Zelma scored 90, 88, and 92 on 3 of the 6 mathematics tests that she took.

[BTGModeratorVI]

Zelma scored 90, 88, and 92 on 3 of the 6 mathematics tests that she took. What was her average (arithmetic mean) score on the 6 tests?

(1) Her average (arithmetic mean) score on 5 of the tests was 90.
(2) Her score on one of the tests was 91.

Answer: E
Source: GMAT prep

[deloitte247]

Let 3 unknown maths test scores = x, y and z

Target question => What was her average (arithmetic mean) score on 6 tests?
$$i.e\ find\ \frac{90+88+92+x+y+z}{6}$$

Statement 1 =>The average (arithmetic mean) score on 5 of the tests was 90
$$i.e\ \ \frac{90+88+92+x+y}{5}=90$$
The expression from this statement does not provide an exact value for any of x, y, or z so we can't find the mean of the 6 test scores. Statement 1 is NOT SUFFICIENT

Statement 2 => Her score on one of the tests was 91, this still leaves us with two unknown variables so we cannot evaluate the mean of the 6 test scores. Statement 2 is NOT SUFFICIENT

Combining both statements together =>
From statement 2, one of her scores was 91
$$If\ x=91\ then\ from\ statement\ 1;\ \frac{90+88+92+91+y}{5}=90$$
$$361+y=450$$
$$y=450-361=89$$
But z is still unknown so we cannot find the value of the 6 test scores.

If z = 91 then two variable x and y remains unknown and mean of the 6 test scores remains unsolved. Since both statements combined together is NOT SUFFICIENT

Answer = E

[Brent@GMATPrepNow]

Zelma scored 90, 88, and 92 on 3 of the 6 mathematics tests that she took. What was her average (arithmetic mean) score on the 6 tests?

(1) Her average (arithmetic mean) score on 5 of the tests was 90.
(2) Her score on one of the tests was 91.

Answer: E
Source: GMAT prep

Given: Zelma scored 90, 88, and 92 on 3 of the 6 mathematics tests

Target question: What was her average (arithmetic mean) score on the 6 tests?

When I SCAN the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the target question. So, I’m going to head straight to……

Statements 1 and 2 combined
Statement 1 tells us that the average score on 5 of the tests was 90.
Statement 2 tells us that her score on ONE of the tests was 91
Important: We cannot assume that the score of 91 (mentioned in statement 2) is DIFFERENT from the five scores mentioned in statement 1) goo

There are several sets of scores that satisfy BOTH statements. Here are two:
Case a: {90, 88, 92, 91, 89, 90}.
Notice that the first 5 scores have an average of 90 (which satisfies the statement 1)
Also notice that 91 is among the first 5 scores (which satisfies statement 2)
This means the sixth score can have ANY value.
If the sixth score is 90 (as we have here), then the average score is 90

Case b: {90, 88, 92, 91, 89, 1,00,000}.
In this case, the average score is much bigger than 90

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent