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Intern  Joined: 02 Apr 2013
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Question Stats: 43% (02:30) correct 57% (02:22) wrong based on 1126 sessions

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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%.

Originally posted by manugmat123 on 24 Apr 2013, 09:01.
Last edited by hazelnut on 07 Oct 2017, 18:55, edited 1 time in total.
Edited the question.
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9

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.

Don't you love doing algebra in the verbal section? :/
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Re: In a certain population, the two most heavily diagnosed diseases are s  [#permalink]

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I think this one is harder than 600-700. Don't you?

thelosthippie 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.

Schistosomiasis, malaria: main diseases. Quote:
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.

Percentages are not equivalent to absolute number. Misleading.

Quote:
B. The percentage of disease cases from malaria has increased over the past 5 years.

Not really. The percentage given for malaria is the arithmetic average for the last 5 years. I.e. the percentages for each year could be manipulated greatly without changing the mean.

Quote:
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%.

Can be true, but doesn't have to. This 30% is really confusing here, but it's a red herring. Don't let it possess your mind.

Quote:
D. Each year over the past five, malaria has accounted for a larger percentage of disease cases than schistosomiasis.

False for the same reason as B.

Quote:
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%.

Percentage value decreased. If the total number increased concurrently, then the total number of diseases had to increase even more. Count the given 30% if you have time on the GMAT, it's not necessary after all. Correct.

Originally posted by HumptyDumpty on 03 May 2013, 04:01.
Last edited by HumptyDumpty on 01 Aug 2014, 06:27, edited 1 time in total.
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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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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 diseases are s  [#permalink]

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E is correct..

A. There were fewer cases of schistosomiasis last year than five years ago...% and no. (quantity) should not be compared..wrong

B. The percentage of disease cases from malaria has increased over the past 5 years....cant say..we only know that the avg. of past five years....wrong

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%. ...well..close one..but it says SOME DISEASE..but we want to know relation with all other disease cases..wrong..

D. Each year over the past five, malaria has accounted for a larger percentage of disease cases than schistosomiasis.,.cant say...same as B

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...if all other cases have increase then they have to increase by more than 30% because schistosomiasis cases have reduced form 40% to 30%..
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Re: In a certain population, the two most heavily diagnosed diseases are s  [#permalink]

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hey thelosthippie...you are posting really good questions..+1 to you

but if you could hold back OA for some time and allow people to discuss w/o knowing OA then it would be more helpful.. Manager  Status: suffer now and live forever as a champion!!!
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Re: In a certain population, the two most heavily diagnosed diseases are s  [#permalink]

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Assume that the total no of cases were initially 100.
Total =100

Malaria = 51

schistosomiasis = 40

other = 9.

schistosomiasis accounts for 40 %;

Let us try to analyze choice E by working from backwards.

Total no of diseases = 100;

An increase of 30 % in total = 130;

Assuming that Malaria and other diseases remian constant , then increase in number of schistosomiasis can be calculated as follows

M =41 O =9 S = 70 ;

70/130 = 53% (more than 30%)
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Re: In a certain population, the two most heavily diagnosed diseases are s  [#permalink]

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manugmat123 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%.

As soon as we see %, there will be some catch with total number of cases.
A) There were fewer cases of schistosomiasis last year than five years ago - Cannot be inferred
B) The percentage of disease cases from malaria has increased over the past 5 years - Cannot be inferred
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%.
This is not possible as "S" % wise went down, so if the total number of cases of "S" went up, the total number of all cases has to go up and not down

D) Each year over the past five, malaria has accounted for a larger percentage of disease cases than schistosomiasis We don't have each year data, cannot be infered
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%.
Looks ok.
Calculation wise.
5 years back for "S" disease
100 Total cases - "S" disease - 40 - Percentage = 40%
if we have to maintain the same cases
Percentage = 30%
"S" disease cases = 40
Then total should be close to 130 as 13*3 = 39
Hence Option E)
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Re: In a certain population, the two most heavily diagnosed diseases are s  [#permalink]

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manugmat123 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%.

E basically says-(if..hypothetical.....)

