Problem Solving

Stockmoose,

You don't replace one variable with anything when you are doing the calculations from the answer choices. All you're doing is plugging in numbers.

When you are doing your first calculation is when you consider "replacing." The fact is, for this question at least, there is no replacing. What you're doing is if you said Z = 100 and X = 25 and Y = 20 is your saying 25% of 100 which .25(100) or (25/100)(100) which both equal 25. But it is 25 +100 because "it was marked up." Then you will take 20 percent of 125 which is .20(125) or 20/100 or 1/5(125) = 25 then you subtract 25 from 125 because they say it was discounted so the final answer is 100. You only use these percentage for your calculation.

When you are plugging in you don't use percentages for the calculation; you only use the numbers you chose for the variables. So for A you would put 10k(100) - [100(100)(25 -20)] - [100(25)(20)] all divided by 10k. Try it that way and see which answer yields the correct result.

If anyone can help me with this one too, I'd be appreciative.

A certain movie star's salary for each film she makes consists of a fixed amount, along with a percentage of the gross revenue the film generates. In her last two roles, the star made $32 million on a film that grossed $100 million, and $24 million on a film that grossed $60 million. If the star wants to make at least $40 million on her next film, what is the minimum amount of gross revenue the film must generate?

Okay, I set up the equation like this: [$32M = f + (p/100)($100M)] - [$24M = f + (p/100)($60M)

My answer was wrong. Turns out I don't need to put in the p/100 and only need to put the p and then solve for p. So question: When do you put the variable over 100 cause I've seen instances where you do?

Well if you used 25/100 and then put that over 100, it would actually be 25/10000 which would be equal to 0.0025. 0.0025 would be 0.25 percent and not 25 percent.

The reason you would know to put 25/100 is due to the definition of percent, or per cent = per one hundred (cent such as in century = 100 years).

So when you have 25 percent, it means 25 per one hundred, or 25/100.

25/100 can be reduced to 1/4, so when you are multiplying by another number like 200, you are taking 1/4 of 200 which is 200/4 which results in 50.

So 50 out of 200 is 25 percent of 200.

That's why you always put the number for the percent over 100 in the original equations because that's how it's defined.

As for VIC and plugging in the numbers (thanks for answering that question, by the way!), you would only plug in 25 because it's already in percent format. You're just telling it you want 25 percent instead of 43 percent, or some other percent value.

For example you can be given the equation:

(x/100)(200) = 50

If you solve for x, you would get 25, so 25/100 is x percent, but the 25 by itself is just the value for the x, the numerator, and so 25 is what you would want to plug in to get 50.

bekkilyn wrote:Well if you used 25/100 and then put that over 100, it would actually be 25/10000 which would be equal to 0.0025. 0.0025 would be 0.25 percent and not 25 percent.

The reason you would know to put 25/100 is due to the definition of percent, or per cent = per one hundred (cent such as in century = 100 years).

So when you have 25 percent, it means 25 per one hundred, or 25/100.

25/100 can be reduced to 1/4, so when you are multiplying by another number like 200, you are taking 1/4 of 200 which is 200/4 which results in 50.

So 50 out of 200 is 25 percent of 200.

That's why you always put the number for the percent over 100 in the original equations because that's how it's defined.

As for VIC and plugging in the numbers (that's for answering that question, by the way!), you would only plug in 25 because it's already in percent format. You're just telling it you want 25 percent instead of 43 percent, or some other percent value.

For example you can be given the equation:

(x/100)(200) = 50

If you solve for x, you would get 25, so 25/100 is x percent, but the 25 by itself is just the value for the x, the numerator, and so 25 is what you would want to plug in to get 50.

Trying to deduce some wisdom from your answer to Stockmoose for my question, I'm guessing that if you are given the total then you should assume that you don't have to put the variable over 100 for percents because it is already in percentage form.

After all if the equation is correct then it must have already consider the percentage form. If however, you are not given the total (or the other side of the equation) then you have to put it over 100 because you must consider percents to get the final answer. Do you agree with that assessment?

It depends on what the question is asking. Stockmoose's question is asking for the final price of an item and not for the actual percent value, so his answer choices are already in percent form, and he's just plugging in for the numerator, x.

So by using this formula for percents:

(Final Price) = (Percent)(Total Price)

(Percent) would already be represented by (x/100) in the equation and he's just putting 25 in for x and then 25/100 is multiplied by (Total Price).

