Official Quant thread for CAT 2013

@Subhashdec2 said:
well i think we should have also taken one more constraint into consideration that is n>=100-n2n>=100n>=50n/100-n100-n=xn=100-xsince n>=50x100-x/x100/x -1factors of 100=99*2=18remove factors >50which is only n=100and we are already not taking it into consideration since n=0 we are taking and n=100 we are not taking(as mentioned in my earlier post)so still it would be the same ans
but bhai among the 18 values, there are ones in which n is -ve also , so i think it's not necessary that n>=50

@techgeek2050 said:
but bhai among the 18 values, there are ones in which n is -ve also , so i think it's not necessary that n>=50
bhai those negative values and values less than 50 are for x

n=100-x

so n will automatically be greater than or equal to 50

If the ratio of sines of angles of a triangle is 1 : 1 : sqrt2 , then the ratio of square of the greatest side to sum of the squares of other two sides is

@vbhvgupta said:
If the ratio of sines of angles of a triangle is 1 : 1 : sqrt2 , then the ratio of square of the greatest side to sum of the squares of other two sides is
a/x=b/x=c/xsqrt(2)
a=b=c/sqrt(2)
a^2=b^2=c^2/2

a^2/b^2+c^2 = 1/1+1/2 =1/3/2 = 2/3
@vbhvgupta said:
If the ratio of sines of angles of a triangle is 1 : 1 : sqrt2 , then the ratio of square of the greatest side to sum of the squares of other two sides is
Sin A : sin B : Sin C = 1: 1: root 2 ==> 1/root2 : 1/root2 : 1 ==> A:B:C = 45:45:90 ;

==> c^2 = a^2 + b^2 ==> c^2/a^2+b^2 = 1


@vbhvgupta said:
If the ratio of sines of angles of a triangle is 1 : 1 : sqrt2 , then the ratio of square of the greatest side to sum of the squares of other two sides is
quite simply it is a 45-45-90 triangle so it would be [rt(2)]^2/(1)^2+(1)^2=1?
@Subhashdec2 said:

a^2/b^2+c^2 = 1/1+1/2 =1/3/2 = 2/3
@ravi.theja said:
Sin A : sin B : Sin C = 1: 1: root 2 ==> 1/root2 : 1/root2 : 1 ==> A:B:C = 45:45:90 ;==> c^2 = a^2 + b^2 ==> c^2/a^2+b^2 = 1


1:1

@vbhvgupta said:
a and b are two alloys of argentum and brass prepared by mixing metals in proportion 7:2 and 7:11 respectively. If equal quantities of two alloys are melted to form a third alloy C, the proportion of argentum and brass in C will be?
7:5?
@techgeek2050
take,
abcd + abc + abd + acd + bcd + ab + ac + ad + bc + bd + cd + a + b + c + d
=> Abcd + abc + abd + acd + bcd + ab + ac + ad + bc + bd + cd + a + b + c + d +1 -1

=> abc(d+1) + abd + acd + bcd + ab + ac + ad + bc + bd + cd + a + b + c + d + 1 -1

=> abc(d+1) + ab( d+1) + acd + bcd + ac + ad + bc + bd + cd + a + b + c + d + 1 -1

=> abc(d+1) + ab( d+1) + ac(d+1) + bcd + ad + bc + bd + cd + a + b + c + d + 1 -1

=>abc(d+1) + ab( d+1) + ac(d+1) + bc (d+1) + ad + bd + cd + a + b + c + d + 1 -1

=> abc(d+1) + ab( d+1) + ac(d+1) + bc (d+1) + a( d+1) + b (d+1)+ c(d+1) + ( d + 1) -1

=> (d+1) [ ... ] -1
if we continue we will end up with

(a+1)(b+1)(c+1)(d+1) -1

2010 = (a+1)(b+1)(c+1)(d+1) rest is easy.

@vbhvgupta said:
a and b are two alloys of argentum and brass prepared by mixing metals in proportion 7:2 and 7:11 respectively. If equal quantities of two alloys are melted to form a third alloy C, the proportion of argentum and brass in C will be?
7/9 7/18
x
1 1

(7/9-x)/(x-7/18 ) = 1/1 ==> x= 21/36 ==> ratio = 21:15 = 7:5
@albiesriram


EDIT: answer is 73 not 77....forgot to subtract 4...
77.... for the abcd+bcd...........=2009 question
@albiesriram said:
8) a> 1?
@iLoveTorres said:
8) a> 1?
NO OA available for this set. Plz. Post your Approach .
@anantn said:
@albiesriram77.... for the abcd+bcd...........=2009 question
bhai approach btana
You can place weights on both side of weighing balance and you need to measure all weights between 1 and 1000. For example if you have weights 1 and 3,now you can measure 1,3 and 4 like earlier case, and also you can measure 2,by placing 3 on one side and 1 on the side which contain the substance to be weighed. So question again is how many minimum weights and of what denominations you need to measure all weights from 1kg to 1000kg.

Puys...I couldnt remember the funda in this question. ..but i remmeber that in problems like this we have to take powers of 3 or powers of 2 in some...can some body refresh the funda behind this type o problems...any links would help
@albiesriram said:
NO OA available for this set. Plz. Post your Approach .
bhai approach would be very long and difficult to be posted there is only 1 way the Sudoku can be completed
@KaranGarcia said:
You can place weights on both side of weighing balance and you need to measure all weights between 1 and 1000. For example if you have weights 1 and 3,now you can measure 1,3 and 4 like earlier case, and also you can measure 2,by placing 3 on one side and 1 on the side which contain the substance to be weighed. So question again is how many minimum weights and of what denominations you need to measure all weights from 1kg to 1000kg.Puys...I couldnt remember the funda in this question. ..but i remmeber that in problems like this we have to take powers of 3 or powers of 2 in some...can some body refresh the funda behind this type o problems...any links would help
powers of 3 man
log3 1000 = 6.xx
7
@Subhashdec2 said:
powers of 3 manlog3 1000 = 6.xx7
I know the answer for this bro..I wanted to know when powers of 2 are used and when powers of 3 are used...could recollect
@KaranGarcia said:
I know the answer for this bro..I wanted to know when powers of 2 are used and when powers of 3 are used...could recollect
when weight can be put only on one side then powers of 2
when both sides of the balance then powers of 3
@albiesriram said:
@techgeek2050take,abcd + abc + abd + acd + bcd + ab + ac + ad + bc + bd + cd + a + b + c + d=> Abcd + abc + abd + acd + bcd + ab + ac + ad + bc + bd + cd + a + b + c + d +1 -1=> abc(d+1) + abd + acd + bcd + ab + ac + ad + bc + bd + cd + a + b + c + d + 1 -1=> abc(d+1) + ab( d+1) + acd + bcd + ac + ad + bc + bd + cd + a + b + c + d + 1 -1=> abc(d+1) + ab( d+1) + ac(d+1) + bcd + ad + bc + bd + cd + a + b + c + d + 1 -1=>abc(d+1) + ab( d+1) + ac(d+1) + bc (d+1) + ad + bd + cd + a + b + c + d + 1 -1=> abc(d+1) + ab( d+1) + ac(d+1) + bc (d+1) + a( d+1) + b (d+1)+ c(d+1) + ( d + 1) -1=> (d+1) [ ... ] -1if we continue we will end up with (a+1)(b+1)(c+1)(d+1) -1 2010 = (a+1)(b+1)(c+1)(d+1) rest is easy.
@Subhashdec2