If 40% x < 30 % y , (where x = total cases 5 years ago and y= total cases in past year)

then ( y-x )/x > 1/3 ( after solving the inequality stated )

hence , increase IN TOTAL number of cases has been more than 33.3 % ( 33.33% is more than 30 %)

The above can be true based on the argument.

Hope the simple inequality helps state why E is right.

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Quote:
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%.

Let X= total number of diseases before 5 years: A=Number of malaria victims before 5 years=40/100 X

Y=total number of diseases now : B=Number of malaria victims now=30/100 Y

Assume worst case A=B that is 40/100*X=30/100*Y
Then Y= 40/30*X= 1*1/3*X
which means that Y is 133.33 % of X.Which means present population is more than 30% of population 5 years ago.
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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.

Notice the pattern of data given. Data regarding malaria is given over a time whereas data at two times is given for Schisto.....

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........Percentage reduction from 40% to 30% cannot infer the number of cases. We need population data as well.

B) The percentage of disease cases from malaria has increased over the past 5 years.......were given overall data for past 5yrs i.e., more than 50% but no info is given regarding change either increase or decrease.

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%.............This choice seems really vague. Keep it aside.

D) Each year over the past five, malaria has accounted for a larger percentage of disease cases than schistosomiasis........In case of malaria we have overall data for 5 years so we cannot say this.

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%............Left over choice and makes a bit sense more than C or nay other choices. This picked out of POE. Pick numbers as
total disease population say TDP 5yrs back is 100
Schi cases are 40
last yr Schi cases are increased to say >40 = 42(since 41 is not mutiple of 3)
42=30%TDP
last yr TDP= 140

difference in TDP is from 100 to 140 is 40% (which is more than 30%)
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ravikrishna1979 wrote:

No where average term is used in argument.
Many said that Each in the (D) is wrong, but when argument clearly says malaria has accounted for more than 50% in the past 5 years
Need clear reason why D is wrong or better than E.

ravikrishna1979

For example salary package of prev 5 yrs in an mnc is as follows
yr1: 3LPA
yr2: 4LPA(increment)
yr3: 3LPA(salary reduced due to lower band..............it happens trust me)
yr4 and 5: Resigned and unemployed for 2 yrs

Overall salary is 2LPA

But can we say each year your salary was more than some X's say 10K.
No right yr4 and 5 you did not have a salary and cannot have more salary than 10K.

Now option D SAYS

Quote:
Each year over the past five, malaria has accounted for a larger percentage of disease cases than schistosomiasis.

Isnt the scenario same? So D is incorrect for same reason.

I hope this helps Intern  B
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Hello,

I can't understand how B is wrong, as the percentage cases of malaria was 60 % 5 years ago and 5 years later it was 70 % as per the premise. That means the percentage cases of malaria has increased.

Also what does statement C actually mean? it doesn't make a lot of sense to me.
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anuj11 wrote:
Hello,

I can't understand how B is wrong, as the percentage cases of malaria was 60 % 5 years ago and 5 years later it was 70 % as per the premise. That means the percentage cases of malaria has increased.

Also what does statement C actually mean? it doesn't make a lot of sense to me.

Hi anuj11 ,

Here are the explanations for B and C:

B) The percentage of disease cases from malaria has increased over the past 5 years.

We are given "Over the past five years, malaria has accounted for more than half of all disease cases". It doesn't mean every year it has increased. I can also every year it was 51%. Now, you can see I can translate this as over the past 5 years, it is more than 50%. Right? So, B is straight out.

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%.

Notice that we are given every detail is %. So, you should never select any option that talks about the actual number.

Let us suppose there are 100 cases out of which 50 are of disease A. Or 50% of A.

Now, If I say next year the cases increased by 60%, that doesn't mean it is 60 or more now.

It may happen that the total cases have reduced to 60 and now A is 60% of these 60 = 36. Hence, a decrease in actual number.

This is the reason I was saying don't treat % questions with actual numbers.

I hope that makes sense. _________________
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Re: In a certain population, the two most heavily diagnosed diseases are s  [#permalink]

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manugmat123 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%.