In your problem, it's asking for the minimum gross revenue for the third film, so it's asking for (Fixed Amount + Percent).

(Fixed + Percent) = 40 million/Total Revenue (for 3rd film)

where Percent = x/100


I'm not sure exactly how to solve the equation because I got stuck trying to determine the fixed amount in order to separate it from the percent amount.

It is asking for a different type of result for Stockmoose's question though, so in your case depending on the answers you are given, you may need to consider the 1/100 for the percent value.

I actually think you helped me inadvertently. I think I'm going to stick with that rule. I will ask one more person before I do but I think that what I said is correct.

The fixed amount is found by subtracting the two equations and solving for the percent or p. Once you get the percent you can plug it back into one of the equations and solve for the fixed amount. My problem was that I put the variable for percent over 100. If you don't do that you should be able to find the fixed amount.

Stockmoose and I had a similar confusion. I used to think I was plugging in the percentage form of the numbers I chose, but in fact you only plug in the numbers you choose. The percent form is only necessary for for arriving at an answer that you will then compare and match with the answer that you get from the answer choices. But again, you will not add the percent of the numbers when doing the answer choices or you will get the wrong answer.

Just spoke to someone about my question and the general rule is as such:

If you include /100 when considering the equation then you will get a number that is a percentage and therefore must be divided by 100. The reason is because if you include /100 you've taken into account the fact that then number - p - whatever it is, is a percentage. Therefore you are only solving for p and not p over 100.

However, if you don't include /100 and just leave p then you will get a decimal. That is because the number you are then solving for is implicitly divided by 100 so if you don't include 100 you'll just get the number that includes it.... If that makes any sense. It makes since to me but if you need a rule it is simply - if you include /100 then you must divide final answer for p by 100, if you don't then you don't have to divide final answer by 100 as it is a decimal. That is of course if you will be using p in another part of an equation. If the question asked what is P and has a list of percents then you need not include /100 because the final answer is in percent form.

This does not relate to your question Moosestock.

mpaudena wrote:Just spoke to someone about my question and the general rule is as such:

If you include /100 when considering the equation then you will get a number that is a percentage and therefore must be divided by 100. The reason is because if you include /100 you've taken into account the fact that then number - p - whatever it is, is a percentage. Therefore you are only solving for p and not p over 100.

However, if you don't include /100 and just leave p then you will get a decimal. That is because the number you are then solving for is implicitly divided by 100 so if you don't include 100 you'll just get the number that includes it.... If that makes any sense. It makes since to me but if you need a rule it is simply - if you include /100 then you must divide final answer for p by 100, if you don't then you don't have to divide final answer by 100 as it is a decimal. That is of course if you will be using p in another part of an equation. If the question asked what is P and has a list of percents then you need not include /100 because the final answer is in percent form.

This does not relate to your question Moosestock.

Wow, I've just read all the posts in this string, and now I'm even more confused. I still don't understand how you know, with certainty, that the VIC question I posted toward the beginning of this thread already includes a percent built into it. And I don't get how you'd know whether to plug in the value (i.e. 25) vs x/100 (25/100). Can someone just simplify this for me?

bekkilyn wrote:It depends on what the question is asking. Stockmoose's question is asking for the final price of an item and not for the actual percent value, so his answer choices are already in percent form, and he's just plugging in for the numerator, x.


***I still am not clear on how you came to the conclusion that the VIC formula definitively includes a percent within it. So what if it simplifies to X/100? That doesn't mean it's a percent, because X could be 1/4, in which case, x/100 would be 4 not 25. Yet, to get the answer correct, you would've had to know, with certainty to use the value of the percent (25). This makes no sense!

So by using this formula for percents:

(Final Price) = (Percent)(Total Price)

(Percent) would already be represented by (x/100) in the equation and he's just putting 25 in for x and then 25/100 is multiplied by (Total Price).

In your problem, it's asking for the minimum gross revenue for the third film, so it's asking for (Fixed Amount + Percent).

(Fixed + Percent) = 40 million/Total Revenue (for 3rd film)

where Percent = x/100


I'm not sure exactly how to solve the equation because I got stuck trying to determine the fixed amount in order to separate it from the percent amount.

