Substituting K and x from given

N = 5T / (T+(5-T)/Y)

T + (5-T) / Y = 5T / N

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

Y = (5-T) N / T(5-N)
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N=5TY/TY+5-T
NTY+5N-NT=5TY
Y(NT-5T)=NT-N5
Y=N(T-5)/T(N-5) = \(\frac{N(5 - T)}{T(5 - N)}\)
IMO A

Every Step Described:

Step 1: substitute k and x out.

K=5T
X=5-T

In the first equation, plug in the values above in place of x and y

N = 5T/T +\(\frac{(5-T)}{Y}\)

Step 2: Multiply both sides by T+\(\frac{(5-t)}{y}\) .

Now we have N(T+\(\frac{(5-t)}{y}\)) = 5T

Step 3: Multiply both sides by y in order to cancel our fractions.

Now we have NTY + 5(N-T) = 5TY

Step 4: Subtract both sides by NTY in order to get Y on a side by itself.

Now we have 5(N-T) = 5TY - NTY

Step 5: Break out the TY on the RHS and the N on the LHS

TY(5-N) = N(5-T)

Step 6: Divide both sides by T(5-N) in order to get Y on the LHS by itself.

Now we have Y = \(\frac{N(5-T)}{T(5-N)}\)

A
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K = 5T
x = 5 - T

N = 5T/(T + (5-T)/y) => N = 5ty/(Ty + 5 - T) => NTy + 5N - NT = 5Ty => y = N(5-T)/(T(5-N))

ANSWER = A

Isn't this the wrong answer
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N=K/(T+x/y)

N=Ky/ (Ty+x)

NTy + Nx = Ky

Nx = (NT-K)*y

(Nx)/ (NT-K) = y

Substitute K=5T and x= 5-T

A it is.


Kudo if helped
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Yes, I have corrected my explanation.

Thanks!
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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:

GMAT assassins aren't born, they're made,
Rich
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k=5T; x=5-T
N*(T+(x/y)) = k
N*(Ty+x) = ky
NTy+Nx = 5Ty
NTy-5Ty = -Nx
y(NT-5T) = -N(5-T)
y(NT-5T) = NT - 5N
y = (NT-5N)/(NT-5T)
y = N(T-5)/T(N-5)
y = -N(5-T)/-T(5-N)
y = N(5-T)/T(5-N)


[option a]

You saved me, man!!!
That's great thank you!

However I think you are wrong in the highlighted part, just a typo...

\(N = \frac{K}{T + \frac{x}{y}}\)

We are asked to express \(y\) in terms of \(N\) and \(T\). In other words we need to replace \(K\) and \(x\) with expressions in terms of \(N\) and/or \(T\)

1. Replacing \(K\) with \(5T\) and \(x\) with \(5 - T\) in the equation

2. \(N = \frac{5T}{T + \frac{5 - T}{y}} = \frac{5Ty}{Ty + 5 - T}\)

3. \(NTy + 5N - TN = 5Ty\)

4. \(NTy - 5Ty = TN - 5N\)

5. \(Ty(N - 5) = N(T - 5)\)

6. \(y = \frac{N(T - 5)}{T(N - 5)}\); this does not match any of the answer options, but if you observe closely then if you multiply the numerator and denominator with -1 then the equation matches option A

7. \(y = \frac{(-1) * N(T - 5)}{(-1) * T(N - 5)} = \frac{N(5 - T)}{T(5 - N)}\)

Ans. A
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Plugging in can be super useful and a faster way of solving some Algebra questions where too many variables are involved. Try plugging in K = 10 and y = 1 (keep in mind some rules like what you see in the denominator and the number should not be the same as what you see in the question or answer choices).

K = 10
T = 2
x = 3
y = 1
N = 2

Target answer: y = 1 (circle it)

Now, plug the value of the variables in the answer choices. Only option A will match.

Thus, the answer is A.

Hope this helps
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