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JoostGrijsen
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If 85 percent of the test takers taking an old paper and pencil GMAT 12 Nov 2014, 05:41
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B
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Difficulty:

15% (low)

Question Stats:

81% (01:31) correct 19% (01:41) wrong based on 125 sessions

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If 85 percent of the test takers taking an old paper and pencil GMAT exam answered the first question on a given math section correctly, and 75 percent of the test takers answered the second question correctly, and 5 percent of the test takers answered neither question correctly, what percent answered both correctly?

A. 60 %
B. 65 %
C. 70%
D. 75%
E. 80%

PS could someone please explain this because the answer in the book was unclear for me.
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B
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Bunuel
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If 85 percent of the test takers taking an old paper and pencil GMAT 12 Nov 2014, 06:34
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JoostGrijsen
If 85 percent of the test takers taking an old paper and pencil GMAT exam answered the first question on a given math section correctly, and 75 percent of the test takers answered the second question correctly, and 5 percent of the test takers answered neither question correctly, what percent answered both correctly?

A. 60 %
B. 65 %
C. 70%
D. 75%
E. 80%

PS could someone please explain this because the answer in the book was unclear for me.
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{Total} = {First correctly} + {Second correctly} - {Both correctly} + {Neither correctly}

100 = 85 + 75 - {Both correctly} + 5

{Both correctly} = 65.

Answer: B.

Theory on Overlapping Sets:
how-to-draw-a-venn-diagram-for-problems-98036.html
advanced-overlapping-sets-problems-144260.html

All DS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=45
All PS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=65

Hope it helps.
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PareshGmat
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If 85 percent of the test takers taking an old paper and pencil GMAT 13 Nov 2014, 01:57
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Answer = B = 65%

Refer diagram below:

Attachment:
over.png
over.png [ 4.86 KiB | Viewed 6653 times ]
Setting up the equation

85 + 75 - x + 5 = 100

x = 165 - 100 = 65%

Answer = B
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If 85 percent of the test takers taking an old paper and pencil GMAT 30 Sep 2019, 07:52
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Solution



Given
    • 85 percent of the test takers answered the first question correctly.
    • 75 percent of the test takers answered the second question correctly.
    • 5 percent of the test takers answered neither question correctly

To find
    • The percent of test takers who answered both the question correctly.

Approach and Working out

A -> %age of Students who answered first question correctly = 85%
B -> %age of Students who answered second question correctly = 75%
Neither A nor B = 5%
A∩ B = ?

Total students = 100%
Total students – neither A nor B = A + B - A∩ B
    • 100 -5 = 85 + 75 - A∩ B
    • 95 = 85 + 75 - A∩ B
    • 10 = 75 - A∩ B
    • A∩ B = 65

Thus, option B is the correct answer.

Correct Answer: Option B
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