Quant Boosters - Hemant Malhotra - Set 7


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


    Number of Questions - 30
    Topic - Quant Mixed Bag
    Solved ? - Yes
    Source - Elite's Grid Prep Forum


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


    Q1) If x + y + z = 13, then what is the maximum value of (x-3)(y-2)(z+1)?
    a) 26
    b) 27
    c) 32
    d) 24


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


    x + y + z = 13
    (x-3) + (y-2) + (z+1) = 9
    now (x-3) * (y-2) * (z+1) will be max when all are equal so 3 * 3 * 3 = 27


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


    Q2) A number X is when divided by 11, 4 and 3 leaves remainders 9, 2 and 1 respectively. The least such X when divided successively by 3, 4 and 11 leaves remainders
    (1) 6,0,0
    (2) 0,1,2
    (3) 0,0,6
    (4) 1,3,10


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


    difference of divisor and remainder is same 11-9=2
    so number will be lcm(11,4,3)-2=130
    now number is 130
    130 mod 3=1
    3* 43 + 1=130
    now 43 mod 4=3
    so 4 * 10+3=43
    now 10 mod 11=10
    so 1,3,10


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


    Q3) The sum of the squares of the first 15 positive integers is equal to 1240. What is the sum of the squares of the second 15 positive integers?
    a) 2480
    b) 3490
    c) 6785
    d) 8215


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


    5 * 31 * 61 - 1240 = 8215
    sum till 30 - sum till 15
    so 1^2+2^2.....30^2-(1^2+2^2+.................15^2)
    = 5 * 31 * 61-1240=8215


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


    Q4) Find the smallest number which when divided by 11, 12 and 15 gives remainders 1, 2 and 3 respectively.


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


    11a + 1 = 12b + 2 = 15c + 3
    now 15c + 3 is divisible by 3
    now 12b + 2 mod 3 = 2
    so this is not possible in any case


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


    Q5) If a = 13 then find the value of a^5 – 14 a^4 + 14 a^3 – 14 a^2 + 14a – 1


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


    Method1- (a-1) * (a^4-13a^3+a^2-13a+1)
    Put a=13
    12(13^4-13^4+13^2-13^2+1)
    Ans: 12

    Method 2
    a^5 - 13a^4-a^4+13a^3+a^3-13a^2-a^2+13a+13-1
    a^4 (a-13) -a^3(a-13) +a^2 (a-13) -a(a-13) +12
    since a-13 = 0 so 12

    Method3- Every question of this type has some pattern and in cat u will never find any question which will take more than 1-2 minutes .. If that is the case then u are not following the basic approach or options to solve that question
    here a^5-14a^4+14a^3-14a^2+14a-1
    here i m concentrating on 14 .. and sign +-+-+- so it will follow same pattern
    if i replace 14 to 2 then also it will follow same pattern but to apply these things you have to give time .
    then a^5-2a^4+2a^3-2a^2+2a-1
    so 13= 1
    so 1-2+2-2+2-1=0
    so our ans is 1-1=0
    so in every case our ans will follow same pattern
    so OA will be 13-1=12
    if here 14=3 and value at y=2 then value will be 1


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


    Q6) If |A| is less then or equal to 6 and |B| is less then or equal to 8, what is the difference between the maximum and minimum possible value of |A-B|


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


    |A| < = 6 so -6 < = A < = 6
    |B| < = 8 so -8 < = B < = 8
    when A=B then |A-B| will be min=0
    when A is positive and B is negative then it will be max or B is positive and A is negative
    A=6 and B=-8 so A-B=14 so |A-B|=14
    so max-min=14-0=14


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


    Q7) In a room 2/5 of all the people are wearing gloves and 3/4 of the people are wearing hats. What is the minimum number of people in the room wearing both hat and gloves


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


    At-least 15% of the total population wears both hat and gloves.
    20 is the least total population where 2/5 and 3/4 can be a whole number.
    so 15% of 20 is 3.


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


    Q8) If a is one of the roots of a^5 – 1 = 0 and a# 1, then what is the value of a^15 + a^16 + a^17 + …. + a^50


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


    a^5-1=0
    (a-1)(1+a+a^2+a^3+a^4)=0
    so 1+a+a^2+a^3+a^4=0
    now a^15(1+a+a^2+a^3+a^4)+a^20(1+a+a^2+a^3+a^4)+
    a^25(1+a+a^2+a^3+a^4+a^5).................a^45((1+a+a^2+a^3+a^4)+a^50
    so every value except a^50 will be zero
    now a^5=1
    so a^50=1
    so OA=1


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


    Q9) Ram, a milkman buys pure milk and adds some water in it before selling. He sells the mixture at a price 10% less than the price of pure milk and makes a profit of 10%. Find the quantity (in liters) of water than he adds to every two liters of pure milk.


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


    Method1= C.P of 1 litre pure milk = 100
    S.P. of 1 litre milk + water = 90 ( 10 % profit)
    C.P of 1 litre milk + water = 90/ 1.1
    100 -------- 1 litre pure milk
    90/1.1------ 9/11 litres
    water/litre = 2/11
    To 9/11 liter pure milk, water added = 2/11
    so to 2 liters pure milk, water added = 4/9

    Method2- Ram spends 100% for milk and sells the mixture for 90 %
    so he loses 10 % of milk, which he compensates by 90 % of water.
    10% -> 90 %
    He compensates for 10% loss and he also makes 10% more so on the whole he will make 20 % (of the milk price)
    So,90% of money of water(or milk) is equivalent to 20% of the profit
    hence ratio 2/9 per litre . So for 2 litres it would be 4/9


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


    Q10) Six jars of cookies contain 18 , 19 , 21 , 23 , 25 and 34 cookies respectively. One jar contains almond cookies only. The other 5 jars contain no almond cookies. A takes three of the jars and B takes two of the others. Only the jars of almond cookies remains. If A gets twice as many cookies as B , how many almond cookies are there ?


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