# Quant Lessons by Saquib Hasnain - Set 1

• Saquib Hasnain did his MBA from IIFT, Delhi and has rich experience in mentoring CAT aspirants in Quant and Data Interpretation  & Logical Reasoning sections. He is currently working as the Academic head at Vistamind, Kolkata.

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

(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)

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 ?

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

Product of the real solution x of the quadratic equation x^2 + 4|x| - 4 = 0.

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

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?

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

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

_ _ _ _ _ _ _ _
Last and first place has to be 5.
5 _ _ _ _ _ _ _ 5
10x10x10x1x1x1
= 1000

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 ?

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

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?

9(a-b) = 63 ....a-b = 7
a+b = 9
a =8 , b = 1
8x+1 = 5(x+8 )
3x = 39
X = 13

817 ^ 673 mod 100 = ?

817^673 mod 4 = 1
817^673 mod 25 = 12
4k+1 = 25q +12
k = 9..
so remainder = 37

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

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

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 ?

So say the speed is v and 2/3v.. the guy saves 2.5hours..if the accident happens 300 further..so he saving that 2.5 hours in that 300m..
Time taken to cover 300m at speed v is 300/v
Time taken to cover 300m at speed 2/3v is 300/(2v/3)
Difference is of 2.5hours..
So 300 (3/2v - 1/v) = 2.5
300 (1/2v) = 2.5
V = 60

After three successive raises, Aftab’s salary became equal to 378/125 of his initial salary. By what percentage was the salary raised the first time if the third rise was twice as high (in percentage) as the second rise and the second raise was twice as high (in percentage) as the first rise?(a) 10% (b) 15% (c) 20% (d) 25%

378 = 6 x 63 = 6 x 7 x 9
125 = 5 x 5 x 5
so, (1 + 1/5) (1 + 2/5) (1 + 4/5)
1/5 = 20%, 2/5 = 40% and 4/5 = 80%

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