Answer: C
- Statement (1): the change in the number of loaves is unknown: with the same number sold, revenue rises 20%, but if sales halved, revenue changes by 1.2×0.5=0.6, a 40% fall. NOT sufficient; eliminate A and D.
- Statement (2): sales fell from 12,000 to 10,000 loaves, a factor of 65, but the price change is unknown. NOT sufficient; eliminate B.
- Together: revenue = price × quantity, so revenue changed by a factor of 1.2×65=1: it did not change at all (0%). SUFFICIENT; the answer is C.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.: Statement (1) alone is not sufficient: the change in the number of loaves is unknown: with the same number sold, revenue rises 20%, but if sales halved, revenue changes by 1.2×0.5=0.6, a 40% fall.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.: Statement (2) alone is not sufficient: sales fell from 12,000 to 10,000 loaves, a factor of 65, but the price change is unknown.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.: Correct. Neither statement alone is sufficient. Statement (1) alone is not sufficient: the change in the number of loaves is unknown: with the same number sold, revenue rises 20%, but if sales halved, revenue changes by 1.2×0.5=0.6, a 40% fall. Statement (2) alone is not sufficient: sales fell from 12,000 to 10,000 loaves, a factor of 65, but the price change is unknown. Together the statements are sufficient: revenue = price × quantity, so revenue changed by a factor of 1.2×65=1: it did not change at all (0%).
EACH statement ALONE is sufficient.: Statement (1) alone is not sufficient: the change in the number of loaves is unknown: with the same number sold, revenue rises 20%, but if sales halved, revenue changes by 1.2×0.5=0.6, a 40% fall.
Statements (1) and (2) TOGETHER are NOT sufficient.: Together the statements are sufficient: revenue = price × quantity, so revenue changed by a factor of 1.2×65=1: it did not change at all (0%).
Percent changes multiply; convert a change given in units (2,000 fewer loaves out of 12,000) into a factor before combining it with a percent change.