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# All of the students who took a certain test answered the two first que

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Math Expert
Joined: 02 Sep 2009
Posts: 64068
All of the students who took a certain test answered the two first que  [#permalink]

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01 Aug 2017, 12:03
00:00

Difficulty:

55% (hard)

Question Stats:

68% (02:07) correct 32% (02:24) wrong based on 73 sessions

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All of the students who took a certain test answered the two first questions on the test. If 60% of the students answered the first question on the test correctly, and 40% of the students answered the second question on the test correctly, then what percent of the students answered neither of the two questions correctly?

(1) 20% of the students answered both the first and the second questions on the test correctly.

(2) Two thirds of the students who did not answer the second question on the test correctly answered the first question on the test correctly.

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Re: All of the students who took a certain test answered the two first que  [#permalink]

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01 Aug 2017, 20:21
1
Bunuel wrote:
All of the students who took a certain test answered the two first questions on the test. If 60% of the students answered the first question on the test correctly, and 40% of the students answered the second question on the test correctly, then what percent of the students answered neither of the two questions correctly?

(1) 20% of the students answered both the first and the second questions on the test correctly.

(2) Two thirds of the students who did not answer the second question on the test correctly answered the first question on the test correctly.

First Correct = FC = 60%
SC = 40%

(1) FCSC = 20%
Only FC + Only SC + FCSC + FWSW = 100%
(60-20)% + (40-20)% + 20% + FWSW = 100%
FWSW = 20%

Sufficient

(2) SW = 60%
SWFC = 2/3 * 60% = 40%
and since FC = 60%
FCSC = 20%
and from here we can calculate FWSW
Sufficient

D
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Re: All of the students who took a certain test answered the two first que   [#permalink] 01 Aug 2017, 20:21