ATI TEAS (Test of Essential Academic Skills) Version 7MathematicsHard

A pharmaceutical company is testing a new drug. In the first phase, 1/3 of the participants reported side effects. In the second phase, 1/4 of the remaining participants reported side effects. What fraction of the total original participants reported side effects in the second phase?

  1. A1/3
  2. B1/4
  3. C1/12
  4. D1/6
Show answer & explanation

Correct answer: D. 1/6

If 1/3 of participants reported side effects in the first phase, then 1 - 1/3 = 2/3 of participants remained. In the second phase, 1/4 of these *remaining* participants reported side effects. So, (1/4) * (2/3) = 2/12 = 1/6 of the total original participants reported side effects in the second phase.

Why the other options are wrong

  • A. This is the fraction from the first phase, not the second.
  • B. This is the fraction of *remaining* participants who reported side effects, not the fraction of the *total original* participants.
  • C. This results from multiplying 1/4 by 1/3, not 2/3 (the remaining participants).

Fraction of a Remainder

Calculating a fraction of a quantity that is itself a remainder after an initial fraction has been removed.

  • First, find the fraction of the whole that remains after the initial event.
  • Then, multiply the second fraction by this remaining fraction.
  • This determines the portion of the original whole represented by the second event.

Memory trick: Find what's left, then take a piece of that rest.

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