It is asking for a different type of result for Stockmoose's question though, so in your case depending on the answers you are given, you may need to consider the 1/100 for the percent value.

Read my bolded statement above, in response to your answer.

Stockmoose16 wrote:

mpaudena wrote:Just spoke to someone about my question and the general rule is as such:

If you include /100 when considering the equation then you will get a number that is a percentage and therefore must be divided by 100. The reason is because if you include /100 you've taken into account the fact that then number - p - whatever it is, is a percentage. Therefore you are only solving for p and not p over 100.

However, if you don't include /100 and just leave p then you will get a decimal. That is because the number you are then solving for is implicitly divided by 100 so if you don't include 100 you'll just get the number that includes it.... If that makes any sense. It makes since to me but if you need a rule it is simply - if you include /100 then you must divide final answer for p by 100, if you don't then you don't have to divide final answer by 100 as it is a decimal. That is of course if you will be using p in another part of an equation. If the question asked what is P and has a list of percents then you need not include /100 because the final answer is in percent form.

This does not relate to your question Moosestock.

Wow, I've just read all the posts in this string, and now I'm even more confused. I still don't understand how you know, with certainty, that the VIC question I posted toward the beginning of this thread already includes a percent built into it. And I don't get how you'd know whether to plug in the value (i.e. 25) vs x/100 (25/100). Can someone just simplify this for me?

Disregard my last post. Instead read the one that I posted at 5:49 pm and see if that works. The simple answer is for VIC never put it in the percentage form when you are calculating the answer choices. That is only use the numbers (e.g., 25) and not (25/100 or .25) when you are calculating the answer choices.

Only use 25/100 or .25 when you are calculating the question asked.

Disregard my last post. Instead read the one that I posted at 5:49 pm and see if that works. The simple answer is for VIC never put it in the percentage form when you are calculating the answer choices. That is only use the numbers (e.g., 25) and not (25/100 or .25) when you are calculating the answer choices.

Only use 25/100 or .25 when you are calculating the question asked.[/quote]

The following question is a VIC, and you need to use X/100 to get the correct answer:

90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x?

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500

Stockmoose16 wrote:Disregard my last post. Instead read the one that I posted at 5:49 pm and see if that works. The simple answer is for VIC never put it in the percentage form when you are calculating the answer choices. That is only use the numbers (e.g., 25) and not (25/100 or .25) when you are calculating the answer choices.

Only use 25/100 or .25 when you are calculating the question asked.

The following question is a VIC, and you need to use X/100 to get the correct answer:

90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x?

125
150
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250
500[/quote]

That question above is not a VIC. VIC stands for Variables in Answer Choices. There are no variables in these answer choices. Only use my method for VICs.

First, before I answer this you have two X's that I am assuming should be two different variable (one is "x pecent" the second is "x students").

Are you sure this problem is written correctly? If so which book are you getting it from so I can try to look it up if I have it. If it is online then copy and paste instead.

Now this is one of those situations where you have to pick numbers as well. Percent problems are problems where you should pick numbers. The difference between this problem and VIC is that you will not be plugging in the numbers into the answer choices.

What you will do is simple find the answer when you pluck numbers. The reason this works is because percents (and ratios) are percents. It doesn't matter what the actual number is because if you are calculating percents the proportion will be the same. E.g., x percent of 100 = 25, x is 25. x percent of 16 = 4, x = 25. x is the same whether the number is 100 or 16. The proportion is still 25% or the ratio of 1/4. Hence, if you are given variables in the question for percents or ratios you can just pick numbers because once you do it the percent calculated will always be accurate.

mpaudena wrote:

Stockmoose16 wrote:Disregard my last post. Instead read the one that I posted at 5:49 pm and see if that works. The simple answer is for VIC never put it in the percentage form when you are calculating the answer choices. That is only use the numbers (e.g., 25) and not (25/100 or .25) when you are calculating the answer choices.

Only use 25/100 or .25 when you are calculating the question asked.

The following question is a VIC, and you need to use X/100 to get the correct answer:

90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x?

125
150
225
250
500

That question above is not a VIC. VIC stands for Variables in Answer Choices. There are no variables in these answer choices. Only use my method for VICs.

First, before I answer this you have two X's that I am assuming should be two different variable (one is "x pecent" the second is "x students").

