What is the average test score of Angela, Barry, Carl, Dennis, and Edward? (1)…

Concept: In Data Sufficiency, a statement (or a combination of statements) is sufficient only if it lets you compute a single, definite value for what is asked. To find the average of a set of scores, you need the sum of every score in the set divided by the count — a statement that gives the sum of only part of the group cannot fix the sum of the whole group; the group only becomes fixed once every member is covered exactly once by the information at hand.

Application

1. The question asks for the average of five scores — Angela, Barry, Carl, Dennis, and Edward — so the total sum of all five scores is needed.

2. Statement (1) gives the average of Barry, Carl, and Edward as 87, so their combined sum is 3 × 87 = 261 — but it says nothing about Angela's or Dennis's scores, so the sum of all five stays unknown.

3. Statement (2) gives the average of Angela and Dennis as 84, so their combined sum is 2 × 84 = 168 — but it says nothing about Barry's, Carl's, or Edward's scores, so the sum of all five stays unknown.

4. Combining both statements: {Barry, Carl, Edward} and {Angela, Dennis} together are exactly the five people in the question, so the combined sum is 261 + 168 = 429, and the average is 429 ÷ 5 = 85.8 — a single definite value.

Cross-check: The two groups named in the statements — {Barry, Carl, Edward} and {Angela, Dennis} — have no person in common and together list all five people, so no score is missing and none is double-counted; the sum 429 is therefore both complete and unique.

Since neither statement alone names all five people, but the two together name every person exactly once, both statements are needed together and neither is sufficient on its own.