# 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)
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
8x-xy +8y +64-64 = 0
x(8-y) - 8 (8-y) = -64
(x-8 ) (y-8 ) = 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 + 4|x| - 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^2-4x-4..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 2-digit 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(a-b) = 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 = 6-4 = 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 ?

63

61

48

42

63

62

61

61