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An epidemic is reported to have broken out in Florida

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vomhorizon
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An epidemic is reported to have broken out in Florida [#permalink] New post   Updated on: 21 Nov 2012, 08:24
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An epidemic is reported to have broken out in Florida. The number of detected instances of a certain disease is reported to have increased by 85% in the last year. What is the lowest number of newly detected instances possible?

(A) 1

(B) 5

(C) 11

(D) 15

(E) 17

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We need to find the MINIMUM possible no. of instances that a disease has been detected (at the present) if it the no. has increased by 85% from the last year (the no. of detected instances of the disease) ..
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E

Originally posted by vomhorizon on 21 Nov 2012, 07:21.
Last edited by vomhorizon on 21 Nov 2012, 08:24, edited 1 time in total.
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Re: An epidemic is reported to have broken out in Florida [#permalink] New post   21 Nov 2012, 10:58
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vomhorizon wrote:
An epidemic is reported to have broken out in Florida. The number of detected instances of a certain disease is reported to have increased by 85% in the last year. What is the lowest number of newly detected instances possible?

(A) 1

(B) 5

(C) 11

(D) 15

(E) 17


Last year, there were n instances of the disease.
This year, the instances have increased by 85% i.e. this year, there are (n + 85% of n) instances of the disease.
The number of newly detected instances = 85% of n

Now the question is: What is the lowest number of newly detected instances possible?
This means we need to find the minimum value of 85% of n.

What are the constraints because of which there must be a minimum value of 85% of n?
The number of cases detected last year and the number of newly detected cases must be an integer. You cannot detect half a case, right?

Can (85/100 * n) be 1? No because in that case, n will not be an integer.
Can (85/100 * n) be 5? No because in that case, n will not be an integer.

Notice that 85 = 5*17.
So 85/100 = 17/20

(17/20 * n) = 17
n = 20 (an integer)

We will not get n as integer in any of the other options.
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Re: An epidemic is reported to have broken out in Florida [#permalink] New post   27 Apr 2016, 13:01
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The number should be a possible factor of 85 so choices C and D are out
out of other possible choices it says that number of patients detected increased 85 %
if we take 1 for plugging in then the number obtained before increase is not a integer same is the case with 5
so correct option - E
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Re: An epidemic is reported to have broken out in Florida [#permalink] New post   03 May 2018, 03:02
SOLUTION
Solution: E

The key to solving this abstract problem is by recognizing that the number of newly detected instances must be an integer; you can’t have a fractional instance of a disease. If you define x as the number of instances last year and n as the number of new instances, then you know that \(n=\frac{85}{100}\).
After simplifying the fraction, this becomes \(n=\frac{17}{20}\) The smallest integer value that is possible for \(x\) is \(20\) so the smallest possible value for \(n\) is \(17\). Correct answer is (E).
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Re: An epidemic is reported to have broken out in Florida [#permalink] New post   04 May 2018, 10:29
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vomhorizon wrote:
An epidemic is reported to have broken out in Florida. The number of detected instances of a certain disease is reported to have increased by 85% in the last year. What is the lowest number of newly detected instances possible?

(A) 1

(B) 5

(C) 11

(D) 15

(E) 17


The key to this problem is realizing that we must have whole number values for both the original number of detected diseases and this year’s new number of cases. If we let the original number of detected diseases = n, then the new number of cases is:

1.85n = 185/100 x n = 37/20 x n = 37n/20

Since the fraction has been reduced to lowest terms, we see that for 37n/20 to be a whole number, then n must be at least 20.

Since 20 x 1.85 = 37, the minimum number of newly detected cases is 37 - 20 = 17 cases.

Answer: E
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Re: An epidemic is reported to have broken out in Florida [#permalink] New post   05 May 2022, 07:35
Can anyone give a descriptive and simple explanation to this question #less jargon
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An epidemic is reported to have broken out in Florida [#permalink] New post   12 May 2022, 22:48
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dipanjandas792 wrote:
Can anyone give a descriptive and simple explanation to this question #less jargon


An epidemic is reported to have broken out in Florida. The number of detected instances of a certain disease is reported to have increased by 85% in the last year. What is the lowest number of newly detected instances possible?

Assume initial deseases = x
increase in desease is 85% = x*185/100 = x*37/20

newly detected instances
= x*(37-20)/20
= x*(17/20)

Asked to find the lowest number of newly detected instances-
if x=20 then newly detected instances 17

if x is other than 20, we will either get decimal value or number of newly detected instances >17

so 17 -E is answer
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Re: An epidemic is reported to have broken out in Florida [#permalink] New post   04 Oct 2023, 11:37
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Re: An epidemic is reported to have broken out in Florida [#permalink]
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