The number of students in College E in the year 2019 is approximately _____ %…

Concept: when one quantity P is described as x% more than another quantity Q, the comparison is always measured against Q, the value that follows the word "than". The relation is x = ((P - Q) / Q) x 100. The base always sits in the denominator, so deciding which figure follows "than" must be settled before any arithmetic is done.

Application: the stem names two different kinds of figure, a whole-college enrolment and a single girls' count, so each has to be read out of the table separately.

1. "Number of students" counts boys and girls together, so P = 1100 + 720 = 1820.

2. "Number of girls in College B in the year 2022" is a single cell of the table, so Q = 1180; because this phrase follows "than", Q is the base.

3. Excess of P over the base: P - Q = 1820 - 1180 = 640.

4. Apply the relation: x = (640 / 1180) x 100 = 64000 / 1180 = 54.24 correct to two decimal places.

5. The choices are whole numbers, so x is approximately 54.

Cross-check: raising the base by the computed percentage must reproduce P. 1180 x 1.5424 = 1820.03, which is the College E enrolment for 2019, so the percentage is consistent with the table.

Contrast: three readings of the same two rows give different answers, and only the base fixed by "than" answers the question asked.

• Putting 1820 in the denominator gives (640 / 1820) x 100 = 35.16, which measures how much smaller 1180 is than 1820, the reverse comparison.

• Counting only the 1100 boys of College E gives 1100 - 1180 = -80, a shortfall instead of an excess, so the girls' column of College E cannot be dropped.

• Reading College B's 2022 boys, 1500, in place of its girls gives (1820 - 1500) / 1500 x 100 = 21.33, which compares a different pair of figures.