In a certain learning experiment, each participant had three trials an

Score in first trial = x
Score in 2nd trial = y
Score in 3rd trial = z

allowed values for x , y and z are -2, -1, 0, 1, 2

final score = x + 2y + 3z

given 2 scores are 1 and -1

so x = 1 or y = 1 or z = 1
and x = -1 or y = -1 or z = -1

sum can be
==> 1 + (2 * -1) + 3z ==> 3z - 1 ==> equation 1
==> 1 + 2y + ( 3* -1) ==> 2y - 2 ==> equation 2
==> -1 + (2 * 1) + 3z ==> 3z + 1 ===> equation 3

for z = -2 equation1 = -6 - 1= -7 and equation 3 = -6 + 1 = -5
for z = -1 equation1 = -3 - 1= -4 and equation 3 = -3 + 1 = -2
for z = 0 equation1 = 0 - 1 = -1 and equation 3 = 0 + 1 = 1
for z = 1 equation1 = 3 - 1 = 2 and equation 3 = 3 + 1 = 4
for z = 2 equation1 = 6 - 1 = 5 and equation 3 = 6 + 1 = 7

for y = -2 equation 2 = 2y - 2 = -4 - 2 = -6
for y = -1 equation 2 = 2y - 2 = -2 - 2 = -4
for y = 0 equation 2 = 2y - 2 = - 2 = -2
for y = 1 equation 2 = 2y - 2 = 2 - 2 = 0
for y = 2 equation 2 = 2y - 2 = 4 - 2 = 2

Among the answer choice all except 6 ( choice E ) can be the final score

1. There are two cases for the total value of first two trials' scores of 1 and -1.

Case 1
Trial 1 = -1. Trial 2 = 1, with weighted score of 2.

-1 + 2 = 1

Case 2
Trial 1 = 1. Trial 2 = -1, with weighted score of -2.

1 + (-2) = -1

2. Add Trial 3 weighted score, 3C, to 1 or -1

Possible values, C, for Trial 3 are -2, -1, 0, 1, or 2

Which answer choice can we not achieve by addition or subtraction of 3C in combination with either 1 or -1?

A. -4. Possible. C is -1, 3C is -3.
-1 - 3 = -4. Reject

B. -2. Possible. C is -1, 3C is -3.
1 - 3 = -2. Reject

C. 1. Possible. C is 0, 3C is 0.
1 + 0 = 1. Reject

D. 5. Possible. C is 2, 3C is 6.
-1 + 6 = 5. Reject

E. 6. Impossible by default. And there is no way to get +5 (to add to Case 1) or +7 (to add to Case 2) from 3 or a multiple of 3.

Answer E

There are 2 possibilities
Case 1: Trial score 1(x) : 1, Trial score 2(y) : -1
(Sum = 1*1 + 2*-1 = -1)
Case 2: Trial score 1(x) : -1, Trial score 2(y) : 1
(Sum = 1*-1 + 2*1 = 1)

As for the third score, there are 5 possibilities each in case 1 and case 2
-2,-1,0,1,2 which has to multiplied by 3 and added to the previous sum(from both cases)
The numbers which has to be added to attain the possible sums are -6,-3,0,3,6.

Possible sums in case 1 : -7,-4,-1,2,5
Possible sums in case 2 : -5,-2,1,4,7

The only possible sum which is not part of this list is 6(Option E)

Took me 03:17 to solve, did it the same way as above. Seems like one of those questions that is just going to take a long-ish time to solve, albeit it is fairly simple.

Final Score = (S1) + (S2 x 2) + (S3 x 3)
given s1 and s2 = 1 or -1
1 + (-2) + 6 = 5 so eliminate 5
1 + (-2) + (-3) = 4 so eliminate 4
-1 + (2) + (-3) = -2
-1 + 2 = 0 = 1 eliminate 1

we are left with 6

Answer E

For this question, i believe the simplest way is to test the answer choices.
From the stem, it flows that her score, before the last trial, will be 1 or -1.
To get -4 as final score she must have 4 or -1. This is possible if she gets -1 in the last trial.
Keep on testing, we see that the answer choices A through D work.
But E does not work: to have 6 as final score, she must get a score of 5 or 7 in the last trial. both value are not multiple of 3.

How do I do this in 2mins?

divyajeswani
You know that the score Anne had from first two trials can be either 1 or -1. So you know that the third trial score i.e. 3x has to be added or subtracted.
It takes while to understand that 3x has 5 possible values - -6, -3, 0, 3 6.

As soon as you realise that -1 or 1 is going to be added or subtracted to multiple of 3, you know that answer can't be a multiple of 3. Thus E.
But you need to see the options first after going through the question and before starting solving it.
rbramkumar has nicely explained the solution theoretically.

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?

My approach:

We're told Anne's first two scores are -1 and 1. From her first two scores, they can either be counted as -1 + 2 = 1 OR 1 -2 = -1.

Her 3rd score will either be 3x - 1 OR 3x + 1.

By trial and error, we can quickly see that there's no way for the final score to be 6. Answer is E.

(A) If the sum of the first two trials is -1 and the third trial is -1, then the sum can be -1 + 3(-1) = -4

(B) If the sum of the first two trials is 1 and the third trial is -1, then the sum can be 1 + 3(-1) = -2

(C) If the sum of the first two trials is 1 and the third trial is 0, then the sum can be 1 + 3(0) = 1

(D) If the sum of the first two trials is -1 and the third trial is 2, then the sum can be -1 + 3(2) = 5

(E) The maximum can be 5; so 6 is not possible

The answer is E

Good buy lengthy process

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Trying Total score can be 3x+1 or 3x-1 would be a faster way.

Response to divyajeswani:

Keep in mind that you don’t need to write any explanations of your reasoning when you take the real test. Here’s the solution without any explanations: since the first two scores of Anne are 1 and -1, either 1 + 2(-1) = -1 or -1 + 2(1) = 1 will be added to her final score. Now we need to find the answer choice which cannot equal one less or one more than three times -2, -1, 0, 1 or 2. We check at most four answer choices and checking each answer choice takes mere seconds. After we eliminate A, B, C, and D; we know the answer is E. I think it is possible to do this under two minutes.

Her sum after two trials will be -1 or 1.

The final score can be 3x+1 or 3x-1, where x is the score on the third trial.

Possible values for 3x+1 = {7, 4, 1, -2, -5}
Possible values for 3x-1 = {-7, -4, -1, 2, 5}

Hy i have a doubt in this Q as i saw this Q i thought its will be solved by using ans choices so i formed equation
1+(-1) +3X=4 and so on but i am not able to solve it only option d is coming without fraction rest all are in fraction
Please help

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