If N=K/(T+x/y), where T

Hi All,

We're given 3 equations to work with (which I'm going to write in increasing order of complexity):
X = 5 - T
T = K/5
N = K/(T + (X/Y))

We're asked for the value of Y in terms of N and T. Most questions that use the phrase "in terms of" are meant to be solved with Algebra. This one can also be solved by TESTing VALUES - and there's a great shortcut in how the answers are written, so if you choose easy numbers to work with, then you can save a lot of time when working through the answers).

IF..... T = 4, then X = 1 and K = 20

When we place those values into the 3rd equation (above), we end up with....
N = 20/(4 + (1/Y))

We want to make the value of Y as simple as possible (since that's what we're solving for), so let's TEST Y = 1... which means that N = 4. At this point we have the values of 5 variables....

T = 4
X = 1
K = 20
Y = 1
N = 4

This certainly looks like a lot of data to keep track of, but it's actually really straight-forward. The answers ask us to deal with just 2 of the variables (N and T). Here, BOTH of those values are equal to 4. We're asked to find the value of Y, which we chose as 1. In simple terms, any time you see a variable in an answer, you should plug-in a "4"... and we're looking for a result that equals 1. There's only one answer that matches....

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorDC wrote:If \(N = \frac{K}{T + \frac{x}{y}}\), where \(T = \frac{K}{5}\) and \(x = 5 - T\), which of the following expresses y in terms of N and T ?

A. \(\frac{N(5 - T)}{T(5 - N)}\)

B. \(\frac{N(T - 5)}{T(5 - N)}\)

C. \(\frac{5 - T}{T(5 - N)}\)

D. \(\frac{5N(5 - T)}{T(1 - 5N)}\)

E. \(\frac{N(5 - T)}{5}\)


OA A

Source: Official Guide

We see that K = 5T. Now, let's isolate y in the given equation:

N = K/(T + x/y)

N(T + x/y) = K

NT + Nx/y = K

Nx/y = K - NT

y = Nx/(K - NT)

Now we can substitute x with (5 - T) and K with 5T:

y = N(5 - T)/(5T - NT)

y = N(5 - T)/[T(5 - N)]

Answer: A