BrainLab wrote:
If p and q are two positive integers and p/q = 1.15, then p can equal which one of the following?
(A) 15
(B) 18
(C) 20
(D) 22
(E) 23
This problem will be best solved using the remainder formula. Let’s first state the remainder formula:
When positive integer x is divided by positive integer y, if integer Q is the quotient and r is the remainder, then x/y = Q + r/y.
We are given that p and q are two positive integers and p/q = 1.15. Thus:
p/q = 1 + 15/100, or Q + r/q = 1 + 15/100
Since 15/100 = 3/20, r/q = 3/20 or r/q = 3k/20k for some positive integer k. We can see that r is 3 or a multiple of 3.
If r = 3, then q = 20 and p = 23.
Since 23 is one of the answer choices, choice E is the correct answer.
Alternate Solution:
Let’s convert the decimal 1.15 to a mixed number and then to an improper fraction:
1.15 = 1 15/100 = 1 3/20 = 23/20
We know that p/q = 1.15, so p/q = 23/20. Thus, one possible value for p is 23.
Answer: E
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