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In a certain learning experiment, each participant had three trials an [#permalink]

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23 Jul 2017, 11:09

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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?

In a certain learning experiment, each participant had three trials an [#permalink]

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23 Jul 2017, 19:24

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carcass wrote:

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?

A. -4

B. -2

C. 1

D. 5

E. 6

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.

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)
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Re: In a certain learning experiment, each participant had three trials an [#permalink]

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25 Jul 2017, 02:27

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.

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?

A. -4

B. -2

C. 1

D. 5

E. 6

If Anne received 1 for her first trial and -1 for her second, then the sum of her first two trials is 1 + 2(-1) = 1 + -2 = -1.

If Anne received -1 for her first trial and 1 for her second, then the sum of her first two trials is -1 + 2(1) = -1 + 2 = 1.

Let’s analyze each answer choice:

A) -4

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) -2

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) 1

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) 5

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) 6

We see there is no way to get a sum of 6.

Answer: E
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In a certain learning experiment, each participant had three trials an [#permalink]

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20 Aug 2017, 07:25

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bfistein wrote:

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.

Not really. There's no need to calculate each individual sums.

2 possible scores for the first two trials 1,-1. Let 3rd trial score = x.

Total score can be 3x+1 or 3x-1. Can never be a multiple of 3. So, 6 (or in that case even -6,-3,0,3,6) can't come.

Re: In a certain learning experiment, each participant had three trials an [#permalink]

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10 Sep 2017, 03:12

carcass wrote:

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?

A. -4

B. -2

C. 1

D. 5

E. 6

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

Re: In a certain learning experiment, each participant had three trials an [#permalink]

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16 Oct 2017, 12:36

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.
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