John took a test that had 60 questions numbered from 1 to 60

Question

The Official Guide For GMAT® Quantitative Review, 2ND Edition

John took a test that had 60 questions numbered from 1 to 60. How many of the questions did he answer correctly?

(1) The number of questions he answered correctly in the first half of the test was 7 more than the number he answered correctly in the second half of the test.
(2) He answered 5/6 of the odd-numbered questions correctly and 4/5 of the even-numbered questions correctly.

Data Sufficiency  
 Question:  29
 Category:   Arithmetic  Fractions
 Page:  155
 Difficulty:  600

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Bunuel · Answer

SOLUTION

John took a test that had 60 questions numbered from 1 to 60. How many of the questions did he answer correctly?

(1) The number of questions he answered correctly in the first half of the test was 7 more than the number he answered correctly in the second half of the test --> F = S + 7. Not sufficient.

(2) He answered 5/6 of the odd-numbered questions correctly and 4/5 of the even-numbered questions correctly. Since there are 30 odd-numbered questions and 30 even-numbered questions, then the number of questions answered correctly is 5/6*30 + 4/5*30. Sufficient.

Answer: B.

Rock750 · Answer

John took a test that had 60 questions numbered from 1 to 60. How many of the questions did he answer correctly?

(1) The number of questions he answered correctly in the first half of the test was 7 more than the number he answered correctly in the second half of the test.
(2) He answered 5/6 of the odd-numbered questions correctly and 4/5 of the even-numbered questions correctly.

(1) Insufficient : He may have answered 2 correctly in the second half and therefore 9 in the first half . So, he could have answered 11correct. Similarly, 3 in the second half and therefore 10 in the first half . so, the result will be 13. Two different answers so (1) is not sufficient.

(2) Sufficient : Given that we know the total number of the questions and also how many odd and how many even there are, the question turns into simple multiplication.

Answer : B

nutshell · Answer

No. of questions answered correctly = ?

(1). FC = SC + 7;
Insufficient as there are 2 variables.

(2). Since the total no. of questions = 60, starting from 1, there will be 30 odd and 30 even questions.
Odd no. of questions correct = (5/6)*30 = 25;
Even no. of questions correct = (4/5)*30 = 24;

So, the total no. of questions answered correctly = 49.

Of course, we don't have to solve these for DS. If we know it is solvable, we can mark the answer and move on.

Ans is (B).

kinjiGC · Answer

Statement 1) out of 30 questions, he answered x+7 and out of next 30 questions, he answered x questions, we still don't know x. Not Sufficient.
Statement 2) As even numbered and odd numbered questions will be mutually exclusive (no overlapping), we know there are 30 odd and 30 even questions.
So we can calculate the number of questions answered.

Hence Option B)

Bunuel · Answer

SOLUTION

John took a test that had 60 questions numbered from 1 to 60. How many of the questions did he answer correctly?

(1) The number of questions he answered correctly in the first half of the test was 7 more than the number he answered correctly in the second half of the test --> F = S + 7. Not sufficient.

(2) He answered 5/6 of the odd-numbered questions correctly and 4/5 of the even-numbered questions correctly. Since there are 30 odd-numbered questions and 30 even-numbered questions, then the number of questions answered correctly is 5/6*30 + 4/5*30. Sufficient.

Answer: B.

rashedBhai · Answer

does first half of the test mean there were 30 questions in the first half?

Posted from my mobile device

ScottTargetTestPrep · Answer

Solution:

Question Stem Analysis:

We must determine the number of questions that John answered correctly on a 60-question test.

Statement One Alone:

Statement one alone is not sufficient. For example, if he answered 4 questions correctly on the second half of the test, then he answered 4 + 7 = 11 questions correctly on the first half of the test. But if he answered 9 questions correctly on the second half of the test, then he answered 9 + 7 = 16 questions correctly on the first half of the test.

Statement Two Alone:

The number of odd numbers in the interval from 1 to 60, inclusive, is: (59 - 1)/2 + 1 = 30. Since John answered 5/6 of the odd-numbered questions correctly, he answered 5/6 x 30 = 25 questions correctly.

The number of even numbers in the interval from 1 to 60, inclusive is (60 - 2)/2 + 1 = 30. Since John answered 4/5 of the even-numbered questions correctly, he answered 4/5 x 30 = 24 questions correctly.

Thus, the number of questions he answered correctly is 25 + 24 = 49.

Statement two alone is sufficient.

Answer: B

totaltestprepNick · Answer

B https://www.youtube.com/watch?v=7SKtMEKHghM Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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