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  • CAT Quant Content - Conceptual Problems [Solved]

    mathbyvemuri

    Member

    Updated: Oct 26, 2024
    Views: 1.3K
    Hi all
    I am a math lover.
    This is introduction to my blog: < Advertisement Removed By Administrator >
    This blog is a hub of CONCEPTUAL problems (of course it is in developing stage). This blog centres around aptitude and reasoning. Generally concentrates on math content of CAT/XAT, GMAT, UPSC, CSAT, GATE, GRE, Placement Exams, Talent Search Exams and all concept and logic oriented exams.
    This is not a sort of stereotypical Q and A content.
    This is not for remembering and reproducing tons of formulas. This is a quest for logic, quest for reasoning, quest for success and kick...

    Through this thread, we will have discussion on those problems and concepts.

    This is not for promoting my blog but to open out myself by giving out what I feel important about math, about strategies in solving quality math problems etc..
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  • mathbyvemuri

    Member • Oct 23, 2011

    In continuation to my earlier post, pl find the following puzzle:
    Q1)Find the number of triangles in the above diagram?
    (A) 32 (B)23 (C)26 (D) 27 (E) 16​


    [​IMG]

    I hope you enjoy this one, this is one of the popular ones on my blog.
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  • mathbyvemuri

    Member • Oct 24, 2011

    Solution for the triangle problem- Q1:

    [​IMG]

    First we start from each of the 3-corners.

    From corner-1 : (1,2,3), (1,4,6), (1,7,10), (1,11,15) --- 4

    From corner-11 : (11,7,12), (11,4,13), (11,2,14) --- 3

    From corner-15 : (15,10,14), (15,6,13), (15,3,12) --- 3




    Now we count all the smallest triangles excluding (1,2,3), (11,7,12) and (15,10,14) which are already considered above:

    (2,4,5), (2,3,5), (3,5,6) ---3

    (4,7,8), (4,5,8), (5,8,9), (5,6,9), (6,9,10) ---5

    (7,8,12),(8,12,13),(8,9,13),(9,13,14),(9,10,14) ---5

    Now by considering “middle 3-points” of each side of the outer triangle, we get the following:

    (2,7,9), (3,8,10), (12,5,14) ---3




    Now by considering “single middle point” of each side of the outer triangle, we get the following:

    (4,6,13) ---1

    So the total number of triangles = 4+3+3+3+5+5+3+1 = 27

    Answer (D)

    How is it??????????????????
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  • mathbyvemuri

    Member • Oct 24, 2011

    Find out second problem here:
    Q2) How many letters of the English alphabet (Capitals)appear same when looked at in a mirror:
    (A) 9
    (B) 10
    (C) 11
    (D)12
    This is a little controversial problem on my blog...
    what do you feel?????
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  • mathbyvemuri

    Member • Oct 25, 2011

    Q3) The interior angles of a polygon are in A.P. If the smallest angle is 120[SUP]0[/SUP] and common difference is 5[SUP]0[/SUP], then the number of sides in the polygon is:
    (A) 7
    (B) 8
    (C) 9
    (D)None of the above
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  • mathbyvemuri

    Member • Oct 26, 2011

    Q4)If the positive real numbers a, b and c are in Arithmetic Progression, such that abc = 4, then minimum possible value of b is:
    (A) 2[SUP]3/2[/SUP]
    (B) 2[SUP]2/3[/SUP]
    (C) 2[SUP]1/3[/SUP]
    (D)None of the above
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  • Ankita Katdare

    Administrator • Oct 26, 2011

    mathbyvemuri
    Find out second problem here:
    Q2) How many letters of the English alphabet (Capitals)appear same when looked at in a mirror:
    (A) 9
    (B) 10
    (C) 11
    (D)12
    This is a little controversial problem on my blog...
    what do you feel?????
    The answer is 11.
    They are: A I H M O T U V W X Y
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  • mathbyvemuri

    Member • Oct 27, 2011

    This Q is a bit ambiguous. Answer may be 10 or 11. Confusion is with theThis Q is a bit ambiguous. Answer may be 10 or 11. Confusion is with the letter ‘Y’.
    If ‘Y’ is written as ‘Y’, which is the most general case, it won’t come under our category of symmetry and answer will be 10. Detailed explanation for this is given in my blog (puzzle-9 on my blog). Let me know your take on that…
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  • Ankita Katdare

    Administrator • Oct 27, 2011

    I feel 'Y' is mostly used as a capital letter. But, yeah It depends on the font we are using. If we consider general case of Times New Roman font, 'Y' is how they taught us to write y in capital.

