Quant Boosters - Hemant Malhotra - Set 1


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Number of Questions - 30
    Answer Keys available - Yes
    Topic - Quant Mixed Bag
    Source - Elite's Grid CAT Preparation Forum


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q1) Sarah intended to multiply a two-digit number and a three-digit number, but she left out the multiplication sign and simply placed the two-digit number to the left of the three-digit number, thereby forming a five-digit number. This number is exactly nine times the product Sarah should have obtained. What is the sum of the two-digit number and the three-digit number?


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    a is a two digit number and b three digit number, so ab is five digit number.
    If a = 12 and b = 123 and we are writing 12123 then we can also write it as 12 x 1000 + 123
    so 1000 * a + b = 9 * (a) * b
    1000/b + 1/a = 9
    so 1000/b will be approx 9 so 1000/9 = 112 (approx value)
    so b = 112 and a = 14
    so sum = 126


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q2) In a ∆ABC, AD & BE are medians and G is the centroid, ∠AGE = 30° , AD=12cm & BE = 18cm. Find the area of the triangle?


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    0_1510118260233_65019c66-dde2-4c62-b938-859db5c5ac47-22853301_876410515866541_7666813808487778688_n.jpg

    ∠AGE = 30
    G will bisect BE in 2:1 ratio so GE = 4 and in same way AG = 12
    so area of AGE = 1/2 * AG * GE * sin30 = 1/2 * 12 * 4 * 1/2 = 12
    so area of ABC will be 6 times of area of AGE =12 * 6 = 72
    [Note - Median divide triangle into 6 equal areas]


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q3) For prime numbers a and b, a + b = 102 and a > b. What is the least possible value of a - b ?


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Question is not important but approach is important here
    Minimum will be when a and b are as close as possible so
    a = 51 + m and b = 51 - m
    where 51 + m and 51 - m both are primes
    at m = 8, 59 and 43 both are prime so minimum difference will be 16


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q4) At Ram's birthday party, the ratio of people who ate ice cream to people who ate cake was 3 : 2. People who ate both ice cream and cake were included in both categories. If 120 people were at the party, what is the maximum number of people who could have eaten both ice cream and cake?


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Those who ate both will be maximum when all who ate cake also ate icecream
    n(A U B) = n(A) + n(B) - n (A intersection B)
    so 120 = 3x + 2x - 2x
    so x = 40
    so Those who ate both = 2x = 80


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q5) How many ordered triples (a, b, c) satisfy the below equation where a, b and c are real numbers.

    (a^2 − 1)^2 + (b^2 −4)^2 + (c^2 − 9)^2 = 0


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    all values will be equal to zero
    a^2 - 1 = 0 so a = +/- 1
    b^2 - 4 = 0 so b = +/- 4
    c^2 - 9 = 0 so c = +/- 3
    so 2 * 2 * 2 = 8


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q6) How many subsets A of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} have the property that no two elements of A sum to 11


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Pairs that makes 11 = (1 ,10), (2 ,9), (3 8), (4 7), (5 6)
    we have 5 pairs and out of each pair only one or none can go to subset A
    so for each pair we have 3 possibilities.
    so number of subsets of A satisfying the condition = 3^5 = 243


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q7) The centroid Of a triangle is at (1, -1) While its orthocentre at (5, 3). The circumcentre of the triangle could be at
    a) (-1, -3)
    b) (8/3, 0)
    c) (0, 8/3)
    d) (7/3, 1/3)


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Centroid bisect ortho and circum in 2:1 ratio
    distance between (1,-1) and (5,3) is sqrt(16+16)=sqrt32
    so distance between centroid and circum should be sqrt32/2
    check by options
    sqrt(4 + 4) = sqrt8
    so OA = A


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q8) A person travels equal distance at a speed of 3 kmph, 4kmph and 5 kmph and takes 1 hour 34 minutes to complete the journey. Find his average speed for the whole journey
    a) 3.83 kmph
    b) 4.62 kmph
    c) 4 kmph
    d) 4.11 kmph


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Basic approach to solve 180/47 = 3.8 approx

    Quick approach - Average speed of journey will be equal to HM always (when equal distance with different speeds)
    HM < AM
    AM = (3 + 4 + 5)/3 = 4
    so HM < 4
    only 1st option satisfies.


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q9) Find the range of T = 2Cos^4θ + Sin^2θ + 3
    a) [1/2, 5]
    b) [2, 3]
    c) [31/8, 5]
    d) [31/7, 4]


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    OA - C

    Method 1 -
    Change in cos or sin
    2cos^4 x + 1 - cos^2x + 3
    let cos^2x = y
    2y^2 - y + 4 = T
    so dT/dy = 4y - 1 = 0
    so y = 1/4
    so 2/16 - 1/4 + 4
    1/8 - 1/4 + 4
    1 - 2 + 32/8 = 31/8 min value
    and max will be 5 when x = 0

    Method 2 - Exam Condition Approach
    max value is 5 at x = 0 so 2 and 4 ruled out
    now square of any thing will not be negative so min will be 3 in (worst cases ignoring sin and cos)
    so only option possible = C


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q10) In the figure given below, if O is the centre of the circle and < BAO = 54 then find < OAD + < OCD

    0_1510119705736_1e6db430-1d39-42f8-85e7-46a4a085db19-image.png

    a) 108
    b) 126
    c) 112
    d) 120


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