CAT Quantitative Aptitude Questions 2022 – PaGaLGuY

Approach?

In how many ways can five letters be placed in five envelopes such that exactly one letter goes into its corresponding envelope ?

Find smallest 10 digit no., all distinct(0-9) which is divisible by 11.

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Q. What is the sum of all natural numbers which are less than 10^100 and are co-prime to it?

please explain in detail!!

Approach?

how many integral solutions exist for the equation 2x^2+ 3y=81 where x,y greater than or equal to zero?

No of non negative integral solutions to a+b+c<=10? Pls suggest the method too.

Aman had 10 packs of cookies, and these packs had 10 different consecutive numbers of cookies in them. If Aman was to choose three packs, then what percent of these triplets would form an increasing AP, with respect to the number of cookies contained in the three packs?


Two squares are chosen at random from the small squares drawn on a chessboard. What is the chance that the two squares chosen have exactly one corner in common?

If the sum of lengths of three sides of a rectangle is 100 units, then find the maximum possible area of the rectangle ?

(1) 1110.9 sq. units

(2) 1250 sq. unit

(3) 990 sq. units

(4) 1008 sq. units

(5) 1225 sq. units

I don't know the ans. please share the approach

Two cyclists are traveling at a speed of 3 km/hr and 10 km/hr around a circular track. What should be the ratio of number of distinct points that they would meet on that track if they travel in the same direction first and in the opposite direction next?

(1) 7 : 13

(2) 3 : 10

(3) 3 : 7

(4) 30 : 13

(5) Cannot be determined

do share the approach...

Can someone help me with this?

How many six-digit numbers can be made by using the first 6 natural numbers such that the digit at the unit's place is greater than the digit at the hundred's place and the number thus formed is a multiple of 4? (Repetition of digits is not allowed.)

(1) 96

(2) 108

(3) 114

(4) 78

(5) 120

How many 4-digit positive integral numbers are there in base 7, if you are counting the numbers in the same base system?

(1) 2058

(2) 5666

(3) 6000

(4) 6666

(5) None of these

What is the most efficient way of solving this?

In this question.. i got a+b+c should be either 5 10 or 15. For a+b+c=5 i got 6 cases. Now for a+b+c=10 how to consider the upper limit as 6 for each of a,b and c?? Also, if there is any other better method to solve..please share..

Approach??

TITA

Suppose 'n' is a positive integer. When [n^2 - 1) is divided by 6, it leaves a remainder of 2. Suppose 'm' is the remainder when 'n' is divided by 7. How many different values can 'm'take?

PLEASE REMEMBER TO MENTION THE APPROACH TOO.THANKS.

How many positive integral values of (x,y) satisfy the equation x^2 - y^2 = 357? Please share approach also.