sandy wrote:
\((n/4)+(r/8) = (s/8) + (t/6)\)
n, r, s, and t are positive integers.
Quantity A: 2n + r
Quantity B: 2s + t
Given:
(n/4)+(r/8) = (s/8) + (t/6) This equation has a lot of fractions. Let's first make things easier by eliminating the fractions.
The denominators are 4, 8, and 6.
The least common multiple of 4, 8 and 6 is 24, so let's multiply both both sides of the equation by 24 to get:
6n + 3r = 3s + 4tNOTICE that Quantity A (2n + r) is SIMILAR to
6n + 3r, Let's use this fact!
Take
6n + 3r = 3s + 4t and divide both sides by 3 to get:
2n + r = s + (4/3)tNow replace Quantity A with
s + (4/3)t to get:
Quantity A:
s + (4/3)tQuantity B: 2s + t
Now subtract s from both quantities AND subtract t from both quantities to get:
Quantity A: (1/3)t
Quantity B: s
At this point, it's impossible to tell which quantity is greater.
So, the answer is D
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep