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# A student has decided to take GMAT and TOEFL examinations

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

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22 Aug 2015, 05:28
Does anyone know how to solve this problem using Double-set Matrix method ?

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

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10 Dec 2015, 01:12
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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A student has decided to take GMAT and TOEFL examinations  [#permalink]

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01 Aug 2016, 17:42
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Enclosing the Matrix method solution.
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Matrix Method.docx [11.52 KiB]

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

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21 Feb 2018, 10:44
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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21 Feb 2018, 11:00
1
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)
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Re: A student has decided to take GMAT and TOEFL examinations  [#permalink]

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15 Aug 2018, 18:43
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.

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

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30 Nov 2018, 00:31
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.
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Re: A student has decided to take GMAT and TOEFL examinations  [#permalink]

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01 Dec 2018, 18:03
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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04 Mar 2019, 00:32
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.

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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Re: A student has decided to take GMAT and TOEFL examinations   [#permalink] 04 Mar 2019, 00:32

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