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21 Jan 2021, 10:15
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
61% (02:28) correct
39%
(02:48)
wrong
based on 174
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The normal dosage of a particular medicine is t tablets per day for each patient. A hospital’s current supply of these tablets will last p patients for d days. If the recommended dosage increases by 20% and the number of patients decreases by one-third, then for how many days will the hospital’s supply last ?
(A) 5d/4
(B) 4d/5
(C) 4pt/5
(D) 4t/5
(E) 4dt/5
(A) 5d/4
(B) 4d/5
(C) 4pt/5
(D) 4t/5
(E) 4dt/5
21 Jan 2021, 10:34
Kudos
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Bunuel
Lets assume numbers for the variables. t = 5, p = 30, d = 2
So, if 30 patients consume 5 tablets per day for 2 days -> the hospital must have 300 tablets.
Now,
the number of patients decreases by one-third(making patients p = 20)
recommended dosage increase by 20%, making daily consumption t = 6
The hospital stock of 300 tablets will last \(\frac{300}{20*6}\) = \(\frac{5}{2}\) days
By substituting values in answer options we can find the solution
(A) \(\frac{5d}{4} = \frac{5*2}{4} = \frac{5}{2}\) (We have a match) (Option A)
PS This is a slightly longer process but it is easier if you are confused with the variables
24 Jan 2021, 06:56
Kudos
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Bunuel
Solution:
The number of tablets currently in the hospital is t x p x d = tpd. If the dosage is increased by 20%, then the new dosage is 1.2t tablets per day for each patient. If the number of patients is decreased by 1/3, then the new number of patients is 2p/3. Therefore, under the new conditions, the current number of tablets can last:
tdp / (1.2t x 2p/3) = d / (6/5 x 2/3) = d / (4/5) = 5d/4 days.
Answer: A
