Data sufficiency reasoning: Practice 1

10 original teaching questions with answers and explanations.

Instructions for this set

Assess each numbered statement independently first. Then assess the combination if needed. A statement is sufficient only if it forces a unique value or a definite yes/no answer to the exact question.

Feedback mode has no time limit or negative marking. The optional timed challenge allows 15 minutes and uses the scoring shown on its rules screen. Those settings are not official assessment rules.

Practise with feedback Optional timed challenge

  1. 1. What is x? (1) x + 4 = 13. (2) x is positive.
    1. Even together insufficient
    2. Statement 1 alone suffices
    3. Statement 2 alone suffices
    4. Only both together suffice

    Reference: q-91b2b8ce-46 · Report this question

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    Answer: B. Statement 1 alone suffices

    Statement 1 fixes x at nine. Positivity alone permits many values, so only statement 1 is sufficient alone.
  2. 2. What is the area of a rectangle? (1) Its length is 8 m. (2) Its width is 5 m.
    1. Statement 1 alone
    2. Statement 2 alone
    3. Only both together
    4. Even together insufficient

    Reference: q-9fb3f11d-78 · Report this question

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    Answer: C. Only both together

    Either dimension alone leaves the other unknown. Together the dimensions give 8 times 5 = 40 square metres.
  3. 3. Is integer n even? (1) n is a multiple of four. (2) n is greater than ten.
    1. Statement 2 alone suffices
    2. Only both together suffice
    3. Even together insufficient
    4. Statement 1 alone suffices

    Reference: q-12740687-75 · Report this question

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    Answer: D. Statement 1 alone suffices

    Every multiple of four is even. Greater than ten permits both even and odd integers.
  4. 4. What is total revenue? (1) Exactly 30 items were sold. (2) Every sold item had the same price.
    1. Even together insufficient
    2. Statement 1 alone
    3. Statement 2 alone
    4. Only both together

    Reference: q-9b22662-95 · Report this question

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    Answer: A. Even together insufficient

    Even together, the common unit price is unknown. Prices of $2 and $3 would give different revenues while satisfying both facts.
  5. 5. Is x greater than 20? (1) x is greater than 25. (2) x equals 30.
    1. Only statement 2 alone
    2. Either statement alone
    3. Neither statement alone
    4. Only statement 1 alone

    Reference: q-d91ad7e6-65 · Report this question

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    Answer: B. Either statement alone

    Both statements independently force yes: anything above 25 is above 20, and 30 is above 20.
  6. 6. What is the average speed of a trip? (1) Total distance is 180 km. (2) Total elapsed time is three hours.
    1. Statement 1 alone
    2. Statement 2 alone
    3. Only both together
    4. Even together insufficient

    Reference: q-d2725df5-106 · Report this question

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    Answer: C. Only both together

    Average speed needs both total distance and total time. Together they give 60 km/h.
  7. 7. What is the cost of the first of ten units? (1) The ten units cost $70 in total. (2) Each of the ten units has the same cost.
    1. Even together insufficient
    2. Statement 1 alone
    3. Statement 2 alone
    4. Only both together

    Reference: q-18a615b3-126 · Report this question

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    Answer: D. Only both together

    Statement 1 allows different individual costs: the first could cost $7 with nine others at $7, or $16 with nine others at $6. Statement 2 gives no amount. Together, equal costs and a $70 total fix the first unit at $7. The question asks for an individual cost, not the average cost.
  8. 8. Is integer k positive? (1) k squared equals 16. (2) k is greater than zero.
    1. Only statement 2 alone
    2. Only both together
    3. Even together insufficient
    4. Only statement 1 alone

    Reference: q-72d0b601-76 · Report this question

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    Answer: A. Only statement 2 alone

    Statement 1 allows k = 4 or -4, so it does not settle positivity. Statement 2 directly forces yes.
  9. 9. What is the original price? (1) The discounted price is $90. (2) The discount was 10% of the original price.
    1. Statement 2 alone
    2. Only both together
    3. Even together insufficient
    4. Statement 1 alone

    Reference: q-48ba968e-109 · Report this question

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    Answer: B. Only both together

    Together they give 90 = 0.90 times original, so original is $100. Neither the discounted price nor discount rate alone fixes it.
  10. 10. What is y? (1) y + z = 10. (2) 2y + 2z = 20.
    1. Statement 2 alone
    2. Only both together
    3. Even together insufficient
    4. Statement 1 alone

    Reference: q-ec3593ab-45 · Report this question

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    Answer: C. Even together insufficient

    Statement 2 is just twice statement 1. Both y = 3, z = 7 and y = 4, z = 6 satisfy the combined information.

Review your method

Return to the data sufficiency reasoning lesson and identify the reasoning step behind each mistake before repeating the set.

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