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08 Nov 2012, 23:46
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C
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Difficulty:
65%
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Question Stats:
57% (02:22) correct
43%
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wrong
based on 196
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In country C, the percentage of men with phones is between 35% and 40%. Do at least half the men with cell phones also have cars?
(1) In country C, between 70% and 75% of the men have cars.
(2) In country C, between 40% and 45% of the men with cars have cell phones
(1) In country C, between 70% and 75% of the men have cars.
(2) In country C, between 40% and 45% of the men with cars have cell phones
09 Nov 2012, 04:50
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In country C, the percentage of men with phones is between 35% and 40%. Do at least half the men with cell phones also have cars?
Say there are 100 men in country C. We are given that between 35 and 40 men have phones. The question asks whether at least half of them also have cars.
100 = {phone} + {car} - {both} + {neither}.
(1) In country C, between 70% and 75% of the men have cars --> between 70 and 75 men have cars. Now, if 35 men have phones, 70 have cars and no one is without any, then only 5 men have both phones and cars, which is less than half of the men having phones (35). But if 40 men have phones, 75 have cars and 10 have neither, then 25 men have both phones and cars, which is more than half of the men having phones (40). Not sufficient.
(2) In country C, between 40% and 45% of the men with cars have cell phones. If there are only 10 men with cars and only 4 of them have both phones and cars, then less than half of the men having phones also have cars (100=40+10-4+56). But if all 100 men have cars and 40 of them have both phones and cars, then more than half of the men having phones also have cars (100=40+100-40+0). Not sufficient.
(1)+(2) Even if there are only 70 men with cars (min possible) and only 40% of them also have phones (min possible), then 70*0.4=28 men have both phones and cars (min possible) and even if there are 40 men with phones (max possible), then still more than half of the men having phones (40) also have cars (28). Sufficient.
Answer: C.
Hope it's clear.
Say there are 100 men in country C. We are given that between 35 and 40 men have phones. The question asks whether at least half of them also have cars.
100 = {phone} + {car} - {both} + {neither}.
(1) In country C, between 70% and 75% of the men have cars --> between 70 and 75 men have cars. Now, if 35 men have phones, 70 have cars and no one is without any, then only 5 men have both phones and cars, which is less than half of the men having phones (35). But if 40 men have phones, 75 have cars and 10 have neither, then 25 men have both phones and cars, which is more than half of the men having phones (40). Not sufficient.
(2) In country C, between 40% and 45% of the men with cars have cell phones. If there are only 10 men with cars and only 4 of them have both phones and cars, then less than half of the men having phones also have cars (100=40+10-4+56). But if all 100 men have cars and 40 of them have both phones and cars, then more than half of the men having phones also have cars (100=40+100-40+0). Not sufficient.
(1)+(2) Even if there are only 70 men with cars (min possible) and only 40% of them also have phones (min possible), then 70*0.4=28 men have both phones and cars (min possible) and even if there are 40 men with phones (max possible), then still more than half of the men having phones (40) also have cars (28). Sufficient.
Answer: C.
Hope it's clear.
General Discussion
PrashantPonde
Joined: 27 Jun 2012
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10 Nov 2012, 12:22
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Good question...Great explanation! +1 to both of you!
