Official Quant thread for CAT 2013

A walks down an up-escalator and counts 150 steps. B walks up the same escalator and counts 75 steps. A takes 3 times as many steps in a given time as B. How many steps are visible on escalator?



Solution Please!!!

how many numbers between 200 and 1200 can be formed using the digits 0,1,2,3(without repetition)?

what is the shortest way to solve this type of qns:

There are four positive integers a,b,c and d such that a+b+c+d+abcd=m and
(abc+bcd+acd+abd)+(ab+bc+bd+ac+ad+cd)=(1154-m).find the value of m.

  • 484
  • 496
  • 502
  • no unique value of m exists
  • 512

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How many of the four digit numbers with non zero digits have the sum of their digits as 12

A. 165
B. 330
C. 132
D. 440

What is the unit digit of LCM of (3^2003 -1) and (3^2003+1) ? The Question has been asked earlier but I want the approach ??

OA is said to be
4 bt hw ?

In a game of basketball, the probability that Michael Jordan baskets the ball is three times mine. The probability never exceeds a third. To beat him in a game, I need to basket the ball myself and have Jordan miss his. If I pick my shot optimally, what is the maximum probability of my winning?

1/16

1/12

5/6

2/5

If p and q are prime numbers such that the numbers p + q and p + 7q are both perfect squares, the value of p is

2

19

31

53

None of these

A walks down an escalator, moving in upward direction, and counts 150 steps. B walks up the same escalator and counts 75 steps. A takes three times as many steps in a given time as B. How many steps are there on the escalator?

120

150

125

130

140

The probability that a randomly chosen positive divisor of 10^99 is not divisible by 10^88, is

How many ordered pairs (x, y), where x and y are integers, satisfy the inequality: (x + 2)^2 + (y – 3)^2 ≤ 4?

1

5

9

11

13

A hexagon is inscribed in a circle. Five of its sides have length 81 and the sixth side has length 31. The sum of the three diagonals from the vertex on the shortest side is

135

144

279

384

324

@ankurkhanna14

Hello All,

If 3 dice are thrown together then what is the probability that the sum of the numbers which come up is divisible by 5?



first check out all d possiblities

first for 5

1,1,3 = 3!/2! = 3

2,2,1=3!/2!=3

now for 10

3,3,4=3!/2!=3

4,4,2=3!/2!=3

2,2,6=3!/2!=3

4,5,1=3!=6

6,3,1=3!=6

5,3,2=3!=6

now for 15

6,6,3=3!/2!=3

5,5,5=1

6,5,4=3!=6

Total possiblities = 43

total outcomes are 6^3 =216


therefore, P(E)=43/216

hope u get it in more derived way.........

@ankurkhanna14

Hello All,

If 3 dice are thrown together then what is the probability that the sum of the numbers which come up is divisible by 5?



A spider has one sock and one shoe for each of its eight legs. In how many different orders can the spider put on its socks and shoes, assuming that, on each leg, the sock must be put on before the shoe?


8!
2^8*8!
(8!)^2
16!/2^8

Let ABCD be a convex quadrilateral with the area 's' and let P, Q, R and S be the midpoints of sides AB, BC, CD, and DA respectively. The sum of the areas of the triangles PBQ and RDS equals

3s/4

2s/3

s/4

cannot be determined

6-digit numbers are formed out of the numerals 1, 2, 3, 4, 5 such that each such number satisfies the following conditions:(i) a numeral either doesn't occur or occurs more than once, and(ii) all occurrences of a numeral occur consecutivelyThen the total number of such numbers is

Two different solutions of honey, milk and water are mixed with each other three times in varying

proportions. The concentration of honey and milk in the three resulting solutions are found to be

(10%, 16%), (12%, 12%) and (16%, x%) respectively. What is the value of x?

(a) 4 (b) 7 (c) 8 (d) 10

In how many ways can 2700 be written as a product of 8 distinct integers?

(a) 6 (b) 0 (c) 4 (d) More than 6

Overturning the common assumption that evolution occurs gradually over hundreds or thousands of years, researchers have found significant genetically-transmitted changes in laboratory populations of soil mites in just 15 generations, leading to a doubling of the age at which the mites reached adulthood and large changes in population size.______________.

1)The age of maturity of the mites in the tubes doubled over about 15 generations, because they were competing in a different way than they would in the wild.

2)The initial change in the mites' environment—from the wild into the laboratory—had a disastrous effect on the population, putting the mites on an extinction trajectory.

3)This is evolutionary rescue in action and suggests that rapid evolution can help populations respond to rapid environmental change.

4)Ecology and evolution are intertwined.