Mo2men wrote:

himu wrote: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%.

Dear GMATGuru,
Could you please help with this question?

Thanks

M --> more than 50% of all disease cases over the past 5 years
S --> 40% of all disease cases 5 years ago, 30% of all disease cases now

For each answer choice:
Try to devise a case that aligns with the information in the passage but CONTRADICTS the answer choice, thus proving that the answer choice does NOT have to be true.

A: There were fewer cases of schistosomiasis last year than five years ago.
5 years ago:'
Total disease cases = 10
S = 40% of 10 = 4
Now:
Total disease cases = 100
S = 30% of 100 = 30
Since there are more S cases now than there were 5 years ago, A does not have to be true.
Eliminate A.

B: The percentage of disease cases from malaria has increased over the past 5 years.
5 years ago:
M = 55%
Now:
M = 51%
Thus, B does not have to be true.
Eliminate B.

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%.
5 years ago:'
Total disease cases = 100
S = 40% of 100 = 40
M = 58% of 100 = 58
Other = 2% of 100 = 2
Now:
Total disease cases = 80'
S = 30% of 80 = 24
M = 70% of 80 = 56
Other = 0
Here, no disease experiences an increase in the number of cases, illustrating that C does not have to be true.
Eliminate C.

D: Each year over the past five, malaria has accounted for a larger percentage of disease cases than schistosomiasis.
Annual percentages for M and S over the past 5 years:
M: 51%, 39%, 60%, 60%, 70%
S: 40%, 40%, 30%, 30%, 30%
The values in red illustrate that D does not have to be true.
Eliminate D.

The correct answer is E.

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%.
5 years ago:
Total disease cases = 100
S = 40% of 100 = 40
Now:
Total disease cases = 130
S = 30% of 130 = 39
Here, the total number of disease cases increases by exactly 30%, with the result that the total number of S cases DECREASES from 40 to 39.
Implication:
For the total number of S cases to INCREASE, the total number of disease cases must increase by MORE THAN 30%.
Thus, E must be true.