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13 Apr 2020, 23:19
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Q23 PS - Solved video solutions by Crackverbal. (I am unable to post link here)
Please look at the video. I am referring to the second part of the video where backsolving is used to solve. Why does x have to be an integer here? I don't understand the logic given in the video.
Thanks
Please look at the video. I am referring to the second part of the video where backsolving is used to solve. Why does x have to be an integer here? I don't understand the logic given in the video.
Thanks
14 Apr 2020, 01:24
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Hello Shekhar89,
The question mentions that the 3 persons earned a total of $780. It also mentions that they were paid in proportion to the work done by them. As such, don’t you think the rate should be constant? Can the rate of payment be different for different persons? Does that sound logical? The clear answer is NO, isn’t it?
Don’t look at GMAT Quant as a test of your Math skills alone – nothing can be farther from the truth, Shekhar. GMAT Quant tests your ability to apply sound logic in solving a Quant question as much as it expects you to apply your knowledge of Math concepts.
Deep down, GMAT also tests your managerial skills. One trait that is tested is whether you are able to take a stand on a real-life problem based on the data that you have.
Now put yourself into the situation defined in the question. Let’s assume these 3 persons (defined in the question) are working under you. For some project, they did some work and raked up a bill of $780. You have already told them that you will pay them in accordance to the proportion of work they completed (makes sense, right? I mean, if someone did more work, you can’t pay him less and vice versa, isn’t it?).
Also, will you pay each one at different rates? Makoto will be paid, say, $33.7 per hour, Nishi will be paid $27. 6 per hour and Ozuro will be paid, say, $19.8 per hour?? On top of all this, you expect 15 * 33.7 + 20 * 27.6 + 30 * 19.8 to yield EXACTLY $780. Can there be anything more far-fetched than this argument? The answer is NO.
Another argument that might come up here is that “What if I use the same decimal to multiply 15, 20 and 30?”. Sure, why not! What IS that decimal? Can you think of ONE common decimal that will yield a total of $780? Of course you cannot. Mathematically, you have one independent equation and three variables. You cannot find a unique solution for every variable, right?
You have eliminated TWO implausible and impossible arguments now (IMO, these arguments shouldn’t even have come up in this question, especially after you watched the mathematical approach to this question. But, nevertheless, I treat every question as a valid question). Clearly, the only way that this equation can be solved is by taking the rate/hr as an integer.
When you are fully prepared to take the test, a lot of the above should happen in a matter of few seconds, mentally. And this is where muscle memory comes into play. If you have solved sufficient number of problems of this type, your muscle memory will automatically kick in, eliminate the impossible situations and before even you know you would be trying to find the integral solutions to the equation.
The only hindrance could be your being over-anxious and questioning your own logic which is otherwise sound. I’m assuming that this was the case in this problem since you HAD actually understood the question when solved the mathematical way.
Hope that answers your query!
Thanks.
PS: Note that the numbers I have considered above (except 780) are just random numbers to put forth my point. It is not to say that these could be the values for the rates.
The question mentions that the 3 persons earned a total of $780. It also mentions that they were paid in proportion to the work done by them. As such, don’t you think the rate should be constant? Can the rate of payment be different for different persons? Does that sound logical? The clear answer is NO, isn’t it?
Don’t look at GMAT Quant as a test of your Math skills alone – nothing can be farther from the truth, Shekhar. GMAT Quant tests your ability to apply sound logic in solving a Quant question as much as it expects you to apply your knowledge of Math concepts.
Deep down, GMAT also tests your managerial skills. One trait that is tested is whether you are able to take a stand on a real-life problem based on the data that you have.
Now put yourself into the situation defined in the question. Let’s assume these 3 persons (defined in the question) are working under you. For some project, they did some work and raked up a bill of $780. You have already told them that you will pay them in accordance to the proportion of work they completed (makes sense, right? I mean, if someone did more work, you can’t pay him less and vice versa, isn’t it?).
Also, will you pay each one at different rates? Makoto will be paid, say, $33.7 per hour, Nishi will be paid $27. 6 per hour and Ozuro will be paid, say, $19.8 per hour?? On top of all this, you expect 15 * 33.7 + 20 * 27.6 + 30 * 19.8 to yield EXACTLY $780. Can there be anything more far-fetched than this argument? The answer is NO.
Another argument that might come up here is that “What if I use the same decimal to multiply 15, 20 and 30?”. Sure, why not! What IS that decimal? Can you think of ONE common decimal that will yield a total of $780? Of course you cannot. Mathematically, you have one independent equation and three variables. You cannot find a unique solution for every variable, right?
You have eliminated TWO implausible and impossible arguments now (IMO, these arguments shouldn’t even have come up in this question, especially after you watched the mathematical approach to this question. But, nevertheless, I treat every question as a valid question). Clearly, the only way that this equation can be solved is by taking the rate/hr as an integer.
When you are fully prepared to take the test, a lot of the above should happen in a matter of few seconds, mentally. And this is where muscle memory comes into play. If you have solved sufficient number of problems of this type, your muscle memory will automatically kick in, eliminate the impossible situations and before even you know you would be trying to find the integral solutions to the equation.
The only hindrance could be your being over-anxious and questioning your own logic which is otherwise sound. I’m assuming that this was the case in this problem since you HAD actually understood the question when solved the mathematical way.
Hope that answers your query!
Thanks.
PS: Note that the numbers I have considered above (except 780) are just random numbers to put forth my point. It is not to say that these could be the values for the rates.
