Official Quant thread for CAT 2013

@sparklingaubade said:
India and Brazil play the Soccer World Cup final in which India defeats Brazil 10 €“ 4. In how many different ways could the goals have been scored given that Brazil never had a lead over India during the match?
41+4 = 45?
Edit : Including 0-0
What will be the remainder when 11111...27 times is divided by 999?
@audiq7 said:
What will be the remainder when 11111...27 times is divided by 999?
111*(100100100...25 digits divided by 9)
=111*(the number is divisible by 9)

so i think the rem is 0..

correct....?
@audiq7 said:
What will be the remainder when 11111...27 times is divided by 999?
0?
@shashankbapat23 soln?
@audiq7 said:
@shashankbapat23 soln?
999=37*3^4
111 is divisible by 37 hence 1111.....27 times will also be divisible
1111...27 times ,sum is 27 which is also divisible by 3^4
hence 0
Mark 1: If the questions can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
Mark 2: If the question can be answered by using either statement alone.
Mark 3: If the questions can be answered by using both statements together, but cannot be answered using either statement alone.
Mark 4: If the question cannot be answered even by using both statements together.

Each question is followed by two statements, A and B. Answer each questions using the following instructions :

Question:
Three professors A, B and C are separately given three sets of numbers to add. They were expected to find the answers to 1 + 1, 1 + 1 + 2 and 1 + 1 respectively. Their respective answers were 3, 3 and 2. How many of the professors are mathematicians?

Statement A : A mathematician can never add two numbers correctly, but can always add three numbers correctly.
Statement B : When a mathematician makes a mistake in a sum, the error is +1 or €“ 1.
@shashankbapat23 is it A?
@shashankbapat23 is it A?
@shashankbapat23 is it A?

no man

@audiq7
@sparklingaubade said:
One writes 268 numbers around a circle such that the sum of 20 consecutive numbers is always equal to 75. The numbers 3, 4 and 9 are written in positions 17, 83 and 144 respectively. Find the number in position 210.
HCF(20, 268) = 4
means numbers will start repeating after 4
Nos. are a, b, c, d, a, b, c, d, a, b, c, d, ......

17th and 1st are same, 83rd and 3rd are same and 144th and 4th are same

So, 3 + 4 + 9 + x = 75/5 = 15
x = -1

So, 2nd number is -1
=> 210th number is -1
@sparklingaubade said:
India and Brazil play the Soccer World Cup final in which India defeats Brazil 10 €“ 4. In how many different ways could the goals have been scored given that Brazil never had a lead over India during the match?
Application of Catalan number

So, no of ways = C(14, 4) - C(14, 3) = 637
@shashankbapat23 pm me the solution of mathematician prblm
@shashankbapat23 said:
Mark 1: If the questions can be answered by using one of the statements alone, but cannot be answered using the other statement alone.Mark 2: If the question can be answered by using either statement alone.Mark 3: If the questions can be answered by using both statements together, but cannot be answered using either statement alone.Mark 4: If the question cannot be answered even by using both statements together.Each question is followed by two statements, A and B. Answer each questions using the following instructions :Question:Three professors A, B and C are separately given three sets of numbers to add. They were expected to find the answers to 1 + 1, 1 + 1 + 2 and 1 + 1 respectively. Their respective answers were 3, 3 and 2. How many of the professors are mathematicians?Statement A : A mathematician can never add two numbers correctly, but can always add three numbers correctly.Statement B : When a mathematician makes a mistake in a sum, the error is +1 or €“ 1.
option 2
@shashankbapat23 said:
Mark 1: If the questions can be answered by using one of the statements alone, but cannot be answered using the other statement alone.Mark 2: If the question can be answered by using either statement alone.Mark 3: If the questions can be answered by using both statements together, but cannot be answered using either statement alone.Mark 4: If the question cannot be answered even by using both statements together.Each question is followed by two statements, A and B. Answer each questions using the following instructions :Question:Three professors A, B and C are separately given three sets of numbers to add. They were expected to find the answers to 1 + 1, 1 + 1 + 2 and 1 + 1 respectively. Their respective answers were 3, 3 and 2. How many of the professors are mathematicians?Statement A : A mathematician can never add two numbers correctly, but can always add three numbers correctly.Statement B : When a mathematician makes a mistake in a sum, the error is +1 or €“ 1.
4?
@shashankbapat23 said:
The number 165 is split into three parts €“ two perfect squares and one perfect cube. If all the three parts are positive and distinct,find the three parts.A. One of the perfect squares is 36.B. The perfect cube is the greatest of the three parts.Each question below is followed by two statements, A and B. Answer each question using thefollowing instructions:Choose 1 if the question can be answered by one of the statements alone, but cannot be answered by using the other statement alone.Choose 2 if the question can be answered by using either statement alone.Choose 3 if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.Choose 4 if the question cannot be answered even by using both the statements together.
36,4,125
36,121,8

option 3
@audiq7 said:
What will be the remainder when 11111...27 times is divided by 999?
To check by 9
Sum of digits is 27 which is divisible by 9
111--------------27times is divisible by 111

So,remainder is 0
What is the maximum number of quadratic equations that can be formed such that both of its roots are the roots of an equation having 4 roots?

4
6
10
12
@shashankbapat23 said:
Mark 1: If the questions can be answered by using one of the statements alone, but cannot be answered using the other statement alone.Mark 2: If the question can be answered by using either statement alone.Mark 3: If the questions can be answered by using both statements together, but cannot be answered using either statement alone.Mark 4: If the question cannot be answered even by using both statements together.Each question is followed by two statements, A and B. Answer each questions using the following instructions :Question:Three professors A, B and C are separately given three sets of numbers to add. They were expected to find the answers to 1 + 1, 1 + 1 + 2 and 1 + 1 respectively. Their respective answers were 3, 3 and 2. How many of the professors are mathematicians?Statement A : A mathematician can never add two numbers correctly, but can always add three numbers correctly.Statement B : When a mathematician makes a mistake in a sum, the error is +1 or €“ 1.
Statement A->1 mathematician 2 no-mathematician
Statement B->2 mathematician 1 non-mathematician
Mark-2

@Cat.Aspirant123 said:
What is the maximum number of quadratic equations that can be formed such that both of its roots are the roots of an equation having 4 roots? 461012
is the answer 12?