Are you sure this problem is written correctly? If so which book are you getting it from so I can try to look it up if I have it. If it is online then copy and paste instead.

Now this is one of those situations where you have to pick numbers as well. Percent problems are problems where you should pick numbers. The difference between this problem and VIC is that you will not be plugging in the numbers into the answer choices.

What you will do is simple find the answer when you pluck numbers. The reason this works is because percents (and ratios) are percents. It doesn't matter what the actual number is because if you are calculating percents the proportion will be the same. E.g., x percent of 100 = 25, x is 25. x percent of 16 = 4, x = 25. x is the same whether the number is 100 or 16. The proportion is still 25% or the ratio of 1/4. Hence, if you are given variables in the question for percents or ratios you can just pick numbers because once you do it the percent calculated will always be accurate.[/quote]

Ah, that's very helpful, but does it always hold true that you use the value of the percent in VIC and you use /100 when the variables are in the question stem only?

Also, the above question is from an MGMAT CAT, so yes, it is correct.

I just took a look at the question. What I said previously still applies regarding picking numbers and the difference between VIC.

This question is more akin the the question I was asking along with your question. The answer I was given is you can do it by doing x/100 or you don't have to. If you don't add x/100 then you have to multiply by 100 to get the percentage. If you do /100 you don't have to multiply by 100 because it will already have considered the percentage.

First pick a number for the total population. Usually when working with percents 100 is a good number. So 40% of 100 = 40. 40x =90; x = 2.25 then multiply times 100. The reason this is so is because you have to consider x/100 = 2.25 so then you'd multiply both sides by 100. But if you already considered it over 100 then you don't have to do it later.

Stockmoose16 wrote:

mpaudena wrote:

Stockmoose16 wrote:Disregard my last post. Instead read the one that I posted at 5:49 pm and see if that works. The simple answer is for VIC never put it in the percentage form when you are calculating the answer choices. That is only use the numbers (e.g., 25) and not (25/100 or .25) when you are calculating the answer choices.

Only use 25/100 or .25 when you are calculating the question asked.

The following question is a VIC, and you need to use X/100 to get the correct answer:

90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x?

125
150
225
250
500

That question above is not a VIC. VIC stands for Variables in Answer Choices. There are no variables in these answer choices. Only use my method for VICs.

First, before I answer this you have two X's that I am assuming should be two different variable (one is "x pecent" the second is "x students").

Are you sure this problem is written correctly? If so which book are you getting it from so I can try to look it up if I have it. If it is online then copy and paste instead.

Now this is one of those situations where you have to pick numbers as well. Percent problems are problems where you should pick numbers. The difference between this problem and VIC is that you will not be plugging in the numbers into the answer choices.

What you will do is simple find the answer when you pluck numbers. The reason this works is because percents (and ratios) are percents. It doesn't matter what the actual number is because if you are calculating percents the proportion will be the same. E.g., x percent of 100 = 25, x is 25. x percent of 16 = 4, x = 25. x is the same whether the number is 100 or 16. The proportion is still 25% or the ratio of 1/4. Hence, if you are given variables in the question for percents or ratios you can just pick numbers because once you do it the percent calculated will always be accurate.

Ah, that's very helpful, but does it always hold true that you use the value of the percent in VIC and you use /100 when the variables are in the question stem only?

Also, the above question is from an MGMAT CAT, so yes, it is correct.[/quote]

Yes, always holds true. Piece of advice. I took the MGMAT too. I took 3 tests from the MGMAT. One from MBA, two from Princeton review and I was stuck where I started - 560. It wasn't until I started to spend considerable time going over my answers that I started to score higher. I recently took my 5th and 6th MGMAT CAT and got 640 and 700. If I spent 1.5 hours on the test, I would spend 5 hours going over everything. I would dissect everything. I would consider my scrap paper to see where my understanding veered from what I was suppose to do. Every time I would come up with a rule as to either a concept I did not understand or a way to determine how to approach similar problems. Also, don't just look at the problem and think you understand the concept, do it and redo it. Make sure you understand it. Make sure that when you do it you don't stumble and need to go back and look. Eventually you'll have filled your gaps of knowledge enough to start scoring higher. Also don't make the mistake of not going over the answers you got right. You may have gotten it right for the wrong reasons. Also, the answer may include concepts that you were not aware of that will help you when there is a variation in the question type.