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In a certain population, the two most heavily diagnosed

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In a certain population, the two most heavily diagnosed [#permalink] New post 24 Apr 2013, 09:01
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43% (02:51) correct 56% (01:46) wrong based on 102 sessions
In a certain population, the two most heavily diagnosed diseases are schistosomiasis and malaria. Over the past five years, malaria has accounted for more than half of all disease cases, and schistosomiasis, which accounted for 40% of all disease cases in the community five years ago, accounted for 30% in the past year.

Which of the following must be true on the basis of the statements above?

A) There were fewer cases of schistosomiasis last year than five years ago.
B) The percentage of disease cases from malaria has increased over the past 5 years.
C) Some disease has experienced an increase in the number of its total cases, as long as the total number of disease cases went down by a number less than 30%.
D) Each year over the past five, malaria has accounted for a larger percentage of disease cases than schistosomiasis.
E) If the total number of schistosomiasis cases increased over the past five years, then the total number of disease cases must have increased by more than 30%.
[Reveal] Spoiler: OA
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Re: In a certain population, the two most heavily diagnosed dise [#permalink] New post 24 Apr 2013, 09:45
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its E :
think like this : if initially the total number of disease were 100 then S accounted for 40 case now if increase these cases of S even to 41 then total number of cases of disease must be made to around 136 ----> which means that total number of diseases have increased by more than 30 percent !!
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Re: In a certain population, the two most heavily diagnosed dise [#permalink] New post 24 Apr 2013, 13:34
In a certain population, the two most heavily diagnosed diseases are schistosomiasis and malaria. Over the past five years, malaria has accounted for more than half of all disease cases, and schistosomiasis, which accounted for 40% of all disease cases in the community five years ago, accounted for 30% in the past year.

Which of the following must be true on the basis of the statements above?

A) There were fewer cases of schistosomiasis last year than five years ago.
Wrong. The fact that the percentage is less than that in the past does not mean the absolute value is also less. ==> Eliminate right away.

B) The percentage of disease cases from malaria has increased over the past 5 years.
Wrong. No information of percentage of disease cases from malaria in the past ==> Eliminate right away.

C) Some disease has experienced an increase in the number of its total cases, as long as the total number of disease cases went down by a number less than 30%.
Wrong. Quite confused. However, it's wrong because of "some disease" is not clear. In this question, we just talk about Malaria and schistosomiasis.

D) Each year over the past five, malaria has accounted for a larger percentage of disease cases than schistosomiasis.
Wrong. Shell game. But it's wrong because it says "Each year".

E) If the total number of schistosomiasis cases increased over the past five years, then the total number of disease cases must have increased by more than 30%.
Correct. five years ago, the number of schistosomiasis cases was 40/100 total number of disease cases (40%). Last year, the number of schistosomiasis was 60 ==> Total number of disease cases was (60 /30%)x100% = 200 ==> Total disease cases increased 100% that is more than 30%.
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Re: In a certain population, the two most heavily diagnosed dise [#permalink] New post 27 Apr 2013, 20:33
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How about a fraction approach?

If the percentage of cases has dropped from 40 to 30, that means there are 3/4 as many cases per 100 as there were before. In order for the actual number to go up, there needs to be an increase in the total disease cases of more than 4/3. (3/4 x 4/3 = 1, so anything greater than 4/3 will lead to an increase.) This means that for the # of cases of schistosomiasis to go up, we need an increase of more than 1/3. E is correct.

C, on the other hand, is saying something that *seems* kind of sensible. If the % of schistosomiasis cases goes down, and the total number doesn't drop drastically, then doesn't something else need to go down? The answer is no. If schistosomiasis goes down, and everything else stays the same, it can represent 30% of all cases without anything else having to go up. This leads to a drop in total cases of about 15%.

To illustrate, imagine that the original breakdown is like this: 51 cases of malaria, 40 cases of schistosomiasis, and 9 cases of flu. What # of schistosomiasis cases would yield a new % of 30 if the # of malaria and flu cases stay the same?
Schist/Total = s/(51+9+s) = .30
s = .3(60 + s)
.7s = 18
s is about 25, so the new total is about 85, which is just a 15% drop.

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Re: In a certain population, the two most heavily diagnosed dise   [#permalink] 27 Apr 2013, 20:33
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