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) ]]>

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) ]]>

(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) ]]>

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 ]]>

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 ]]>

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 ]]>

Last and first place has to be 5.

5 _ _ _ _ _ _ _ 5

10 x 10 x 10 x 1 x 1 x 1 = 1000 ]]>

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 ]]>

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 4 = 1

817^673 mod 25 = 12

4k+1 = 25q +12

k = 9..

so remainder = 37 ]]>

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 ]]>

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 ]]>

(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% ]]>

Say a 3 digit number is abc.

Now there are 4 ways to choose a, 4 ways for b and 4 ways for c = > There are 4 *4 * 4 = 64 three-digit numbers that can be made using 1,2,3 and / or 4.

Let’s write all these numbers one below another to add them up. Now each digit would appear 16 times in ones place.

Their sum = 16 *(1 + 2+ 3 + 4) = 160

Similarly the tens place would add up to 160 and the hundreds place too.

So the actual sum = 160 (1 + 10 + 100) = 160 * 111 = 17760

]]>