Official Quant thread for CAT 2013

@amresh_maverick said:
1> How long is the side of the largest equilateral triangle that can be inscribed in a square whose side has length 1 ?
2+root3 hai kya??
@amresh_maverick said:
1> How long is the side of the largest equilateral triangle that can be inscribed in a square whose side has length 1 ?
check out #19593 from @scrabbler
@Logrhythm said:
check out #19593 from @scrabbler
Bhai
_/\_

When N is divided by D gives a remainder of 52. The no 5N is divided by D gives a remainder of 4. How many values of D are possible ?

@Logrhythm said:
(-2)^11^22^33^44%5..11^22^33^44%4(-1)^even = 1=> (-2)^1%5 = 2 or -3...EDIT: -2 nahi 2 hoga...
@scrabbler said:
Is baar 2?7^4k+1/5...regardsscrabbler
@amresh_maverick said:
why -2 rem 7/5 is 2 naa

OA-2...........

If x/y + y/z +z/x = 1
Find the value of (x^3 + y^3 + z^3)/xyz?

@amresh_maverick said:
When N is divided by D gives a remainder of 52. The no 5N is divided by D gives a remainder of 4. How many values of D are possible ?

3 values??

64,128,256
@amresh_maverick said:
When N is divided by D gives a remainder of 52. The no 5N is divided by D gives a remainder of 4. How many values of D are possible ?
3 hai kya??
m getting 64,128 and 256
@amresh_maverick said:
When N is divided by D gives a remainder of 52. The no 5N is divided by D gives a remainder of 4. How many values of D are possible ?
N = x*D + 52 --- (1)
5N = y*D + 4 --- (2)
(1)*5 -> 5N = 5x*d + 260 --- (3)
(2) - (3) -> y*D - 5x*D = 256
D(y-5x) = 2^8
so D can be 64,128 and 256
hence 3 values...
@amresh_maverick said:
When N is divided by D gives a remainder of 52. The no 5N is divided by D gives a remainder of 4. How many values of D are possible ?
3?

regards
scrabbler

@bs0409 said:
OA-2...........If x/y + y/z +z/x = 1Find the value of (x^3 + y^3 + z^3)/xyz?
3 hai kya

Given x and y are integers and 5x^2 + 2y^2 =5922 , what can be the unit digit of y ?

options should be given here

3 ,5 ,7 ,9

@amresh_maverick said:
Given x and y are integers and 5x^2 + 2y^2 =5922 , what can be the unit digit of y ?
1 or 9? Not solved fully, just possibilities eliminate karke...

Edit: With options, 9...

regards
scrabbler

@amresh_maverick said:
Given x and y are integers and 5x^2 + 2y^2 =5922 , what can be the unit digit of y ?
1 or 6??
@amresh_maverick said:
Given x and y are integers and 5x^2 + 2y^2 =5922 , what can be the unit digit of y ?options should be given here3 ,5 ,7 ,9
tab 9 yar..
@amresh_maverick said:
Given x and y are integers and 5x^2 + 2y^2 =5922 , what can be the unit digit of y ?options should be given here3 ,5 ,7 ,9
My take -9
@amresh_maverick said:
Given x and y are integers and 5x^2 + 2y^2 =5922 , what can be the unit digit of y ?options should be given here3 ,5 ,7 ,9
tab 9 yar..
@scrabbler said:
1 or 9? Not solved fully, just possibilities eliminate karke...regardsscrabbler
M also getting 6 as a possibility....anyone getting 6?
@amresh_maverick @bs0409
@amresh_maverick said:
Given x and y are integers and 5x^2 + 2y^2 =5922 , what can be the unit digit of y ?
5x^2 = 2(2961 - y^2)
x^2 = 2(2961-y^2)/5
y^2 should end in 1 or 6...
so units of y can be 9 or 1 or 6

dnt knw how to prove if these can have integer solutions or not...

@amresh_maverick @bs0409 @scrabbler
If x is even then 5*x^2 will end in a zero..
so 2y^2 = 5922 - 5x^2
unit digit will end in 2
so y^2 can be (unit digit ) 1 or 6....
ab eska root :
so can so 1 , 9 , 6
if there is a mistake please point out..
@saurav205 said:
3..
@mailtoankit said:
I + II + III = 100I + 2*II + 3*III = 150150 + II + III - 2*II - 3*III = 1002*III = 150 - 100 - 442*III = 6III = 3 ?
its 3..