Quant Boosters - Shashank Prabhu, CAT 100 Percentiler - Set 6


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Number of Questions - 30
    Topic - Quant Mixed Bag
    Solved ? : Yes
    Source : Learningroots forum


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q1) Solve both equations and choose the correct option
    i) x^2 + 0.2x = 4.83
    ii) y^2 + 4.62 = 4.3y
    a) x > y
    b) x ≥ y
    c) x < y
    d) x < y
    e) x = y


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    483=161×3=7×23×3=21×23
    (x+2.3)(x-2.1)=0
    462=2×231=2×3×77=2×3×7×11=22×21
    (y-2.2)(y-2.1)=0
    So x < = y


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q2) The cost price of an article increases by Rs. 100. The selling price increases by 10%. If the profit decreases from 15% to 10%, what is the original cost price?


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    original CP -> x , final x+100
    original SP ->y , final 1.1y
    y-x / x = 0.15 ; 1.1y-x-100 / x+100 = .1
    Solve for x = 2000/3


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q3) In a race, A beats B by 100 m and C by 180 m. If B beats C by 90 m, what is the length (in m) of the race?


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    When A is at Finish Point, gap between B and C is 80m. When B covers the remaining 100m, the gap increases by 10m. Thus to make the gap of 10m, B has to cover 100m.
    Hence, to make the gap of 90m, B must cover 900m


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q4) A bag contains 9 red cards numbered 1, 2, 3 …, 9 and 9 black cards numbered 1, 2, 3 …, 9. In how many ways can we choose 9 out of the 18 cards so that there are exactly 3 duos, where a duos means a red card and a black card with the same number?
    a. 80640
    b. 13440
    c. 18480
    d. 1680


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    The 3 numbered cards can be chosen in 9c3 = 84 ways. Post that, we need to select cards such that the numbers don't repeat. So, the first card can be chosen from the remaining 12 cards in 12 ways, the second card in 10 ways and the third card in 8 ways. However, as the order is not important, we will have to divide it by 3!. So, 84 * 12 * 10 * 8/3! = 84 * 16 * 10 = 13440


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q5) The angles of a convex pentagon are in an arithmetic progression. Which of the following can never be the value of any of its angles?
    (1) 36°
    (2) 35°
    (3) 34°
    (4) All of these


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    4 is perfect. If the angles are a-2d, a-d, a, a+d and a+2d, a=108. The largest angle will be less than 180 as it is a convex pentagon. So, 108+2d greater than 36


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q6) The number of distinct points at which the curve y^3 - 5y^2 + x^2 + 6y - 5x = 0 intersects either the x-axis or the y-axis is


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    If x=0, y^3-5y^2+6y=0, y=0 or 2 or 3
    If y=0, x^2-5x=0, x=0 or 5
    (0,0)(0,2)(0,3)(5,0) are the only points (0,0) was common to both the cases.


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q7) A number x is such that it can be expressed as a + b + c = x where a, b and c are the (only) factors of x. How many numbers below 200 have this property?


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    6 is the only such number.
    The other perfect numbers are 28, 496, 8128...


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q8) Gautam decided to go to a temple only on first and the last day of a year. He continues to go to the temple in this fashion till the time he finds that he has visited the temple atleast once on each of the different days of a week. The minimum number of days required to achieve this is


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Starting from the last day of a non leap year you get x and x+1, if the next year is a leap year, you get x+2 as the last day. Then x+3, x+3, x+4, x+4, x+5, x+5, as the first and the last days and finally x+6 as the first day of the new year. 4 years and 2 days... 1463 days.


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q9) What is the smallest possible positive integer such that the product of all its digits equals 9! ?


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    9! = 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9
    2^7 * 3^4 * 5 * 7
    5 and 7 cannot be increased further so they have to be present as it is. We can reduce the numbers by joining various powers of 2 and 3. The highest power of 2 that is a single digit is 8 and the highest power of 3 that is a single digit is 9. So, we are left with 2 * 8 * 8 * 9 * 9 * 5 * 7. We cannot tweak these numbers any further and so, it will be 2578899.


  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS


    Q10) Three elements a, b and c are selected from the set A = {2, 3, 5, 6, 7} to form a three-digit number ‘abc’, where a < b < c. Similarly, two elements p and q are selected from the set B = {0, 1, 8, 9} to form a two-digit number ‘pq’, where p > q. Let, M be the total number of all the possible values of ‘abc’ and N be the total number of all the possible values of ‘pq’. What is the value of (M-N)?


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