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On a certain 50-question test, each correct answer is worth

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On a certain 50-question test, each correct answer is worth [#permalink] New post 17 Feb 2013, 09:00
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

72% (02:20) correct 28% (01:09) wrong based on 211 sessions
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

[Reveal] Spoiler:
The correct answer is: Statements (1) and (2) taken TOGETHER are NOT SUFFICIENT.

---

I understand why the Statement (2) is inconclusive, however I'm struggling with the first one.

At worst she could have answered 10 questions correctly in the first part and none in the second. What about the best option?

In Kaplan they explain at best she could have answered 25 questions in the first and 15 in the second part. Why? Why not 30 and 20, respectively? It adds up to 50 questions.

Once again thank you in advance for the clarification :)
[Reveal] Spoiler: OA
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Re: If the minimum passing score on the test is 60... [#permalink] New post 17 Feb 2013, 14:28
The reason she can't answer 30 correctly is that there are only 25 questions on the first half of a 50 question exam.
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Re: On a certain 50-question test, each correct answer is worth [#permalink] New post 22 Feb 2013, 08:26
Expert's post
langus91 wrote:
I've got a problem with the question below. Any help would be much appreciated!

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

[Reveal] Spoiler:
The correct answer is: Statements (1) and (2) taken TOGETHER are NOT SUFFICIENT.

---

I understand why the Statement (2) is inconclusive, however I'm struggling with the first one.

At worst she could have answered 10 questions correctly in the first part and none in the second. What about the best option?

In Kaplan they explain at best she could have answered 25 questions in the first and 15 in the second part. Why? Why not 30 and 20, respectively? It adds up to 50 questions.

Once again thank you in advance for the clarification :)



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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Re: On a certain 50-question test, each correct answer is worth [#permalink] New post 25 Feb 2013, 02:38
langus91 wrote:
Hey guys,

I've got a problem with the question below. Any help would be much appreciated!

---


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

[Reveal] Spoiler:
The correct answer is: Statements (1) and (2) taken TOGETHER are NOT SUFFICIENT.

---

I understand why the Statement (2) is inconclusive, however I'm struggling with the first one.

At worst she could have answered 10 questions correctly in the first part and none in the second. What about the best option?

In Kaplan they explain at best she could have answered 25 questions in the first and 15 in the second part. Why? Why not 30 and 20, respectively? It adds up to 50 questions.

Once again thank you in advance for the clarification :)



case(1) let no. of questions answered in 2nd half is x
so questions answered in 1st half are x + 10
score = 2(x + x+10) = 20 +4x....nothing can be said

case 2 ...not sufficient..as total correctly answred can be 26, 27,.......50


using both case 1 and case 2
total questions answered correctly
2x + 10 > 25
2x>15
x>7.5
so minimum x = 8
hence score = 20+4x8
= 20 + 32
= 52
= pass

hence option(c)
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Re: On a certain 50-question test, each correct answer is worth [#permalink] New post 25 Feb 2013, 07:18
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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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Re: On a certain 50-question test, each correct answer is worth [#permalink] New post 26 Feb 2013, 19:00
(1) insufficient: more than 10 questions of the first half, but not sure of the second half
(2) insufficient: more than a half of questions, may be 26, 27, 28, 29 questions, the results are not higher than 60 --> cannot pass
(1) + (2) insufficient
==> Answer is E
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Re: On a certain 50-question test, each correct answer is worth [#permalink] New post 29 Dec 2013, 15:42
langus91 wrote:
Hey guys,

I've got a problem with the question below. Any help would be much appreciated!

---


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

[Reveal] Spoiler:
The correct answer is: Statements (1) and (2) taken TOGETHER are NOT SUFFICIENT.

---

I understand why the Statement (2) is inconclusive, however I'm struggling with the first one.

At worst she could have answered 10 questions correctly in the first part and none in the second. What about the best option?

In Kaplan they explain at best she could have answered 25 questions in the first and 15 in the second part. Why? Why not 30 and 20, respectively? It adds up to 50 questions.

Once again thank you in advance for the clarification :)


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 :)
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Re: On a certain 50-question test, each correct answer is worth [#permalink] New post 08 May 2014, 05:02
jlgdr wrote:
langus91 wrote:
Hey guys,

I've got a problem with the question below. Any help would be much appreciated!

---


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

[Reveal] Spoiler:
The correct answer is: Statements (1) and (2) taken TOGETHER are NOT SUFFICIENT.

---

I understand why the Statement (2) is inconclusive, however I'm struggling with the first one.

At worst she could have answered 10 questions correctly in the first part and none in the second. What about the best option?

In Kaplan they explain at best she could have answered 25 questions in the first and 15 in the second part. Why? Why not 30 and 20, respectively? It adds up to 50 questions.

Once again thank you in advance for the clarification :)


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 :)


Can we take this assumption ? I mean it is not explicitly specified
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Re: On a certain 50-question test, each correct answer is worth [#permalink] New post 08 May 2014, 07:07
Expert's post
himanshujovi wrote:
jlgdr wrote:
langus91 wrote:
Hey guys,

I've got a problem with the question below. Any help would be much appreciated!

---


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

[Reveal] Spoiler:
The correct answer is: Statements (1) and (2) taken TOGETHER are NOT SUFFICIENT.

---

I understand why the Statement (2) is inconclusive, however I'm struggling with the first one.

At worst she could have answered 10 questions correctly in the first part and none in the second. What about the best option?

In Kaplan they explain at best she could have answered 25 questions in the first and 15 in the second part. Why? Why not 30 and 20, respectively? It adds up to 50 questions.

Once again thank you in advance for the clarification :)


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 :)


Can we take this assumption ? I mean it is not explicitly specified


Half of 50 is 25, isn't it?
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Re: On a certain 50-question test, each correct answer is worth [#permalink] New post 09 May 2014, 13:10
stat#1: says if x questions answered rightly on second half then x+10 answered rightly on the first half . X could be anything including 0. So insuff

Stat#2: the number of questions answered rightly > 25, so insuff as it could be 26,27,28...

Stat#1 + stat#2: x+10+x>p where p>25 => 2x>p-10 => x>(p-10)/2 where x and p are positive integers .It give both below and above 60 range so insuff
Re: On a certain 50-question test, each correct answer is worth   [#permalink] 09 May 2014, 13:10
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