Official Quant thread for CAT 2013

King " Bhai Mere " has a cellar of 1000 bottles of delightful and very expensive wine.

A neighboring queen plots to kill him and sends a servant to poison the wine. Fortunately (or say unfortunately) the king's guards catch the servant after he has only poisoned one bottle. Alas, the guards don't know which bottle but know that the poison is so strong that even if diluted 100,000 times it would still kill the king. Furthermore, it takes two days to have an effect. The king decides he will get some of the prisoners in his vast dungeons to drink the wine.


Being proficient in logic and MATH he knows he can identify the poisoned bottle and will still be able to drink the rest of the wine (999 bottles) at his anniversary party in 3 days time.

1) What is the minimum number of prisoners "Bhai Mere" has to sacrifice to identify the wine bottle ?

2) What is the minimum number of prisoners "Bhai Mere" has to sacrifice if he has to use minimum possible wine in the process ?

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B is a biased die. Chances of it showing a two is 1/4.Find the minimum nmbr of times B must be rolled so tht th chance of a two appearing at least once is at least 1/2.


2
4
3
5
6

In a number system the product of 44 and 11 is 2124. The number 3111 of this system, when converted to the decimalnumber system, becomes ?

Please explain

Let X be a four-digit positive integer such that the

unit digit of X is prime and the product of all digits

of X is also prime. How many such integers are

possible?

A. 4 B. 8 C. 12

D. 24 E. None of these


If x and y are real numbers, then the minimum value

of x^2 + 4xy + 6*y^2 – 4y + 4 is

A. – 4 B. 0 C. 2

D. 4 E. None of the above


A manufacturer has 200 litres of acid solution which

has 15% acid content. How many litres of acid

solution with 30% acid content may be added so

that acid content in the resulting mixture will be

more than 20% but less than 25%?

A. More than 100 litres but less than 300 litres

B. More than 120 litres but less than 400 litres

C. More than 100 litres but less than 400 litres

D. More than 120 litres but less than 300 litres

E. None of the above

A manufacturer produces two types of products- A

and B, which are subjected to two types of

operations, viz. grinding and polishing. Each unit

of product A takes 2 hours of grinding and 3 hours

of polishing whereas product B takes 3 hours of

grinding and 2 hours of polishing. The manufacturer

has 10 grinders and 15 polishers. Each grinder

operates for 12 hours/day and each polisher 10

hours/day. The profit margin per unit of A and B are

Rs. 5/- and Rs. 7/- respectively. If the manufacturer

utilises all his resources for producing these two

types of items, what is the maximum profit that the

manufacturer can earn?

A. Rs.280/- B. Rs.294/- C. Rs.515/-

D. Rs.550/- E. None of the above


In an equilateral triangle ABC, whose length of each

side is 3 cm, D is a point on BC such that

BD = 1/2CD. What is the length of AD?

A. root5 cm B.root6 cm C. root7 cm

D. root8 cm E. None of the above



In the AMS library, there are 8 books by Stephen Covey and 1 book by Vinay Singh in shelf A. At the same time, there are 5 books by Stephen Covey in shelf B. One book is moved from shelf A to shelf B. A student picks up a book from shelf B. Find the probability that the book by Vinay Singh.


(1) is still in shelf A
(a) 1/3 (b) 8/9
(c) 3/4 (d) none of these


(2) is in shelf B
(a) 3/54 (b) 4/54
(c) 5/54 (d) none of these

(3) is taken by the student
(a) 3/54 (b) 1/54
(c) 2/27 (d) none of these

Two dice are rolled one after the other. The probability that the number on the first is smaller than the number on the second, is (a) 1/2 (b) 7/18 (c) 3/4 (d) 5/12 (e) None of these

A owes B Rs 456.75 payable 4 and a half months hence and B owes A Rs 455.51 payable 3 months hence. If they agree to settle their account by a ready money payment, what sum should be paid over and to whom, reckoning the rate of true discount at 4% per annum?

A man derives his income from the investment of Rs. 4150 at a certain rate of simple interest and Rs. 3500 at 1% higher. His whole income for 4 years is Rs. 1211. Find the rates of interest.

If the compound interest on a certain sum for 2 years at 3% be Rs 101.5 , what should be the simple interest?

LCM of three natural numbers=150. How many set of three natural numbers are possible?


112

48

178

142

NOT


Dont just post the answer. Give your method too !


"BHAI MERE (P) LTD " wants to hire 5 students for different posts.priority(rank) for these posts varies from 1 to 5
a student guessed the rank as A,B,C,D,E......
later upon declaration of result it was found tht not only did he get each student out of his/her position,none of the students in his ranking correctly followed her immediate predecessor.
another student guessed D,A,E,C,B..even his guess was wrong.
it was found tht he had got 2 positions correct and 2 students in his ranking correctly followed their immediate predecessors...
which of the following is true abt the correct rank order?????


1>>A got 3rd position
2>>B got 4th postn
3>>C got 2nd postn
4>>D got 1st postn
5>>E got 4th postn
6>>wtf is it?? :mg:

@Shubh.i >>bhai 11pm wale quant sessions kbse lena str kr rahe ho????? 😁mgmg😁

5 identical dice are thrown. Find the total number of different outcomes possible.

From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a

consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and

counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to

step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated

would be the contender numbered 2.

Q -
Which position should a contender choose if he has to be the leader?

A. 3 B. 67 C. 195 D. 323 E. 451


|x-10|+|x-20|+|x-30|+|x-40|=178

solutions nikalne ka method?

A person borrows Rs.5,00,000 from a bank and under the agreement he agrees to pay Rs.50,000 at the end of each 6 months together with an interest of 5% on the opening balance of each period.Find the total interest paid by him till clearing the loan.