Official Quant thread for CAT 2013


@jain4444 Thanks for the solution.
The latest registration number issued by the Delhi Motor Vehicle Registration Authority is DL-5S 2234 . If all the numbers and alphabets before this have been used up then find how many vehicles have a registration number starting with DL- 5 ?plz provide detailed explanation.....ans=182216
number using alphabets less than S = 10*10*10*10*18 - 18 = 179982
BUT WHY DID YOU SUBTRACT 18???
@ani6 said:
@jain4444 Thanks for the solution.The latest registration number issued by the Delhi Motor Vehicle Registration Authority is DL-5S 2234 . If all the numbers and alphabets before this have been used up then find how many vehicles have a registration number starting with DL- 5 ?plz provide detailed explanation.....ans=182216number using alphabets less than S = 10*10*10*10*18 - 18 = 179982BUT WHY DID YOU SUBTRACT 18???
because i considered that "0000" was not a valid number

Triangle having perimeter = 100.

all side integeral.
How many triangle possible. ?

@jain4444 334 numbers?

n^2 + n mod 9 = 2

so,every 9 numbers,there would be 3 numbers on dividing it by 9 leaves remainder 2

A positive integer is written on each face of a cube. On each vertex, the product of the 3 numbers on the faces containing the vertex is written. If the sum of the numbers on the vertices is 1298, what is the sum of the numbers on the faces?
@jain4444 said:
A positive integer is written on each face of a cube. On each vertex, the product of the 3 numbers on the faces containing the vertex is written. If the sum of the numbers on the vertices is 1298, what is the sum of the numbers on the faces?
let the nos on faces of cube be a,b,c,d,e,f where a and f are on opposite faces.

so a/c to problem:
(abc+abd+ace+ade)+(fbc+fbd+fce+fde)=1298
a(bc+bd+ce+de)+f(bc+bd+ce+de) =2*11*59;
also bc+bd+ce+de =(b+e)(c+d)
so, (a+f)(b+e)(c+d)=2*11*59
compare both sides,
so a+f+b+e+c+d=2+11+59=72


@jain4444 said:
A positive integer is written on each face of a cube. On each vertex, the product of the 3 numbers on the faces containing the vertex is written. If the sum of the numbers on the vertices is 1298, what is the sum of the numbers on the faces?
ace+ade+acf+adf+bce+bde+bcf+bdf=1298
a(ce+de+cf+df) + b(ce+de+cf+df)=1298
(a+b)(ce+de+cf+df)=1298
(a+b)(c+d)(e+f)=1298=11*2*59

OA=72.
@jain4444 said:
For how many positive integers n ‰¤ 1000, is the digit root of n^2 + n + 1 equal to 3?P.S - The digit root of a number is a single digit value obtained by iterative digit sums. For example, the digit root of 31^2 + 31 + 1 = 993 would be 3 since 9 + 9 + 3 = 21 , 2 + 1 = 3.
1,4,7,10,13...... So on
1000=1+(n-1)3
334 numbers
Find the number of pairs of coprime integers (n,m) such that 1≤n≤m≤20.
K is a 3 digit number .K1, K2, K3 are numbers obtained when K is in base 5,7 and 9 respectively. The units place in K1, K2, K3 is 2. How many such possible K values are there a) 0 b) 1 c) 2 d) 3

Selling price of a shirt and a coat is Rs. 4000. The cost price of a shirt is 58.33% of the cost price of a coat and so amount of profit on both the shirt and coat is same, then the price of the shirt could be:


a) 2100
b) 2525
c) 2499
d) 1120

@jain4444 said:
Find the number of pairs of coprime integers (n,m) such that 1≤n≤m≤20.
133??
@sa1m007 said:
K is a 3 digit number .K1, K2, K3 are numbers obtained when K is in base 5,7 and 9 respectively. The units place in K1, K2, K3 is 2. How many such possible K values are there a) 0 b) 1 c) 2 d) 3
d) 3
@Dexian Plzz ....... Tell me what is ur Approach !!
@sa1m007 said:
@Dexian Plzz ....... Tell me what is ur Approach !!
5*7*9 = 315
315 wen represented in base 5, 7, 9 will havee units digit as 0 in all 3 cases.
so 317 will have 2 in its units place in all 3 bases..
next number shud be 315*2+2=632
next 315*3+2=947...

@sa1m007 said:
K is a 3 digit number .K1, K2, K3 are numbers obtained when K is in base 5,7 and 9 respectively. The units place in K1, K2, K3 is 2. How many such possible K values are there a) 0 b) 1 c) 2 d) 3
LCM (5 , 7 , 9) = 315

so , number is in form of 315n + 2

=> n could have = 1 or 2 or 3 , 3 values
@jain4444 128?

Another Question came like this ........ 1024*2065 + 2564*2653 + 5216*5645 is in octal form ........ find number of digit 6 that comes after multiplication ?? .......... Can u plzz help !!

@Shrutim90 said:
Selling price of a shirt and a coat is Rs. 4000. The cost price of a shirt is 58.33% of the cost price of a coat and so amount of profit on both the shirt and coat is same, then the price of the shirt could be:a) 2100b) 2525c) 2499d) 1120
d)1120
@Shrutim90 said:
Selling price of a shirt and a coat is Rs. 4000. The cost price of a shirt is 58.33% of the cost price of a coat and so amount of profit on both the shirt and coat is same, then the price of the shirt could be:a) 2100b) 2525c) 2499d) 1120
SP of shirt = x
SP of coat = (4000 - x)

let CP of coat = 300y
CP of shirt = 175y

x - 175y = 4000 - x - 300y
=> 2x + 125y = 4000

from option only 1 value will satisfy this i.e. 2100