If \(\dfrac{2}{x}+\dfrac{3}{y}=4\) and \(xy=5,\) then \(3x+2y=\)

VJesus12 wrote: ↑

Mon May 11, 2020 6:17 am

If \(\dfrac{2}{x}+\dfrac{3}{y}=4\) and \(xy=5,\) then \(3x+2y=\)

(A) \(\dfrac{1}{5}\)

(B) \(\dfrac{1}{4}\)

(C) \(\dfrac{4}{5}\)

(D) \(4\)

(E) \(20\)

[spoiler]OA=E[/spoiler]

Source: GMAT Paper Tests

Given: 2/x + 3/y = 4
To eliminate the fractions, multiply both sides of the equation by xy to get: 2xy/x + 3xy/y = 4xy
Simplify to get: 2y + 3x = 4xy
IMPORTANT: Notice that the left side of the equation (2y + 3x) is the exact value we're trying to evaluate.

Since we're told that xy = 5, we can take: 2y + 3x = 4xy
And replace xy with 5 to get: 2y + 3x = 4(5)
Simplify: 2y + 3x = 20
In other words: 3x + 2y = 20

Answer: E

Cheers,
Brent

VJesus12 wrote: ↑

Mon May 11, 2020 6:17 am

If \(\dfrac{2}{x}+\dfrac{3}{y}=4\) and \(xy=5,\) then \(3x+2y=\)

(A) \(\dfrac{1}{5}\)

(B) \(\dfrac{1}{4}\)

(C) \(\dfrac{4}{5}\)

(D) \(4\)

(E) \(20\)

[spoiler]OA=E[/spoiler]

Simplifying the first equation, we have:

(2y + 3x) / (xy) = 4

Since xy = 5, we have:

(2y + 3x)/5 = 4

2y + 3x = 20

Answer: E