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Okay, let's break this baby down. First of all, this is a classic "Inference" question, based on the flow of the question stem. It asks for a fact that "must be true" on the basis of the facts the stimulus. "Must be true" has a very high burden of proof. We can use this as leverage to eliminate answer choices. Any answer choice that could possibly be false can be quickly eliminated. We know from the problem that 5 years ago the cases of schistosomiasis were $$40\%$$ of the total. Thus, $$S_\text{(5 yrs ago)}= (\frac{2}{5})T_\text{(5 yrs ago)}$$. We also know that last year the number of schistosomiasis cases were $$30\%$$ of the last year's total. Thus, $$S_\text{(Last)}= (\frac{3}{10})T_\text{(Last)}$$.

Let's take a look at each answer choice in turn:

(A) There were fewer cases of schistosomiasis last year than five years ago.
Wrong. This is a classic trap that I like to call in my classes a "Statistical Stretch." The text of the problem only gives us percentage information, not numerical values. While the percentage of the schistosomiasis cases dropped over the 5 year period, we don't know what happened to the total number of cases. If the total number of cases drastically increased, it is possible for the number of cases to go up, even if the percentage drops. (For example, $$40\%$$ of $$100$$ is $$40$$, while $$30\%$$ of $$200$$ is $$60$$.) Get rid of "A".

(B) The percentage of disease cases from malaria has increased over the past 5 years.
Wrong. Once again, we can destroy this answer choice because of the "must be true" requirement. We only know that malaria accounted for more than half of all disease cases over the past 5 years, but we don't know how this percentage may have changed over time. It could have easily gone from $$60\%$$ to $$50\%$$, with the average still being above $$50\%$$. The percentage didn't have to increase over time. Answer choice "B" can be swiftly eliminated.

(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. This also fails the "must be true" requirement. The easiest way to show this is to focus on the boundary established in this question. (In other words, we could check if it is possible to have NO increases in disease cases, even if the total number of disease cases went down by $$30\%$$.) We just need one counter-example that shows "C" doesn't have to be true. Since the problem never gives us any numbers besides percentages, we can invent our own numbers. I call this strategy "Easy Numbers" in my classes.

So, let's assume that the original number of cases was $$100$$. $$50$$ of those could be malaria cases, and $$40$$ of them could be schistosomiasis. That leaves $$10$$ for another possible disease (let's say "toe fungus.") If five years later the number of cases went down by $$30\%$$, then we would only have $$70$$ total cases. Schistosomiasis would have $$30\%$$ of the $$70$$ (or $$0.3*70 = 21$$ cases. Malaria could still take $$49$$ of those cases. But this would leave $$0$$ cases of our mysterious toe fungus. Since since this situation disproves that the cases of some disease MUST increase, then answer choice "C" fails the "must be true" test. Eliminate it.

(By the way, if you are thinking, "But wait, you only had 50 malaria cases in that example! The problem says that malaria accounted for more than half of all disease cases!", you likely made a couple of assumptions that created poor logic. First of all, the phrase "half of all disease cases" is an aggregate across all five years. There might be some years where the number of cases exceeds $$50\%$$ and some that might be lower than $$50\%$$, as long as the total across all the years is sufficiently high. You might have also missed the fact that, in our hypothetical example, the total number of malaria cases dropped, but the percentage of malaria cases rose precipitously -- $$49$$ of $$70$$ total cases would actually be a whopping $$70\%$$ of the total that year.)

(D) Each year over the past five, malaria has accounted for a larger percentage of disease cases than schistosomiasis.
Wrong. Once again, this can be destroyed with a single-counterexample that proves it doesn't have to always be true. As mentioned in the above analysis, while the question stem states that "Over the past five years, malaria has accounted for more than half of all disease cases," this doesn't mean that malaria must exceed $$50\%$$ each year. There might be some years where the number of cases exceeds $$50\%$$ and some that might be lower than $$50\%$$, as long as the total across all the years is sufficient high. It is possible that in the third year there was a spike of schistosomiasis cases, coinciding with a temporary drop in malaria cases. The phrase "each year" in this problem CANNOT be justified. Get rid of "D".

