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
_________________
5-star rated online GMAT quant
self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.