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Intern  Joined: 01 Apr 2015
Posts: 47
Re: A student has decided to take GMAT and TOEFL examinations  [#permalink]

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Does anyone know how to solve this problem using Double-set Matrix method ?

Thanks.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8001
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: A student has decided to take GMAT and TOEFL examinations  [#permalink]

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2
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

A student has decided to take GMAT and TOEFL examinations, for which he has allocated a certain number of days for preparation. On any given day, he does not prepare for both GMAT and TOEFL. How many days did he allocate for the preparation?

(1) He did not prepare for GMAT on 10 days and for TOEFL on 12 days.
(2) He prepared for either GMAT or TOEFL on 14 days.

->When you modify the original condition and question, this question is frequently given on GMAT math, which is “2 by 2 question” like the table below.
Attachment: GCDS cyberjadugar A student has decided (20151210).jpg [ 27.69 KiB | Viewed 1171 times ]

There are 3 variables(a, b, c), which should match with the number of equations. Therefore, 3 equations are needed. For 1), 1 equation, for 2) 1 equation, so we need 1 more equation. So, E is likely to be the answer. In 1) & 2),
1) Two equations b+c=10, a+c=12
2) One equation a+b=14
Based on 1) and 2), the answer is unique, which is sufficient. Therefore, the answer is C.

-> For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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GMAT 1: 730 Q48 V42 GMAT 2: 750 Q50 V41 A student has decided to take GMAT and TOEFL examinations  [#permalink]

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3
Enclosing the Matrix method solution.
Attachments Matrix Method.docx [11.52 KiB]

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Appreciate any KUDOS given ! Manager  B
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Re: A student has decided to take GMAT and TOEFL examinations  [#permalink]

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I have a doubt here. Is the question asking us to find : total number of days for GMAT= Prepared + not prepared and total number of days for TOEFL = prepared days + not prepared??
Are both my equations correct ??
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Re: A student has decided to take GMAT and TOEFL examinations  [#permalink]

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longhaul123 wrote:
I have a doubt here. Is the question asking us to find : total number of days for GMAT= Prepared + not prepared and total number of days for TOEFL = prepared days + not prepared??
Are both my equations correct ??

Hi

Yes, I think thats what the question is asking us to find - 'the total days allocated for preparation' - which include days devoted to only GMAT study, days devoted to only TOEFL study and days devoted to neither study (there is no day of both GMAT and TOEFL study as stated in the question)
Thread Master - Part Time MBA Programs S
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Re: A student has decided to take GMAT and TOEFL examinations  [#permalink]

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Arthur1000 wrote:
Is this a badly worded question? - it tells me that how many days of preparation has the student taken, but if he has studied for neither GMAT or TOEFL then this idle day is not a day of preparation and doesnt count.

Therefor the answer is D, both can give us the answer

I see your point, but how could it be a D? If anything it should be a B.. I got the answer C but the wording can be confusing after reading this.
Intern  B
Joined: 19 Nov 2018
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GMAT 1: 710 Q49 V36 GPA: 2.36
Re: A student has decided to take GMAT and TOEFL examinations  [#permalink]

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Another way to think about it:

On days that we study for one, we are not studying for the other, therefore if you look at the days where you do not study for one of the tests, but do not take a full rest day, then you know you are studying for the other exam. So-
No GMAT (but not full rest day) + Rest = 10
No TOEFL (but not full rest day) + Rest = 12

Then you can add the two equations together to get:
No GMAT (not full rest day) + No TOEFL (not full rest day) + 2*rest days = 22

That is the info from #1 and alone is insufficient.

From #2 we know that the total days studying is 14, which alone is insufficient.

Since we know that we can not study both on any one day #2 tells us:
No GMAT (not full rest day) + No TOEFL (not full rest day) = 14
Add the two equations together and you get 14 + 2*rest days = 22
solving for rest days =4
Thus 14 days studying and 4 days resting = 18 days total prep which gives us the answer of C, meaning both statements together are sufficient.

Hope this helps.
Intern  B
Joined: 11 Sep 2013
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Re: A student has decided to take GMAT and TOEFL examinations  [#permalink]

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This one can be solved by using the double-set matrix. See attached double-set matrix below for more clarification.
We are looking for the Total days; label it with an X. So, we are looking to solve for X.

Statement (1) ALONE is Insufficient (Eliminate AD) because we cannot solve for X.
GMAT + TOEFL = (X-10) + (X-12)
No Info for GMAT + TOEFL = ?

Statement (2) ALONE is Insufficient (Eliminate B) because we cannot solve for X.
GMAT + TOEFL = 14
X=?

Together Statement (1) and (2) SUFFICIENT. Correct answer choice: (C)
From Statement (1) we have GMAT + TOEFL = (X-10) + (X-12)
From Statement (2) we have GMAT + TOEFL = 14
Combining both statements we get the following equation
14 = 2X - 22
36 = 2X
18 = X

The total is 18 Days.
Attachments TOEFL vs GMAT.png [ 23.27 KiB | Viewed 253 times ]

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Re: A student has decided to take GMAT and TOEFL examinations  [#permalink]

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A student has decided to take GMAT and TOEFL examinations, for which he has allocated a certain number of days for preparation. On any given day, he does not prepare for both GMAT and TOEFL. How many days did he allocate for the preparation?

(1) He did not prepare for GMAT on 10 days and for TOEFL on 12 days.
(2) He prepared for either GMAT or TOEFL on 14 days.

From, raceacademy's training material.

we can solve this question using 2x2 matrix..

----------------prepare gmat------- not prepare gmat-----total
prepare toefl----0------------------0-------------------x
not prepare toefl--0-----------------0------------------12
total-----------y-------------------10----------------total

from given info we know
x+y=14
y=total-10
x=total-12
y=14-x
solve for x,y,total
we get
y=8; gmat
x=6; toefl
total=14;
IMO C
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If you liked my solution then please give Kudos. Kudos encourage active discussions. Re: A student has decided to take GMAT and TOEFL examinations   [#permalink] 04 Mar 2019, 00:32

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