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13 Jul 2024, 00:39
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Amy attempts 5 math tests, each test consisting of 50 multiple-choice questions worth 2 points each. Questions are based on the following topics: Geometry, Algebra and Combinatorics. No question is based on more than one topic. She notices that the total number of points per topic is the same across the 5 tests. She scores the maximum possible points for each topic in at least one of the tests. Given below are her test scores based on each topic across the 5 tests.
Ata later date, it was revealed that out of the 250 questions in the 5 tests, a total of 2 questions were printed incorrectly, not necessarily from the same test. It was announced that 2 points each would be awarded for these questions, unless already done so.
For any given test, find the approximate difference between the greatest possible percentage increase in score and the least possible percentage increase in score.
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28 Aug 2024, 03:57
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It was announced that 2 points each would be awarded for these questions, unless already done so.
The least change will be 0 (Considering Amy had already got 2+2 points for the 2 incorrect questions).
Assuming that both the questions were on the same test. (Just assuming!)
The greatest % change will be when Amy is awarded 4 extra points on the test where she has scored the least. Clearly, she has scored the least on Test Number 4
Lets award here 4 points and see % change :
% change = [(22 + 20 + 22 + 4) - (22 + 20 + 22)] / 100
= 400/64 = 6.25%
6.25% is the highest answer in the drop down, so we wouldn't check cases where both the questions were from different tests. [That'd be too lengthy to do!]
[Clearly not a solid approach and possibly we got lucky with our assumption but as they say in GMAT, options are a part of the question and hence, a part of the reasoning!]
The least change will be 0 (Considering Amy had already got 2+2 points for the 2 incorrect questions).
Assuming that both the questions were on the same test. (Just assuming!)
The greatest % change will be when Amy is awarded 4 extra points on the test where she has scored the least. Clearly, she has scored the least on Test Number 4
Lets award here 4 points and see % change :
% change = [(22 + 20 + 22 + 4) - (22 + 20 + 22)] / 100
= 400/64 = 6.25%
6.25% is the highest answer in the drop down, so we wouldn't check cases where both the questions were from different tests. [That'd be too lengthy to do!]
[Clearly not a solid approach and possibly we got lucky with our assumption but as they say in GMAT, options are a part of the question and hence, a part of the reasoning!]
16 Jan 2025, 11:14
Kudos
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1. The greatest possible percentage increase in a test score happens when both "bonus" questions were on it - which is an increase of 4 points. Let's calculate it for all 5 of Amy's test scores.
- Test 1: \(\frac{(4 + 20 + 40 + 30) - (20 + 40 + 30)}{20 + 40 + 30} * 100\% \approx 4.44\%\).
- Test 2: \(\frac{(4 + 6 + 40 + 28) - (6 + 40 + 28)}{6 + 40 + 28} * 100\% \approx 5.41\%\).
- Test 3: \(\frac{(4 + 10 + 42 + 36) - (10 + 42 + 36)}{10 + 42 + 36} * 100\% \approx 4.55\%\).
- Test 4: \(\frac{(4 + 22 + 20 + 22) - (22 + 20 + 22)}{22 + 20 + 22} * 100\% = 6.25\%\).
- Test 5: \(\frac{(4 + 20 + 26 + 34) - (20 + 26 + 34)}{20 + 26 + 34} * 100\% = 5\%\).
Test 4 has the greatest possible percentage increase.
2. The least possible percentage increase in a test score happens when no "bonus" questions were on it - which is a change of 0 points. It doesn't matter for which test this happens to, as the change will still be 0%.
3. We are asked to find the difference between these values, which is 6.25% - 0% = 6.25%.
- Test 1: \(\frac{(4 + 20 + 40 + 30) - (20 + 40 + 30)}{20 + 40 + 30} * 100\% \approx 4.44\%\).
- Test 2: \(\frac{(4 + 6 + 40 + 28) - (6 + 40 + 28)}{6 + 40 + 28} * 100\% \approx 5.41\%\).
- Test 3: \(\frac{(4 + 10 + 42 + 36) - (10 + 42 + 36)}{10 + 42 + 36} * 100\% \approx 4.55\%\).
- Test 4: \(\frac{(4 + 22 + 20 + 22) - (22 + 20 + 22)}{22 + 20 + 22} * 100\% = 6.25\%\).
- Test 5: \(\frac{(4 + 20 + 26 + 34) - (20 + 26 + 34)}{20 + 26 + 34} * 100\% = 5\%\).
Test 4 has the greatest possible percentage increase.
2. The least possible percentage increase in a test score happens when no "bonus" questions were on it - which is a change of 0 points. It doesn't matter for which test this happens to, as the change will still be 0%.
3. We are asked to find the difference between these values, which is 6.25% - 0% = 6.25%.
