On a certain 50-question test, each correct answer is worth 2 points, with no penalty for incorrect answers. If the minimum passing score on the test is 60, did Ethel pass the test?

(1) Ethel answered 10 more questions correctly on the first half of the test than on the second half
(2) Ethel answered more than half of the questions on the test correctly

Hi langus91, you've got the logic down perfectly. Statement 1 indicates there could have been 10 correct answers in the first half and 0 in the second half, or 11-1, or 12-2, etc. So the minimum score the student could get while satisfying this equation is 20/100. Assuming more and more answers are answered correctly, we end up at 25-15 (that is, all questions correct on the first half and 60% correct on the second half, which leads to 80/100 total score.

As you indicated in your spoiler, you were unsure about a 30-20 split, which was addressed by JimGMATPrepster. However, even if you're unsure of this on test day it won't stop you from getting the correct answer as 20-10 or above will lead to a passing grade on the exam. Even putting the two conditions together, Ethel could have correctly answered questions in any of the following proportions:
18-8, (total 26/50, more than half)
19-9,
20-10,
21-11,
22-12,
23-13,
24-14,
25-15 (total 40/50, maximum score of 80/100)

The first two are failing grades, while the final five are passing grades. Hence why the answer is E. The GMAT can be a very unforgiving exam, but you can still get the right answer even if you make little conceptual mistakes like this one.

Hope this helps!
-Ron
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Hi jbishit, your analysis is correct, however the passing grade is 60. Putting the two conditions together, Ethel got either 52, 56, 60, 64, 68, 72, 76 or 80 on the test. 2 fails and 6 passes. This is classic insufficiency as we have possible answers on both sides of the minimum passing grade. It can't be (C).

Hope this helps!
-Ron
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This too should be pretty straightforward

Let's see what question stem says

It says there are 50 questions, you need to answer at least 30 to pass and you get 2 points for each correct answer, while no penalties for incorrect answers

Did she pass the test?

1) She answered 10 more correct on the second half than on the first half

So first half is 25 questions of course, let's try picking some numbers to proof this statement

First option she answered 1 correctly in the first half and 11 correctly on the second half, she failed the test
Second option she answered 15 correctly in the first half and 25 correctly on the second half, she passed the test

Hence, Insuff

2) She answered more than 25 questions correctly

Obviously insuff

(1) + (2)

Choices now incorporating second statement could be

She answered 8 correctly in first half and 18 correctly on second half, 26 total she failed
She answered 10 correctly in first half and 20 correctly on the second half, 30 total she passed

Hence E

Hope it helps
Consider providing Kudos if you find it easy to follow

Cheers!
J

Half of 50 is 25, isn't it?
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Bunuel is this really a combination question?
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