statement II alone is sufficient.
  4. Both statements together are sufficient, but neither alone is.
  5. Even both statements together are not sufficient.
Show solution
  1. Statement I alone still allows 30 or 41 (and more).
  2. Statement II alone still allows 29 or 38 (and more).
  3. Both together fix the answer at 74.
  4. So: Both statements together are sufficient, but neither alone is.

Answer: Both statements together are sufficient, but neither alone is.

Example 3 · level 3

Three villages, Bilaspur, Rampur and Devgarh, are different places. A straight road runs from Bilaspur to Rampur and another from Rampur to Devgarh; each road runs due north–south or due east–west. In which direction is Devgarh from Bilaspur? I. Rampur is 4 km due south of Bilaspur. II. Rampur lies due south of Bilaspur.

  1. Statement I alone is sufficient, but statement II alone is not.
  2. Statement II alone is sufficient, but statement I alone is not.
  3. Either statement I alone or statement II alone is sufficient.
  4. Both statements together are sufficient, but neither alone is.
  5. Even both statements together are not sufficient.
Show solution
  1. Statement I alone still allows south or north (and more).
  2. Statement II alone still allows north or south (and more).
  3. Both together still allow south or north (and more).
  4. So: Even both statements together are not sufficient.

Answer: Even both statements together are not sufficient.

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