Official Quant thread for CAT 2013

Any Suggestions on Books for Quant and LR ??

From mock 3:

QuantExpert - TestCentre

ABC is a triangle with /_CAB = 15' /_ABC = 30'. If M is the midpoint of AB then /_ACM =
(a) 15' (b) 30' (c) 45' (d) 120'


In how many ways 3600 can be written as multiple of its distinct factors.

In hw many ways 3600 can be written in 3 distinct factors?

A train met with an accident 60km away from station A. It completed the remaining journey at 5/6th of the original speed and reached station B 1hr 12mins late. Had the accident taken place 60km further, it would have been only 1hr late. what was the original speed of the train?

What is the distance b/w A and B?















any shortcut for this ??

If k is a natural number such that 1≤ k ≤ 78, for how many values of k is the tens digit of 31k equal to 6?

a8

b15

c7

d16

How to solve?

7/b + 8/a=-1
a,b-non zero integers
for how many values of a,b is a+b positive?

There are four machines and it is known that exactly two of them are faulty. They are tested in random order till both the faulty machines are identified. The probability that only 2 tests will be equired to identify the 2 faulty machines is

a) 2/3

b) 1/6

c) 1/3

d) 5/6


Shudnt d answer be 2/3?? total ways=4!/2!2!=6, favourable ways when 2 D's are in the first 2 attempts and ok machines in last 2 attempts ie=2*2=4...hence prob=4/6=2/3..where am i going wrong???

😲

All the positive divisors of 2010 are arranged in a straight line not in a particular order. In how many ways they can be arranged so that a pair of any two consecutive numbers, selected at random, is co prime

Consider two positive integers 'a' and 'b' such that (a^a)*(b^b) is divisible by 2000. What is the least possible value of the product 'a*b' ?

Consider two positive integers 'a' and 'b' such that (a^b)*(b^a) is divisible by 2000. What is the least possible value of the product 'ab' ?

x = ± 1 ± 2 ± 3 ± 4 ± 5 ± 6 ± 7 ± 8 ± 9 ± 10 ± 11 ± 12 ± 13. How many different possible values can x take ?

A = _ 4 _ 5 _ 6 _ ........... _ 99 _ 100 _ 101

In how many ways _ can be replaced by - or + (subtraction or addition symbols) such that A = 0 ?

A rope 20m long is randomly cut into two segments, each of which is used to form the perimeter of a square.

(a) Find the probability that the larger square has an area greater than 9 m^2

(b) Find the probability that the total area of the two squares is greater than 20.5 m^2

Mary has enrolled in 6 courses: Chemistry, Physics, Math, English, French and Biology. She has one textbook for each course and wants to place them on a shelf. How many ways can she arrange the textbooks so that the English textbook is placed before the French textbook?



Help Puys !

Only using Euler's toitent please.
Step by step

Rem [ (2^2002 )/ 1001 ]

A shopkeeper sold a certain number of toys all at a certain price.The number of toys he sold is a three digit number with the tens and the units digit being the same and non zero.The price of each toy is a two digit number.By mistake he reversed the digits of both numbers i.e number of toys sold and the price of each toy.In doing so he found that at the end of the day,the stock account showed 792 items more than what it actually was.

what could be actual number of toys sold ?

A. 911
B. 119
C. 199
D. 991

OA : A.

But I couldn't get the answer.Here's my approach :

N = 100a + 10b + b = 100a + 11b
After reversing N = 100b + 10b + a = 110b+a

Subtracting them we get : 99(b-a)= 792 => b-a = 8
hence b=9 and a = 1.
Original number = 100a+11b = 199. What wrong with my approach ??


how many even natural numbers divisiible by 5 can be foormed with the digits 0,1,2,3,4,5,6 repitition not allowed?

how many even natural numbers divisiible by 5 can be foormed with the digits 0,1,2,3,4,5,6 repitition not allowed?

1-how many numbers smaller than 2*10^8 and are divisible by 3 can be written by means of digit 0, 1 and 2 ( exclude singlew and double didgits )

2-how many different 7-digi number are there the sum of whose digits are odd?