In a phase III clinical trial of Dosaxin, a new drug, patients receive

Question

In a phase III clinical trial of Dosaxin, a new drug, patients received a progressively growing dosage of Dosaxin for a few days. On the first day, each patient received 15 milligrams of Dosaxin. On each of the following days, the daily dosage was m milligrams greater than the dosage received the day before, reaching a dosage of 43 milligram on the last day of the trial. For how many days did the trial last, if each patient received a total amount of 145 milligrams of Dosaxin during the whole trial ?

A. 4
B. 5
C. 6
D. 7
E. 9

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A. 4
B. 5
C. 6
D. 7
E. 9

700-Level question!!!

This is a  PS Butler Question

Check the links to other Butler Projects: 
 
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$!vakumar.m · Answer

First day of trial = 15 mg dosage
2nd day = 15 + m mg dosage 
and so on till the last day(say n+1 days) = 15 + nm = 43 mg (given)
on solving above, mn = 28

Now the total dosage received by each patient by the end of whole trial is 145 mg
15 + 15 + m + 15 + 2m ..... + 15 + nm = 145
15(n+1) + m (1+2+3..+n) = 145
15(n+1) + mn(n+1)/2 =145
substituting mn = 28 and solving we get
m = 7 and n = 4
therefore the trial lasted 5 days 
Answer B

Regor60 · Answer

No need to go very far to solve this.

Each day following the first the dosage increases by m until the last day the dose is 43.

So the dosage on the last day is:

15 + (n-1)m = 43

So, m(n-1) = 28. We know n must be an integer so m must also be an integer.

So, the pairs of numbers satisfying the above, m and n, respectively could be:

1 29
2 15
4 8
7 5
14 3
28 2

Only 5 above appears among the answer choices

Posted from my mobile device

PoeticArtillery · Answer

First dose, a = 15.
15, 15+m, 15+2m,15+3m ...... (15+nm = 43)
difference of dosage between any two days = m
Since each dosage everyday remains the same. The pattern of the trial are in arithmetic progression.

Sum of all dosages = 145
Sum of arithmetic progression = n/2 (first day + last day)
n/2(15+43) = 145
58n = 290
n = 5. Tada!!

AP is a nice and simple yet handy tool. However, this problem can be solved purely using logic.

muhammaddk92 · Answer

We can use number properties here.

As difference is always a constant m we can use the fact that Sum for a evenly spaced set is   / 2.

We know the Last value, first value and sum and need to find N. N = 5.

bumpbot · Answer

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In a phase III clinical trial of Dosaxin, a new drug, patients receive

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