Official Quant thread for CAT 2013

What is the highest possible value of 'n' for which 31024 – 1 is divisible by 2n?

Two non-intersecting circles with radii 'r' units and '2r' units have their centres at a distance of 2√3r units. Find the length of the direct common tangent to the circles.

  • √10r units
  • √11r units
  • root13 r
  • 3r
  • 3√2units

0 voters

A test consists of 4 sections.Ech section has a maximum of 45 marks.Find the number of ways in which one can qualify the test .If the qualifying marks is 90.

5^x=6^y=30^7 then find (x*y)/(x+y)

There are 8 orators A,B,C,D,E,F,G,H. In how many ways can the arrangements be made so that A always comes before B and B always comes before C? Plz xplain...

  • 8!/6!
  • 8!/3!
  • 5!*3!
  • 8!/(5*3!)

0 voters

In how many ways can a black or white rook can be in placed on a chess board so that they are never in attacking positions.


Please explain the solutions

A train covers a certain distance moving at a speed of 60kmph .Howewer it halts for a fixed time every hour,its average speed would turn out to be 50kmph.for how much hour the train halt every houur?
ANS:10 min
PLz provide explanation.

Bell and Bolt run at speeds of 9 m/s and 9.9 m/s respectively on a 105-metre long circular track. They start simultaneously from the same point and run in opposite directions. How many times will they meet by the time Bolt covers 600a m?

ans:10 times

There are three urns numbered 1, 2 and 3. Urn 1 has 2 black balls and 3 white balls. Urn 2 has 1 black ball and 2 white balls. Urn 3 has 2 black balls and 1 white ball. A person who is blindfolded, picks a ball from urn 1, puts it into urn 2, picks a ball from urn 2 and puts it into urn 3 and finally picks a ball from urn 3 and puts it into urn 1. What is the probability that at the end of round 1 all the urns have exactly the same composition as they originally started off with?

a)5/8 b)2/5 c)3/5 d)1/4 e)3/8

In a class of 33 students, 20 play cricket, 25 play

football and 18 play table tennis. 15 play both

cricket and football, 12 play football and table

tennis, 10 play table tennis and cricket. Each

student plays at least one game. Find the number

of students.

11. How many students play only cricket?

a. 5 b. 6 c. 2 d. 3 e. 7

12. How any students play all the 3 games?

a. 5 b. 7 c. 2 d. 3 e. 4

13. How many students play only 2 games?

a. 16 b. 18 c. 20 d. 22 e. 24

how to solve questions like-

1.find range of |2x-1|-|x+5|+3

2.How many integral solutions are possible for eq-|2x-5|+|x-7|

pl. solve and explain.....

ramit and amit travel with uniform speed from A to B and B to A respectively, via the same route. ramit starts at 5:00 am while amit starts 4 hours later. they meet, on the way, at 1:10 pm. At what time do they reach their destinations, if both reach at the same time?

  • 6:30 pm
  • 7pm
  • 8pm
  • 7:30 pm

0 voters

Q.


If one root of the equation (I-m)x^2 + I x + 1 = 0 is double of the other root and is real, Find the greatest value of m ?

A. 9/8 (OA)
B. 8/7
C. 8/6
D. 7/5
E. 5/7


Anil and dhiraj run a 4 KM race on a circular track 400m long in d same direction.if their speeds are in d ratio3:2,how many times does anil pass dheeraj?

  • 5
  • 2
  • 4
  • 3

0 voters

AT what time b/w 8 o'clock n 9 o'clock will d hours and min hand make anangle of 72 degree wid each odr.

  • 8 hr 568/11
  • both a and b
  • none of dese
  • 8 hr 306/11

0 voters

A stamp collector decides to put all his stamps in a new album. If he puts 20 stamps on one sheet, there will be some left over; if he puts 23 stamps on a sheet, there will be at least one empty sheet left in the album. If the stamp collector is presented with an additional new album of the same kind, each sheet holding 21 stamps, he will be left with a total of 500 stamps. How many sheets are there in the first album?


a 11

b 12

c 13

d 10

e Data insufficient


Plz post detailed explanation. Thnx 😃


can someone please explain how to find remainders....please explain all the methods with examples

Log(base3x)3+log(base27)3x=-4/3 Value of x?

the product of 4 consecutive even numbers is always divisible by...?

Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4 (

A) 110 (B) 1,100 (C) 9,900 (D) 10,000 (E) 12,100