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UPCAT Mathematics practice question 13: A quantity is increased by 20% and the result is then decreased by 20%. Compared with the original, the final value is

Correct answer

A. 4% smaller

Multiplying by 1.20 and then 0.80 gives 0.96 of the original, a 4% decrease. The two percentages are taken from different bases, so they do not cancel.

A quantity is increased by 20% and the result is then decreased by 20%. Compared with the original, the final value is

  1. 4% smallerCorrect
  2. unchanged
  3. 4% larger
  4. 20% smaller

Why A is correct

Multiplying by 1.20 and then 0.80 gives 0.96 of the original, a 4% decrease. The two percentages are taken from different bases, so they do not cancel.

Why the other options are wrong

B unchanged
Assumes the two percentages cancel. They do not, because the 20% increase is taken from the original and the 20% decrease from the larger post-increase figure.
C 4% larger
Right magnitude, wrong direction. Multiplying by 1.20 then 0.80 gives 0.96, which is below 1.
D 20% smaller
Applies only the decrease and ignores the increase entirely.
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