Official Quant thread for CAT 2013

In a right angled triangle, area and perimeter are equal in magnitude. If inradius is 20% of the circum radius, then the area of the triangle is ???

Which one of the following conditions must p, q and r satisfy so that the following system of linear simultaneous equations has at least one solution, such that p + q + r ≠ 0?

x+ 2y – 3z = p

2x + 6y – 11z = q

x – 2y + 7z = r


a. 5p –2q – r = 0

b. 5p + 2q + r = 0

c. 5p + 2q – r = 0

d. 5p – 2q + r = 0

Let a, b, c, d be four integers such that a+b+c+d = 4m+1 where m is a positive integer. Given m,

which one of the following is necessarily true?

a. The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2–2m+1

b. The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2+2m+1

c. The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2–2m+1

d. The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2+2m+1


I don hav OA..Plz share ur approach

If a = ten's digit of 29^543 and b = ten's digit of 72^342, the ratio a/b is ????

1. positive integral soln a+b+c }

2. Find the total number of ways in which 6 distinct rings can be put in 4 empty bags of different colour??

If log(10)x - log(10) x^1/2 = 2 log(x)10, then the possible value of x is given by

a)10

b)1/100

c)1/1000

d)100

e)none


don hav OA...share ur approach plz

If (1/3)log(3) M + 3 log(3) N = 1 + log(0.008) 5, then

a)M^9 = 9/N

b)N^9=9/M

c)M^3=3/N

d)N^9=3/M


Don hav OA...plz share the approach

Q1. In how many ways can we arrange 5 people in 8 seats in a straight line?
Q2. In how many ways can we arrange 5 out of 8 people in 5 seats in a straight line??

Two sticks of equal length are broken into 2 unequal pieces each. If p and q are the lengths of the smaller pieces of the 2 sticks and p>q, then the probability that p >= 4q is ???

@Homer1 check it 😃

if a,b,c are the sides of a triangle, then a^2+b^2+c^2 = k*(ab+bc+ca).
then the range of possible values of k is ???
1. 1 2. 1 3. 1 4. 0
Don't have the OA..

How many ways we can arrange 8 people round a square table with 2 seat on each side??


1^781 + 2^781 ....+ 9^781

Don't have OA.

Find the sum of the values of x such that |x+2| + |x-3| + |x+4| + |x+5| = 18
a.2.5 b.-3.5 c.-4.5 d.-5
Please share the approach as well.

can any one tell me the applications of digital sum

A man arrives at a railway station 1.5 hr before the time at which he had ordered his carriage to meet him. He walks at the rate of 4 kmph and meets the carriage 8km from his house and reaches 1 hour earlier than usual time. What's the speed of the carriage and distance from the station to his house? Approach pls 😃 Thanks in advance 😃

find the number of even factors of 40320 which can be expressed as a difference of square of a natural number in atleast one way?

approach please?

A number is formed by multiplying the 1st 100 natural number multiples of 5. What will be the highest power of 25 in that number ? solution? @Shubh.i @anandmadhav

  • 24
  • 124
  • 62
  • NOTA

0 voters

How many natural numbers are there with 24 factors where 2,3,5 are the only prime factors ?

a) 36

b) 27
c) 12

d) 9
Solution @anandmadhav @Shubh.i

For the following question, someone please help with approach