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  1. #1
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    Q. 15: A hotel charges different prices for the same meal in two different locations. The demand function in each location is given by:
    P1 = 50 - 4Q1 in Location 1
    P2 = 80 - 3Q2 in Location 2
    The hotel's cost function is TC = 120 + 8Q, where Q = Q1 + Q2. Note that in general, the profit is maximized at Q* when (dTC/dQ) = (dP/dQ). The price and quantity at Locations 1 and 2 respectively for which the hotel's profit is maximized are:
    (A) P1 = 29.2 P2 = 44 Q1 = 5.2 Q2 = 12
    (B) P1 = 44 P2 = 29.2 Q1 = 5.2 Q2 = 12
    (C) P1 = 44 P2 = 29.2 Q1 = 12 Q5.2 = 12
    (D) None

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    Default Quant Thread For CAT 2010 (Number system + Algebra + Arithmetic)

    Hi People,

    Please use this thread for Quant discussions (for CAT 2010 and other MBA exams of the coming season) related to Number system, Algebra and Arithmetic

    Some very simple rules

    1. Please do not spam.
    2. Try to post a solution and not just the key.
    3. Post any and every doubt you have, it helps everyone learn.
    4. Be polite and civil

    Good Luck!
    Last edited by TestFunda; 03-Feb-10 at 11:37 AM.

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    Quote Originally Posted by implex View Post
    Hi People,

    Please use this thread for quant discussions for CAT 2010 and other MBA exams of the coming season..

    Some very simple rules

    1. Please do not spam.
    2. Try to post a solution and not just the key.
    3. Post any and every doubt you have, it helps everyone learn.
    4. Be polite and civil

    Good Luck!
    hey implex....can we have separate threads fer the different topics in Quant,just as we did fer the 2009 CAT....eg-Number systems,geometry,arithmetic etc...?

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    Quote Originally Posted by nyc_chirag View Post
    hey implex....can we have separate threads fer the different topics in Quant,just as we did fer the 2009 CAT....eg-Number systems,geometry,arithmetic etc...?
    I dont think that is a very good idea, as some of the threads do not get much attraction and users post queries from all topics in one thread only, hence it is a good idea to keep all in one thread itself.

    Implex

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    Quote Originally Posted by implex View Post
    I dont think that is a very good idea, as some of the threads do not get much attraction and users post queries from all topics in one thread only, hence it is a good idea to keep all in one thread itself.

    Implex
    Thanks for the initiative to start the prep for 2010 but i feel that having separate threads help in categorizing the problems...last year also almost 90% of the threads contained problems specific to it and it was only towards the fag end of the season that there was overlapping.

    a person who wants to do a geometry problem can goto the specific thread for the same.

    I hope we can discuss it because end of the day its the ease with which one can access the topic one desires matters
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    Quote Originally Posted by sumit2goody View Post
    Thanks for the initiative to start the prep for 2010 but i feel that having separate threads help in categorizing the problems...last year also almost 90% of the threads contained problems specific to it and it was only towards the fag end of the season that there was overlapping.

    a person who wants to do a geometry problem can goto the specific thread for the same.

    I hope we can discuss it because end of the day its the ease with which one can access the topic one desires matters
    Having multiple threads distributes the traffic and in the end only one or two threads remain active the rest see almost negligible participation.

    There is one other reason to have one thread, users who want to post multiple questions in one post with varying topics, will either post all of them in one thread or not post. It is highly unlikely to expect a user to post one question from a set of five in thread A other in thread B and rest in thread C.

    But in the end if users want we can have separate threads.

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    I agree there should be different threads for different topics..
    Rest can be under miscellaneous

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    Quote Originally Posted by implex View Post
    Having multiple threads distributes the traffic and in the end only one or two threads remain active the rest see almost negligible participation.

    There is one other reason to have one thread, users who want to post multiple questions in one post with varying topics, will either post all of them in one thread or not post. It is highly unlikely to expect a user to post one question from a set of five in thread A other in thread B and rest in thread C.

    But in the end if users want we can have separate threads.
    hey Im...if ppl want to post multiple doubts let them post on the single thread,if convenient fer them,but there are a very few cases with multiple doubt,as seen in the 2009 thread the multiple doubts started cropping only at the end of the xam season,see if we want to narrow down on the thread count,we can make 2 threads 1)-Number Sys+Arithmetic+Algebra+Misc 2)Geometry....What do u think?

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    i think implex has a valid point...!

    nyways it would be nice if we had minimum no. of threads.. chirag's suggestion seems good to me...!!!

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    i guess 2 threads is the answer, as a res the traffic will nt be diverted and we can have maximum no of ppl working together on a single prob,thus more point of views....also most of the CAT ques test concepts frm more than 1 topics,so 2 threads makes sense,bifurcating into two broad topics 1)No.Sys+Algebra 2)Geometry ans Mensuration...what do u think ppl?...lets have a vote count and see,if this idea is a real deal?...

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    1 thread looks a better idea.

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    i am with you chirag...but i just like to bifurcate one more may be PnC and probability as it is the topic wiht most distinct presence

    so i suggest 3 threads

    1. Number system + algebra + arithmetic
    2. geometry + mensuration
    3. PnC + probability + Miscellaneous
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    fair enough...i think 3 threads will be a good Idea...what do others think?...i vote fer 3 threads..

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    Quote Originally Posted by sumit2goody View Post
    i am with you chirag...but i just like to bifurcate one more may be PnC and probability as it is the topic wiht most distinct presence

    so i suggest 3 threads

    1. Number system + algebra + arithmetic
    2. geometry + mensuration
    3. PnC + probability + Miscellaneous
    Pnc and probability go inside algebra itself. Most of the number theory questions test your p and C only.

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    Please use this thread for Quant discussions related to Number System, Algebra and Arithmetic.

    TFAdmin

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    lemme start the thread officially by posting some of the basic short cuts and formulas used in quant...the file is attached.
    Attached Files

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    PROB No.1:

    If 'a' is a real number and the equation (a-2)(x-[x])^2 +2(x-[x])
    +a^2 =0 (where [x] denotes the greatest integer <=x) has no integral solution and has exactly one solution in (2,3), then 'a' lies in the interval

    a. (-1,2) b. (0,1) c. (-1,0) d. (2,3)

    --------------------------------------------------------------------

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    (a-2)(x-[x])^2 +2(x-[x])+a^2 =0

    If any root of the equation is positive then all the coefficients of any power of x will not be positive.
    2(x-[x]) and a^2 can not be negative. so only (a-2) has to be negative.
    a-2<0 => a<2

    if we take a=1 then eqation will not be satisfied.
    so i go for option(3)
    ie., (-1,0)

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    For how many values of n each of n+9, 16n+9, 27n+9 becomes a perfect square.

    (a)1, (b)2, (c)3,(d)4,(e)5.

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    Quote Originally Posted by pk_gt1 View Post
    For how many values of n each of n+9, 16n+9, 27n+9 becomes a perfect square.

    (a)1, (b)2, (c)3,(d)4,(e)5.
    ans (a)..... for n=0

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