(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 -- but some people fall for the trap here. This answer contains a "Hypothetical" (the phrase "If the total number of schistosomiasis cases increased over the past five years...") With inference questions, you can normally eliminate answers that clearly contain new information not mentioned in the conclusion. After all, you logically can't conclude something that you haven't already talked about! In my classes, I call this strategy the "No-New-Information Filter." It can be a powerful analysis tool for Inference questions. However, Hypotheticals trick test-takers into thinking that an answer choices contains information that goes beyond the facts in the problem. But hypotheticals aren't facts. They are just possibilities. In essence answer choice E states, "Given what we know, if we also knew that the total number of schistosomiasis cases increased over the past five years, then we could conclude..." It requires a little bit of math to show this. The hypothetical in this answer choice tells us that, for purposes of analysis, we can assume that $$S_\text{(Last)}>S_\text{(5 yrs ago)}$$. Plugging in the first two equations into the hypothetical gives us:

$$S_\text{(Last)}>S_\text{(5 yrs ago)}$$
$$(\frac{3}{10})T_\text{(Last)}>(\frac{2}{5})T_\text{(5 yrs ago)}$$
$$T_\text{(Last)}>(\frac{10}{3})(\frac{2}{5})T_\text{(5 yrs ago)}>(\frac{4}{3})T_\text{(5 yrs ago)}$$

Thus, the total amount of disease cases increased by more than $$\frac{1}{3}$$, or about $$33\%$$. This is more than the minimum $$30\%$$ required by answer choice E. Thus, it must always be true. E is the right answer.

Now, let’s look back at this problem from the perspective of strategy. For those of you studying for the GMAT, it is far more useful to identify patterns in questions than to memorize the solutions of individual problems. This problem can teach us several solid patterns seen throughout the GMAT. First and foremost, use the wording of the problem as leverage to attack the problem. Extreme statements such as "must be true" are easy pickings. We can eliminate any answer that could possibly be false. Second, when a problem gives you percentages or ratios without totals, inventing your own "Easy Numbers" can turn abstract ideas into concrete possibilities. Lastly, the GMAT loves to conceal the right answers by hiding them behind constructions that we might not be expecting (such as the "Hypotheticals" in this question.) Don't fall for the traps. Focus on exactly what the problem is asking. And that is how you think like the GMAT.
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Originally posted by AaronPond on 08 Mar 2019, 14:43.
Last edited by AaronPond on 09 Mar 2019, 14:25, edited 2 times in total.
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Re: In a certain population, the two most heavily diagnosed diseases are s  [#permalink]

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My only gripe with this question is that the answer is a hypothetical. I've never seen hypotheticals as answers to CR Inference questions. If anyone has official questions they can argue against me with then please link me.

Here are the official explanations
For this “inference” question, the correct answer must be true based upon the data given in the stimulus. You learn in the stimulus that over the past five years malaria accounted for more than half of all disease cases. IMPORTANTLY, this does not mean that malaria accounted for more than half of all cases each year. You also learn that 5 years ago, schistosomiasis accounted for 40% of all cases but only accounted for 30% over the past year. IMPORTANTLY, you have no idea what percentage schistosomiasis accounted for during the intervening years.

(A) is not necessarily true because you do not know whether the total pie increased. If the pie increased dramatically, then 30% of the bigger number could be larger than 40% of the smaller number.

For (B), no evidence is given about what happened to the percentage data for malaria over the 5 years. All you know is that, in total, malaria accounted for over 50% in that 5 year period.

(C) is likely false, and certainly not guaranteed. If the total number of disease cases went UP, then you would be sure of this. But if the total pie went down by 30%, then all diseases could have experienced a decrease.

For (D), you do not know what the percentages were for each of the intervening years, so you cannot be sure of the statement.

(E) must be true. If the total number of schistosomiasis cases increased, then you know that 30% of last years total disease cases must be greater than 40% of the total disease cases 5 years ago. This guarantees a ratio of 4:3 for this year's disease total to the total 5 years ago, assuring a 33.3% increase. Answer is (E).

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Here's how I went from 430 to 710, and how you can do it yourself: Re: In a certain population, the two most heavily diagnosed diseases are s   [#permalink] 11 Aug 2019, 16:01

# In a certain population, the two most heavily diagnosed diseases are s  