Quant Boosters - Sagar Gupta - Set 2


  • Being MBAtious!


    Number of Questions - 30
    Topic - Quant Mixed Bag
    Solved ? - Yes
    Source - Compilation of posts from Sagar Gupta - 99.2 Percentile in CAT 2015 (Quant)


  • Being MBAtious!


    Q1) If x, y and z are whole numbers such that x ≥ y,then how many solutions are possible for the equation x + y + z = 36?
    (a) 361
    (b) 323
    (c) 382
    (d) 342


  • Being MBAtious!


    [ 38c2 - 19 ] /2 = 342 , when x > y and x < y
    when x > = y
    342 + 19 = 361


  • Being MBAtious!


    Q2) In a group if 80% drink tea and 60% drink coffee,what is the maximum percentage of people drinking either tea /coffee but not both?


  • Being MBAtious!


    I + II = 100
    I + 2 II = 140
    II = 40
    I = 60


  • Being MBAtious!


    Q3) 1 unit of A is made by mixing 4 units of B and 5 units of C. 1 unit of B is made by mixing 1 unit of X, 4 units of Y and 1 unit of Z. 1 unit of C is made by mixing 2 units of X, 6 units of Y and 1 unit of Z. The weight of 1 unit each of X, Y and Z is 5 kgs, 3 kgs and 8 kgs respectively. What is the total weight of Y required to make 1400 kgs of A?
    (1) 630 kgs
    (2) 720 kgs
    (3) 690 kgs
    (4) 870 kgs
    (5) 570 kgs


  • Being MBAtious!


    A = 4B + 5C
    B = X + 4Y + Z
    C = 2X + 6Y + Z
    X = 5 , Y = 3 , Z = 8
    B = 5 + 12 + 8 =25
    C = 10 + 18 + 8 = 36
    A = 100 + 180 = 280
    280 of A with 46Y or 46*3 = 138
    690 kgs for 1400 kgs of A


  • Being MBAtious!


    Q4) Find HCF of 2^100 - 1, 2^120- 1 ?


  • Being MBAtious!


    HCF (2^a -1, 2^b -1) = 2^(HCF a, b) - 1
    = 2^20 - 1


  • Being MBAtious!


    Q5) Find last two digits of 15 * 37 * 63 * 51 * 97 * 17


  • Being MBAtious!


    15 * 37 * 63 * 51 * 97 * 17 mod 100
    15 * 37 * (-37) * 51 * (-3) * 17 mod 100
    45 * 37^2 * 17^2 * 3 mod 100
    45 * 89 * 03 * 69
    35


  • Being MBAtious!


    Q6) A five digit number divisible by 3 is to be formed using numbers 0, 1,2,3,4,5 without repetition . The total number of ways in which this can be done is....
    a. 216
    b. 240
    c. 600
    d. 3125


  • Being MBAtious!


    1 + 2 + 3 + 4 + 5 = 15
    -> 5! ways
    0 + 1 + 2 + 4 + 5 =12
    ->5! - [ 5! /5 ] =120 - 24 =96
    total 120 +96 =216


  • Being MBAtious!


    Q7) The total number of ways of selecting two numbers from the set {1,2,3,4,......,30}, so that their sum is divisible by 3, is
    a. 95
    b. 145
    c. 190
    d. None of the above.


  • Being MBAtious!


    3k, 3k + 1, 3k + 2
    divisible by 3:
    case 1 : 3k + 3k
    10 * 9 = 90 ways
    case 2 : (3k+2) + (3k+1)
    10 * 10 = 100 ways
    total = 190 ways


  • Being MBAtious!


    Q8) Train X started from point A at 9:00 am with a speed 72km/hr towards station Y. 2 hrs after train Y starts from point B towards X at a speed of 90 km/hr. They cross each other at 1:30 pm. But owing to signal problems at 12:00 noon the speeds of both the trains is reduced by same quantity such that they now cross each other at 4:30 pm. Calculate the new speed of train that started from point A.


  • Being MBAtious!


    Train X starts at 9:00 am @72 km/hr
    at 11:00 am, it is 144 kms from A
    A...144 kms...A'......d...........B
    Now Y starts from B at 11:00am @90 km/hr
    A' and B is the position at 11:00 am
    :
    They should have met at 1:30pm
    72 * 2.5 + 90 * 2.5 = d =405 kms
    :
    But they meet at 4:30 pm
    from 11:00 to 12:00 , they travel at normal speed
    Distance reduced = 72+90=162
    Distance between them at 12:00 = 243 kms
    Now they reduce their speed by k
    (72-k) * 4.5 + (90-k) * 4.5 =243
    k=54
    72-54 =18km/hr


  • Being MBAtious!


    Q9) abcd is a 4 digit perfect square, then if each digit is increased by 3 the number is still a perfect square. Find abcd.


  • Being MBAtious!


    abcd = x^2
    1000a +100b +10c +d = x^2
    1000(a+3) +100(b+3) +10(c+3) +d+3 = y^2
    y^2-x^2=3000 +300 + 30 + 3
    y^2 - x^2 = 3 [ 1000 +100 +10 +1 ]
    y^2 - x^2 =3333
    3333=101*33
    y+x =101
    y-x =33
    y = 67
    x = 34
    x^2 =1156


  • Being MBAtious!


    Q10) What is the remainder when 72 to the power 7202 is divided by 625?


Log in to reply
 

Looks like your connection to MBAtious was lost, please wait while we try to reconnect.