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gmatbull
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During a recent evaluation, X students were given a two-ques Updated on: 04 Jan 2026, 08:56
Originally posted by gmatbull on 01 Feb 2014, 20:52.
Last edited by Bunuel on 04 Jan 2026, 08:56, edited 3 times in total.
Renamed the topic, edited the question and added the OA.
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79% (02:01) correct 21% (02:46) wrong based on 248 sessions

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During a recent evaluation, X students were given a two-question test. If 1/5 of the students answered the first question correctly, and, of those students, 1/2 answered the second question correctly, which of the following expressions indicates the number of students who did NOT answer both questions correctly?

(A) x/10
(B) x/5
(C) 5x/7
(D) 9x/10
(E) 9x

Show Spoiler
Correct Ans is 9x/10- supported by CASE 2 in attachment

How would the question be asked if it were ONLY the intersection of those who got both questions wrong?
See CASE 1 in attachment

Thanks to respond with any other sample questions

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2 cases.docx [13.24 KiB]
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D
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Bunuel
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During a recent evaluation, X students were given a two-ques 02 Feb 2014, 01:56
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gmatbull
During a recent evaluation, X students were given a two-question test. If 1/5 of the students answered the first question correctly, and, of those students, 1/2 answered the second question correctly, which of the following expressions indicates the number of students who did NOT answer both questions correctly?

(A) x/10
(B) x/5
(C) 5x/7
(D) 9x/10
(E) 9x

Show Spoiler
Correct Ans is 9x/10- supported by CASE 2 in attachment

How would the question be asked if it were ONLY the intersection of those who got both questions wrong?
See CASE 1 in attachment

Thanks to respond with any other sample questions
Show more

Say x = 10:

The number of students who answered the first question correctly = 10*1/5 = 2;
Of those 2 students, 1/2 answered the second question correctly, thus 2*1/2 = 1 student answered both questions correctly.

If 1 student answered both questions correctly, then the remaining 9 students did NOT answer both questions correctly.

Now, plugging x = 10, and see which of the options gives 9. Only D fits.

Answer: D.

As for your question, for case 1 the question would be "which of the following expressions indicates the number of students who answered both questions WRONG?"

Hope it's clear.
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During a recent evaluation, X students were given a two-ques 02 Feb 2014, 06:10
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i got it....

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During a recent evaluation, X students were given a two-ques 29 Mar 2015, 07:58
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gmatbull
During a recent evaluation, X students were given a two-question test. If 1/5 of the students answered the first question correctly, and, of those students, 1/2 answered the second question correctly, which of the following expressions indicates the number of students who did NOT answer both questions correctly?

(A) x/10
(B) x/5
(C) 5x/7
(D) 9x/10
(E) 9x

Show Spoiler
Correct Ans is 9x/10- supported by CASE 2 in attachment

How would the question be asked if it were ONLY the intersection of those who got both questions wrong?
See CASE 1 in attachment

Thanks to respond with any other sample questions
Show more


Let x = 10.

1/5th students answered the first question correctly = 1/5 * 10 = 2.
Of those 2 students, 1/2 answered the second question correctly = 1/2 * 2 = 1.
This is the number of students who answered BOTH questions correctly.

Hence there are 9 students who did NOT answer both questions correctly.
i.e, 9 out of 10 did not answer both questions correctly.
Hence 9x/10.

Hence option (D).

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During a recent evaluation, X students were given a two-ques 12 Oct 2020, 04:54
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can anyone solve this by Matrix method.
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During a recent evaluation, X students were given a two-ques 04 Jan 2026, 08:55
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gmatbull
During a recent evaluation, X students were given a two-question test. If 1/5 of the students answered the first question correctly, and, of those students, 1/2 answered the second question correctly, which of the following expressions indicates the number of students who did NOT answer both questions correctly?

(A) x/10
(B) x/5
(C) 5x/7
(D) 9x/10
(E) 9x

Show Spoiler
Correct Ans is 9x/10- supported by CASE 2 in attachment

How would the question be asked if it were ONLY the intersection of those who got both questions wrong?
See CASE 1 in attachment

Thanks to respond with any other sample questions
Show more
Deconstructing the Question
Total students = \(x\).

1. Students who answered the first question correctly:
\(\frac{1}{5}x\)

2. Students who answered the second question correctly (from the group above):
\(\frac{1}{2} \times (\frac{1}{5}x) = \frac{1}{10}x\)

This \(\frac{1}{10}x\) represents the students who answered BOTH questions correctly (since they got the first right AND the second right).

Target Question
Find the number of students who did NOT answer both questions correctly.
This is the complement of the group we just found.

\(\text{Not Both} = \text{Total} - \text{Both}\)
\(\text{Not Both} = x - \frac{1}{10}x\)
\(\text{Not Both} = \frac{10x}{10} - \frac{1x}{10} = \frac{9x}{10}\)

Answer: D
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