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29 Jun 2021, 05:45
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
68% (03:35) correct
32%
(03:51)
wrong
based on 222
sessions
History
Date
Time
Result
Not Attempted Yet
In a locality of 40 houses, each house is subscribed to at least one newspaper from amongst, The Sun, Daily Mail and Daily Mirror. 24 houses subscribe to Daily Mirror. 13 houses subscribe to both The Sun and Daily Mirror. 26 houses subscribe to Daily Mail out of which 16 also subscribe to The Sun. There is no house which subscribes to The Sun alone. 7 houses subscribe to all three newspapers. How many houses subscribe to only two newspapers?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
23 Jul 2021, 07:48
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7 houses get all three papers.
13 get the Sun and the Mirror (and possibly the Mail), so 6 houses get only the Sun and the Mirror.
16 get the Sun and the Mail (and possibly the Mirror), so 9 houses get only the Sun and the Mail.
Finally, 26 get the Mail. The rest, or 14 houses, must get the Sun only, the Sun and the Mirror only, or the Mirror only. But we know 0 get the Sun only, and 6 get the Sun and the Mirror only. The remaining 8 must get the Mirror only. Since 24 houses in total get the Mirror, and since 7 get all three, 6 get the Sun and Mirror only, and 8 get the Mirror only, the remaining 3 houses must get only the Mirror and the Mail.
So 6 + 9 + 3 = 18 houses get exactly two papers.
Of course it's easier to draw a Venn diagram when working all of this out.
13 get the Sun and the Mirror (and possibly the Mail), so 6 houses get only the Sun and the Mirror.
16 get the Sun and the Mail (and possibly the Mirror), so 9 houses get only the Sun and the Mail.
Finally, 26 get the Mail. The rest, or 14 houses, must get the Sun only, the Sun and the Mirror only, or the Mirror only. But we know 0 get the Sun only, and 6 get the Sun and the Mirror only. The remaining 8 must get the Mirror only. Since 24 houses in total get the Mirror, and since 7 get all three, 6 get the Sun and Mirror only, and 8 get the Mirror only, the remaining 3 houses must get only the Mirror and the Mail.
So 6 + 9 + 3 = 18 houses get exactly two papers.
Of course it's easier to draw a Venn diagram when working all of this out.
General Discussion
23 Jul 2021, 07:31
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Can someone post the solution please?
