Bunuel wrote:
Jack took an exam of 45 questions, how many questions did he answer correctly?
(1) The number he answered incorrectly is twice the number of questions he did not attempt at all.
(2) The total number of questions he answered incorrectly or did not attempt is 3/9 of all questions.
Given: Jack took an exam of 45 questions Target question: How many questions did he answer correctly? Statement 1: The number he answered incorrectly is twice the number of questions he did not attempt at all. This statement doesn't feel sufficient, so I'll TEST some scenarios.
There are several scenarios that satisfy statement 1. Here are two:
Case a: Jack answered 42 questions correctly, 2 questions incorrectly, and did not attempt 1 question. In this case, the answer to the target question is
Jack correctly answered 42 questionsCase b: Jack answered 39 questions correctly, 4 questions incorrectly, and did not attempt 2 question. In this case, the answer to the target question is
Jack correctly answered 39 questionsSince we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/dat ... lug-values Statement 2: The total number of questions he answered incorrectly or did not attempt is 3/9 of all questions.Key property: For each of the 45 questions on the exam, there are three possible cases:
#1 - Jack did not attempt the question
#2 - Jack correctly answered the question
#3 - Jack incorrectly answered the questionStatement 2 tells us that 3/9 of the questions were EITHER answered incorrectly (case #3) OR not attempted (case #1).
This means the REMAINING 6/9 of the questions were answered correctly (case #2)
So,
the number of questions answered correctly = 6/9 of 45 = 2/3 of 45 = 30Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
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