    I am not a CAT aspirant, but are such ambiguous questions asked in the actual test?
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  • mathbyvemuri

    Member • Oct 31, 2011

    Solution:
    Given that smallest interior angle = 120[SUP]0[/SUP] and common difference 5[SUP]0[/SUP]
    ∴the series of interior angles is 120[SUP]0[/SUP], 125[SUP]0[/SUP], 130[SUP]0[/SUP],….
    Exterior angle = 180[SUP]0[/SUP] – Interior angle
    ∴the series of corresponding exterior angles is 60[SUP]0[/SUP],55[SUP]0[/SUP],50[SUP]0[/SUP],…
    This is a decreasing Arithmetic Progression with
    initial term ‘a’ = 60; common difference ‘d’ = -5;
    Let the polygon has ‘n’ sides.
    Sum of n terms of AP = n(2a+(n-1)d)/2 ----- >(1)
    Sum of exterior angles of any polygon = 360[SUP]0[/SUP] ----- >(2)
    From (1) and (2),
    360 = n(2a+(n-1)d)/2
    360 = n(120+(n-1)(-5))/2
    360 = n(125-5n)/2
    720 = 5n(25-n)
    144 = n(25-n)
    Instead of solving the equation, we go for checking multiple choice options one by one:
    Put n = 7, 144 = 7(18) wrong
    Put n = 8, 144 = 8(17) wrong
    Put n = 9, 144 = 9(16) correct
    ∴ Answer is (C)
    Check for more related problems on my blog
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  • mathbyvemuri

    Member • Nov 3, 2011

    (Q5) In tennis, service alternates for each game between the two players and the first player to win 6 games wins. A player winning 6-2 indicates that 8 games were played, of which the winning player won 6 and loosing player won 2.
    Rafa beat roger in a set of tennis, winning 6 games to Roger’s three. Five games were won by the player who did not serve. Who served first?

    (1)Rafa (2) Roger (3) Inconsistent (4) Indeterminate

    This is a good puzzle... Check out solution on my blog please...
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  • mathbyvemuri

    Member • Nov 24, 2011

    Q6) The micromanometer in a certain factory can measure the pressure inside the gas chamber from 1 unit to 999999 units. Lately this instrument has not been working properly. The problem with the instrument is that it always skips the digit 5 and moves directly from digit 4 to 6. What is the actual pressure inside the gas chamber if the micromanometer displays 003016?
    (1)2201 (2)2202 (3)2600 (4)2960 (5)None of these options

    This is a tricky one on numbers, for solution check for Numbers-17 problem on my blog on math
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  • mathbyvemuri

    Member • Dec 19, 2011

    (Q7)
    Find the number of integers lying between 100 and 400 (excluding the two) and divisible by any one of the numbers 2 or 3 or 5 or 7?​
    Solution for this problem can be found at 'Numbers-22' on my 'Blog on Math' link provided right down at my signature. Let me know any other simpler way out is possible, given the limited availability of time in the competitive exams.​
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  • graphite

    Member • Jul 16, 2012

    (Q8)
    Consider the following three polynomials
    P1(x)=ax2-bx-c, P2(x)= bx2-cx-a, P3(x)=cx2-ax-b
    Here a, b, c are non-zero real numbers. Let there exits a real number w, then P1(w)=P2(w)=P3(w) then

    (1)ab+bc+ca=0 (2) a3+b3+c3=0 (3) a=b=c (4)a+b+c=0
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  • Lalit77

    Member • Jul 30, 2012

    mathbyvemuri
    Find out second problem here:
    Q2) How many letters of the English alphabet (Capitals)appear same when looked at in a mirror:
    (A) 9
    (B) 10
    (C) 11
    (D)12
    This is a little controversial problem on my blog...
    what do you feel?????
    ans. option C
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  • Lalit77

    Member • Jul 30, 2012

    mathbyvemuri
    This Q is a bit ambiguous. Answer may be 10 or 11. Confusion is with theThis Q is a bit ambiguous. Answer may be 10 or 11. Confusion is with the letter ‘Y’.
    If ‘Y’ is written as ‘Y’, which is the most general case, it won’t come under our category of symmetry and answer will be 10. Detailed explanation for this is given in my blog (puzzle-9 on my blog). Let me know your take on that…
    then a,t also dont have to consider..So the actual answer is 8 now.Accordingly your options are wrong.
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  • graphite

    Member • Aug 25, 2012

    Consider a quadratic equation;
    x2 + 7x – 14(a2 + 1) = 0, … (where a is an integer)
    For how many different value of a, the equation will have at least one integer root?



    A) 0 B) 1 C) 2 D) More than 2
    ​

    ​
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  • Nithyasri

    Member • Aug 26, 2012

    ans for q.4
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