Quant Boosters  Quant Mixed Bag  Set 1

Number of Questions  30
Topic  Quant Mixed Bag
Solved ? : Yes
Source : Collection of solved questions from mentors like
Sabyasachi Mishra, IIT Kharagpur, CAT 100 percentiler
Saquib Hasnain (IIFT)
Tanveer Iqbal (Aduro Classes)
Ashutosh Mishra (CatOMania)

Q1) Find the ordered pairs of positive integer solutions for 1/x + 1/y = 1/8

[Credits : Saquib Hasnain]
(x+y)/xy = 1/8
8x + 8y = xy
8xxy +8y +6464 = 0
x(8y)  8 (8y) = 64
(x8 ) (y8 ) = 64
64 can be expressed at 2^6 can be expressed as a product of two factors in 7 ways (as order of factor will matter in this case,1x64 and 64x1 will be considered as two cases)

Q2) A Man buys 2 articles for 1980 each and he gains 10% on the first and loses 10% on the next. Find his total gain/loss percent ?

[Credits : Saquib Hasnain]
The number 1980 is irrelevant here.
if the CP is same and if I gain x% on one and loss x% on the other it is always no profit no loss..
example CP = 100 each.. 10% profit = 110 and 10% loss = 90
Total CP = 200. total SP = 110+90 = 200

Q3) Product of the real solution x of the quadratic equation x^2 + 4x  4 = 0.

[Credits : Saquib Hasnain]
First take x > 0 and find the roots..it will be 2root(2) 2 and 2root(2)2..we can neglect the second one..since it is not x > 0
not take x < 0 and find the roots for x^24x4..you will get..
2root(2) +2 and 2root(2)+2..we can neglect the second one..since it is not x < 0
so product of roots is 
{2root(2) 2}{2root(2)+2} which is  (2root(2)  2)^2

Q4) Two dogs start running around a 410 m circular track from same point at the same time in opposite direction and with speed ratio 7:9. How far from the starting point will they meet for the 7th time?

[Credits : Saquib Hasnain]
Divide the circle into 16 parts(since moving in opp direction, number of meeting points is sum of ratio of speed)..speed ratio is 7:9..so everytime 1st guy moves 7,other moves 9, they meet at one point..for 7th meet, this guy has to move 7x7 = 49 parts..16x3 = 48 parts brings it to starting point..so his 49th movement makes him meet for the 7th time..so he needs to move 1 part from the starting points..which is 410/16 = 25.625

Q5) How many number of 8 digit palindrome is divisible by 5 ?

[Credits : Saquib Hasnain]
Last and first place has to be 5.
5 _ _ _ _ _ _ _ 5
10 x 10 x 10 x 1 x 1 x 1 = 1000

Q6) A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately,A beginning in how many days,the work will be completed ?

[Credits : Saquib Hasnain]
let the total work be 36 units.
A can do 36/9 = 4 units/day
B can do 36/12 = 3 units/day
In two days, the can complete 7 units
to complete 35 units, they will take 10 days..
left units is 1 which A will complete on the 11th day, taking 1/4th day.
so 10 1/4 days

Q7) When a 2digit number is reversed, the new number is reduced by 63 and the sum of these individual numbers is 9. Now if these same numbers are converted into base x the larger number becomes 5 times that of the smaller one.The value of x?

[Credits : Saquib Hasnain]
9(ab) = 63
a  b = 7
a + b = 9
a =8 , b = 1
8x+1 = 5(x+8 )
3x = 39
x = 13

Q8) 817 ^ 673 mod 100 = ?

[Credits : Saquib Hasnain]
817^673 mod 4 = 1
817^673 mod 25 = 12
4k+1 = 25q +12
k = 9..
so remainder = 37

Q9) If the equation x^4  4x^3 + ax^2 + bx + 1 = 0 has 4 positive roots, then a + b = ?

[Credits : Saquib Hasnain]
Product is 1..sum is 4..all roots are positive..so all of them have to be 1..
a = 4C2 = 24/4 = 6
b = 4C3 = 4
so a+b = 64 = 2

Q10) A train after covering 1200 km meets with an accident and due to this it proceeds at 2/3 of its original speed and arrives at the station in 5 hours. Had the accident taken place after covering a distance of 300 km further, it would have arrived 2.5 hours earlier. What is the speed of the train ?