James deposited $1,000 each in two investment schemes X and Y. Scheme

Question

James deposited $1,000 each in two investment schemes X and Y. Scheme X doubles the invested amount every 7 years and scheme Y doubles the invested amount every 14 years. If James withdraws $500 from scheme X at the end of every 7th year, how many years will it take for the total amount invested in schemes X and Y to amount more than $40,000?

A. 14
B. 28
C. 42
D. 56
E. 70

A. 14
B. 28
C. 42
D. 56
E. 70

stne · Answer

Please refer to the attached table. Investment q Gmat.jpg Ans C Hope it's clear.

RahulJain293 · Answer

Bunuel  Could you please help with OE?

gmattyfatty · Answer

stne  is there a simple equation to solve without needing to write out a table?

stne · Answer

gmattyfatty  ,

Thank you for your query. I am not sure whether we can have a single equation for all that is happening in this question. There are quite a few things happening in this question. Not sure why you would even try to find one. I think it's best to proceed step by step and try to get to the answer. Even if you are able to devise an equation it will only be applicable for this question and not in general. So it's best to proceed in a non-formulaic way so one can attempt any such questions.

Hope it helps.

gmattyfatty · Answer

stne

You would want to find one because, although this question uses simple numbers and a small time frame, a question with more complex numbers and a larger time frame might arise, making creating a table very impractical and time consuming for a test such as the GMAT. Also, it's clear based on the table that an equation can indeed be abstracted, as we can see that the numbers are moving by a factor of 2^n

Having mathematics behind a solution does not mean we don't proceed step by step. It simply means we can understand the problem algebraically. That being said I don't believe an equation would only be applicable to this question, as math is often not applicable to only one specific thing.

stne · Answer

gmattyfatty ,

The table is just to make the solution easier to understand for all forum members, it doesn't mean in the exam I am going to make a table and solve this question. It's just there to make the solution easier to understand.

Have you seen me using a table for all my posts? or have you seen all the questions in this forum being solved by equations? That may be your own personal preference.

Each question has a unique way of solving, why do you think I would use one where it is too complex and too time-consuming, In fact for this question it is the other way around. Creating an equation is too time-consuming and complex, at least for me, for an exam such as the GMAT. You would want a simple and quick approach to solving this question.

Let's not get into unnecessary arguments!

If you can make an equation and solve the question, why don't you do so and enlighten every one of us, with an alternate way to the solution? That could really help. I am always open to learning new things. Thanks.

gmattyfatty · Answer

stne Apologies. When you said "Not sure why you would even try to find one...Even if you are able to devise an equation...it's best to proceed in a non-formulaic way", to me it meant that it does mean you are going to make a table to solve this question, not that it is only there for the question to be easier to understand. Also not sure if you perceive that we are arguing as my initial question was simply "is there a simple equation to solve without needing to write out a table?". The answer could have been "no" or "if there is i'm not aware of it. The table was faster for me". I also asked because I was trying to determine the equation myself to get a better understanding but got a couple of different answers so i thought maybe you had one. Unfortunately i do not follow your account to know whether or not you "Have you seen me using a table for all my posts". Here's the equation, only lightly confirmed by a friend with more math background: To determine the value in each account we do this: Total = Principal * Rate^Frequency Y = 1000*2^(n/14) X = 1000*2^(n/7) - 500*2^(n/7 - 1) --> we subtract 1 because we do not remove 500 from the initial deposit Adding together we get: 1000*2^(n/14) + 1000*2^(n/7) - 500*2^(n/7 - 1) > 40000 Divide by 500: 2 * 2^(n/14) + 2 * 2^(n/7) - 2^(n/7-1) > 80 2^(n/14 + 1) + 2^(n/7 + 1) - 2^(n/7-1) > 80 Now for easier math and testing of numbers, lets instead assume n is in 14 year chunks and abstract the equation: 2^(n+1) + 2^(2n+1) - 2^(2n - 1) > 80 We see here that 2 < n < 3 because if n = 2 (28 years) --> 2^3 + 2^5 - 2^3 = 32 n = 3 (42 years) --> 2^4 + 2^7 - 2^5 = 112 and we are looking for the minimum number that gets us 80. This limits us to options B and C and since it cannot be B because 32 < 80, it must be C Hope it helps.

stne · Answer

Yes, you can definitely use this, if it's faster for you in GMAT.

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James deposited $1,000 each in two investment schemes X and Y. Scheme

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