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If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following

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If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following [#permalink] New post   21 Sep 2019, 05:11
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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. \(\frac{N(5 - T)}{5}\)


PS47302.01
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following [#permalink] New post   21 Sep 2019, 05:18
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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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Re: If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following [#permalink] New post   13 Dec 2019, 12:35
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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:
Show Spoiler
A


GMAT assassins aren't born, they're made,
Rich
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following [#permalink] New post   21 Sep 2019, 06:01
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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


gmatt1476 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. \(\frac{N(5 - T)}{5}\)


PS47302.01
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If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following [#permalink] New post   01 Nov 2019, 17:37
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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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Re: If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following [#permalink] New post   05 Nov 2019, 18:28
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gmatt1476 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. \(\frac{N(5 - T)}{5}\)


PS47302.01


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
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If N = K/(T + x/y), where T = K/5 and x = 5 T which of the following [#permalink] New post   16 Nov 2019, 07:09
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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.
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following [#permalink] New post   05 Dec 2020, 06:52
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gmatt1476 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. \(\frac{N(5 - T)}{5}\)

PS47302.01


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

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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Re: If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following [#permalink] New post   28 Jan 2021, 03:07
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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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Re: If N = K/(T + x/y), where T = K/5 and x = 5 T which of the following [#permalink] New post   07 Jun 2022, 12:38
Expert Reply
The secret of this question is to develop the algebra as much as you can before substitute the variables.
Develop the equation using x, y and k and only after having the y in the left side of the equation and x and k in the right side you use the two additional equations to disappear with x and k having only N and T in the right side and y in the left side. This type of question is very recurrent in the official material.
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 T which of the following [#permalink] New post   18 Nov 2022, 12:49
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gmatt1476 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. \(\frac{N(5 - T)}{5}\)


PS47302.01


n (t + x/y) = k
nt + nx/y = k
nx/y = k - nt
1/y = (k - nt)/nx
y = nx/(k - nt); k = 5t; x = 5-t
y = n(5-t)/(5t-nt)
y = n(5-t)/t(5-n)

Option A

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If N = K/(T + x/y), where T = K/5 and x = 5 T which of the following [#permalink] New post   05 May 2023, 22:46
gmatt1476 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. \(\frac{N(5 - T)}{5}\)


PS47302.01


Bunuel KarishmaB can you please share links to more questions like these? Looking for some more practice for these type of qs.Thank you!
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 T which of the following [#permalink] New post   06 May 2023, 00:13
Expert Reply
RenB wrote:
gmatt1476 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. \(\frac{N(5 - T)}{5}\)


PS47302.01


Bunuel KarishmaB can you please share links to more questions like these? Looking for some more practice for these type of qs.Thank you!


7. Algebra



For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 T which of the following [#permalink] New post   31 Jul 2023, 21:58
Step 5: Break out the TY on the RHS and the N on the LHS

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

Can you elaborate how this was done
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 T which of the following [#permalink] New post   14 Nov 2023, 03:45
EMPOWERgmatRichC wrote:
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:
Show Spoiler
A


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


Hi Rich,

This is a really powerful strategy on a question like this and a real time-saver. I am trying to think of scenarios where such a strategy can and cant be deployed and I wonder:
1. Here we are able to assume y = 1, only because we are supposed to solve in terms of y and there are no constraints on Y, right? In similar Q's, I guess we can "assume" the value of the variable that we are supposed to solve for?
2. Are there any specific situations, where this will not be a prudent strategy, leading to errors?

Thanks
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 T which of the following [#permalink] New post   14 Nov 2023, 11:26
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TargetMBA007 wrote:
EMPOWERgmatRichC wrote:
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:
Show Spoiler
A


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


Hi Rich,

This is a really powerful strategy on a question like this and a real time-saver. I am trying to think of scenarios where such a strategy can and cant be deployed and I wonder:
1. Here we are able to assume y = 1, only because we are supposed to solve in terms of y and there are no constraints on Y, right? In similar Q's, I guess we can "assume" the value of the variable that we are supposed to solve for?
2. Are there any specific situations, where this will not be a prudent strategy, leading to errors?

Thanks


Hi TargetMBA007,

Most GMAT questions are written so that they can be approached in more than one way - so as an appraoch, TESTing VALUES works on lots of different questions. Obviously, there are certain questions that are strictly about doing Algebra/Arithmetic in terms how they're set up (meaning that the unknowns aren't really "variables", they're locked-in values that we don't know yet - and have to solve for). For example, a standard 2-variable, 2-equation 'system' question only has one solution (even though it includes 2 'variables') - and we'll almost always have to do Algebraic work to find that solution. In those situations, you could potentially TEST VALUES to 'narrow down' to what the solution would be, but that would not be an efficient way to answer the question.

Much of this comes down to your training and memory (about prior questions that you have worked through). You'll start to recognize when certain approaches will be faster than others - but to maximize your performance, you have to hone a number of different skills (and not just rely on the same approach for every question).

