GMAT Practice Question: In a certain learning experiment, each participant had three trials and was assigned, for each...
Question
In a certain learning experiment, each participant had three trials and was assigned, for each trial, a score of either -2,-1,0,1, or 2 . The participant's final score consisted of the sum of the first trial score, 2 times the second trial score, and 3 times the third trial score. If Anne received scores of 1 and -1 for her first two trials, not necessarily in that order, which of the following could NOT be her final score?
- -4
- -2
- 1
- 5
- 6
Topics: calculations
Solution
Step 1
We first name the trial scores x, y, and z, and write the final score S as a literal expression so we can test each case.
S = x + 2\times y + 3\times z x \text{ is either } 1 \text{ or } -1 y \text{ is either } 1 \text{ or } -1 z \text{ is one of } -2, -1, 0, 1, \text{ or } 2
Step 2
We then try the case where the first trial gives a 1 and the second gives a -1 to simplify S in terms of z.
S = 1 + 2\times (-1) + 3\times z S = -1 + 3\times z
Step 3
We then list each possible third score and find the resulting S in this first case.
z = -2, \text{ gives } S = -1 + 3\times (-2) = -7 z = -1, \text{ gives } S = -1 + 3\times (-1) = -4 z = 0, \text{ gives } S = -1 + 3\times 0 = -1 z = 1, \text{ gives } S = -1 + 3\times 1 = 2 z = 2, \text{ gives } S = -1 + 3\times 2 = 5
Step 4
We then try the case where the first trial gives a -1 and the second gives a 1 to get a new expression for S.
S = -1 + 2\times 1 + 3\times z S = 1 + 3\times z
Step 5
We then list each possible third score and find S in this second case.
z = -2, \text{ gives } S = 1 + 3\times (-2) = -5 z = -1, \text{ gives } S = 1 + 3\times (-1) = -2 z = 0, \text{ gives } S = 1 + 3\times 0 = 1 z = 1, \text{ gives } S = 1 + 3\times 1 = 4 z = 2, \text{ gives } S = 1 + 3\times 2 = 7
Step 6
We combine the scores from both cases and see which answer choice does not appear.
-7, -5, -4, -2, -1, 1, 2, 4, 5, \text{ and } 7
Answer
6
