Amy attempts 5 math tests, each test consisting of 50 multiple choice

Question

https://gmatclub.com/forum/download/file.php?id=82505 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. As a percentage of the total points scored across the 5 tests, approximately GRAPH_1_PLACEHOLDER more percent points did Amy lose in Algebra than in Geometry? For any given test, find the approximate difference GRAPH_2_PLACEHOLDER between the greatest possible percentage increase in score and the least possible percentage increase in score. GMAT-Club-Forum-hsglf3nz.png

HarshavardhanR · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=84365 Harsha GMAT-Club-Forum-9q3e014b.png

Sajjad1994 · Answer

Hi  sayan640

Replied to your DM.

samarpan.g28 · Answer

Sajjad1994  can you please post the OA?

Tia0001 · Answer

I think the answer to qn 1 is wrong. She score more points in the red pie. So could not be losing more points in that subject matter.

Parul981 · Answer

Solution for first question

andrewxt111 · Answer

That is the case because the maximum number of points for Algebra is higher than Geometry. Since she got the max score at least once, the highest score for each section is the max score (42 for algebra and 36 for geometry). While, percentage wise she scored more points in algebra, she lost only a total of 30 points across all geometry sections, compared to 42 in algebra, comprising a larger share of the lost points among all points scored.

Hope that helps!

Edit: The solution itself is as follows:

Sum up all the points she scored. This is 396.

Calculate missed points in each sections (as said before, 42 and 36).

Percentages: Algebra 10.6%
                   Geometry 7.57%

Difference is ~3%, which is the correct answer

Sazimordecai · Answer

Nice explanation.
Can you help me with question 2 ?

Posted from my mobile device

andrewxt111 · Answer

Q2 is mostly just trying to trick you into making an avoidable mistake. It asks for the difference between the greatest and the smallest percentage increases between test scores. There are only two instances of increases in scores. 2 to 3 and 4 to 5. Without even calculation, we can see that 4 to 5 will have a greater percentage increase.

From here its a simple percentage exercise:

%increase 4 to 5:  (20+26+34)/(22+20+22) - 1 = 25%
%increase 2 to 3: (10+42+36)/(6+40+28) - 1 = ~18.9%
diff = 25-18.9 = 6.1%.

Since it says approximate, we do not worry about the fact that no answer exactly coincides, so we choose 6.25%, which is the correct answer.

vestenhaus · Answer

Hi,
"Calculate missed points in each sections (as said before, 42 and 36)."
I think there is a typo: "36" should be "30".

anirchat · Answer

Why did you not consider the non-consequtive tests ? Based on that the lowest % increase would be from Test2 and Test5.
 Sajjad1994

vikash905 · Answer

Q1: Maximum Point allotted to Algebra is 42, so points lost in algebra in 5 tests are (2+2+0+22+16) =42 whereas points lost in Geometry is (6+8+0+14+2) =30. Therefore 
(42/396) *100 =10.6% and (30/396) *100 = 7.57%. Difference between them is (10.6-7.57) =3.03%

chris1223 · Answer

can someone help with this question

cheshire · Answer

Is there something specific you need help with? Otherwise I would look at the most helpful reply under this post as its a good solution.

Amy attempts 5 math tests, each test consisting of 50 multiple choice

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