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

Contact Rich at: Rich.C@empowergmat.com
www.empowergmat.com
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 T which of the following [#permalink] New post   14 Nov 2023, 17:51
EMPOWERgmatRichC wrote:
Hi TargetMBA007,

Most GMAT questions are written so that they can be approached in more than one way - so as an appraoch, TESTing VALUES works on lots of different questions. Obviously, there are certain questions that are strictly about doing Algebra/Arithmetic in terms how they're set up (meaning that the unknowns aren't really "variables", they're locked-in values that we don't know yet - and have to solve for). For example, a standard 2-variable, 2-equation 'system' question only has one solution (even though it includes 2 'variables') - and we'll almost always have to do Algebraic work to find that solution. In those situations, you could potentially TEST VALUES to 'narrow down' to what the solution would be, but that would not be an efficient way to answer the question.

Much of this comes down to your training and memory (about prior questions that you have worked through). You'll start to recognize when certain approaches will be faster than others - but to maximize your performance, you have to hone a number of different skills (and not just rely on the same approach for every question).

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

Contact Rich at: Rich.C@empowergmat.com
www.empowergmat.com

[/quote]

Thanks Rich, appreciate your inputs.
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 T which of the following [#permalink] New post   24 Dec 2023, 21:48
EMPOWERgmatRichC wrote:
TargetMBA007 wrote:
EMPOWERgmatRichC wrote:
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:
Show Spoiler
A


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


Hi Rich,

This is a really powerful strategy on a question like this and a real time-saver. I am trying to think of scenarios where such a strategy can and cant be deployed and I wonder:
1. Here we are able to assume y = 1, only because we are supposed to solve in terms of y and there are no constraints on Y, right? In similar Q's, I guess we can "assume" the value of the variable that we are supposed to solve for?
2. Are there any specific situations, where this will not be a prudent strategy, leading to errors?

Thanks


Hi TargetMBA007,

Most GMAT questions are written so that they can be approached in more than one way - so as an appraoch, TESTing VALUES works on lots of different questions. Obviously, there are certain questions that are strictly about doing Algebra/Arithmetic in terms how they're set up (meaning that the unknowns aren't really "variables", they're locked-in values that we don't know yet - and have to solve for). For example, a standard 2-variable, 2-equation 'system' question only has one solution (even though it includes 2 'variables') - and we'll almost always have to do Algebraic work to find that solution. In those situations, you could potentially TEST VALUES to 'narrow down' to what the solution would be, but that would not be an efficient way to answer the question.

Much of this comes down to your training and memory (about prior questions that you have worked through). You'll start to recognize when certain approaches will be faster than others - but to maximize your performance, you have to hone a number of different skills (and not just rely on the same approach for every question).

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

Contact Rich at: Rich.C@empowergmat.com
www.empowergmat.com


Hi Rich,

Just as a follow-up on this, when I pick T = 1, I get, K = 5, X = 4, Y = 1, and finally N = 1.
This gives me 2 correct answers when plugging in, i.e. A and C.
Wonder, what I might be doing wrong here?

EMPOWERgmatRichC
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 T which of the following [#permalink] New post   26 Dec 2023, 06:46
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Hi Rich,

Just as a follow-up on this, when I pick T = 1, I get, K = 5, X = 4, Y = 1, and finally N = 1.
This gives me 2 correct answers when plugging in, i.e. A and C.
Wonder, what I might be doing wrong here?

EMPOWERgmatRichC[/quote]

Hi TargetMBA007,

You didn't do anything "wrong" here - it's just that the numbers you chose narrowed the answers down to two choices: the correct answer and one of the wrong ones. At this point, could either 'guess' from among those two options (since one of them has to be the correct answer) or choose another set of numbers and 'test' again (keeping in mind that you would only have to check Answers A and C - since they are the only ones that are left).

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

Contact Rich at: Rich.C@empowergmat.com
www.empowergmat.com
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 T which of the following [#permalink] New post   26 Dec 2023, 19:15
EMPOWERgmatRichC wrote:
Hi Rich,

Just as a follow-up on this, when I pick T = 1, I get, K = 5, X = 4, Y = 1, and finally N = 1.
This gives me 2 correct answers when plugging in, i.e. A and C.
Wonder, what I might be doing wrong here?

EMPOWERgmatRichC


Hi TargetMBA007,

You didn't do anything "wrong" here - it's just that the numbers you chose narrowed the answers down to two choices: the correct answer and one of the wrong ones. At this point, could either 'guess' from among those two options (since one of them has to be the correct answer) or choose another set of numbers and 'test' again (keeping in mind that you would only have to check Answers A and C - since they are the only ones that are left).

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

Contact Rich at: Rich.C@empowergmat.com
www.empowergmat.com[/quote]

Thanks Rich, are there any clues in the stem, that enable us to pick numbers that would avoid a situation, where we end up with 2 potential answers? or any general best practices when picking numbers for such questions? I also wondered, if generally 1 is not a great choice in PS questions?
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 T which of the following [#permalink]
26 Dec 2023, 19:15
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