Official Quant thread for CAT 2013

MBA CAT 2024
7221
@htomar said:
ABCD is a rectangle with AD = 10. P is a point onBC such that ˆ  APD = 90 °. If DP = 8 then thelength of BP is ___?A. 6.4 B. 5.2C. 4.8 D. 3.6E. None of the above
3.6?
7222
@htomar said:
ABCD is a rectangle with AD = 10. P is a point onBC such that ˆ  APD = 90 °. If DP = 8 then thelength of BP is ___?A. 6.4 B. 5.2C. 4.8 D. 3.6E. None of the above
3.6
p.s - figure attachd,,dnt go wd my drawing . i dnt wrk wid pen
7223
@htomar said:
ABCD is a rectangle with AD = 10. P is a point onBC such that ˆ  APD = 90 °. If DP = 8 then thelength of BP is ___?A. 6.4 B. 5.2C. 4.8 D. 3.6E. None of the above
D. 3.6

DP = 8
AD = 10
AP = 6
area = 1/2 * 8 * 6 = 1/2 * 10 * h
AB = h = 4.8
BP = sqrt(6^2 - 4.8^2) = 6 sqrt (1 - 0.8^2) = 6*0.6
BP = 3.6
7224
@htomar said:
ABCD is a rectangle with AD = 10. P is a point onBC such that ˆ  APD = 90 °. If DP = 8 then thelength of BP is ___?A. 6.4 B. 5.2C. 4.8 D. 3.6E. None of the above
7225
125369872
*9865831463
1236878027AB9882736,
also A is 4 times B,then find the values of A and B.
7226
@19rsb said:
125369872*98658314631236878027AB9882736,also A is 4 times B,then find the values of A and B.
1+2+5+3+6+9+8+7+2 = 43 = 9a - 2
9+8+6+5+8+3+1+4+6+3 = 53 = 9b - 1

Product = 81ab - 9a - 18b + 2 = 9k + 2

1236878027AB9882736 = 1236878027AB9882734 + 2
1 + 2 + 3 + 6 + 8 +7 + 8 + 2 + 7 + A + B + 9 + 8 + 8 + 2 + 7 + 3 + 4 = 9k
A + B + 4 = 9x
A + B = 9x - 4
A + B = 5 or A + B = 14

Since A = 4B
A = 4
B = 1

7227
@grkkrg said:
1+2+5+3+6+9+8+7+2 = 43 = 9a - 29+8+6+5+8+3+1+4+6+3 = 53 = 9b - 1Product = 81ab - 9a - 18b + 2 = 9k + 21236878027AB9882736 = 1236878027AB9882734 + 21 + 2 + 3 + 6 + 8 +7 + 8 + 2 + 7 + A + B + 9 + 8 + 8 + 2 + 7 + 3 + 4 = 9kA + B + 4 = 9xA + B = 9x - 4A + B = 5 or A + B = 14Since A = 4BA = 4B = 1
but calculator gives A+B=14, A=6, B=8
7228
@htomar Found people giving a lil round abt soln, dunno if othrs feel the same

The sample space is simply 9^5
Possible cases: 9C2(5C1 + 5C2 + 5C3 + 5C4) as 5C0 and 5C5 would mean they were just checked by one person.
Probability = 40/2187
7229

@krum said:
but calculator gives A+B=14, A=6, B=8
then it's a wrong question
A is not four times B
7230
If Sn denotes the sum of the first n terms in an Arithmetic Progression and S1 : S4 = 1 : 10 then the ratio of first term to fourth term is
1) 1 : 3
2) 2 : 3
3) 1 : 4
4) 1 : 5
7231
@krum said:
but calculator gives A+B=14, A=6, B=8
yaa as per calculator and as per calculation(condition given into the question) there is a difference.....that is why I was confused
Matter of the moment is that I dont hav d OA
something is wrong in the question itself .what say@grkkrg ,@krum
7232
@htomar said:
If Sn denotes the sum of the first n terms in an Arithmetic Progression and S1 : S4 = 1 : 10 then the ratio of first term to fourth term is1) 1 : 3 2) 2 : 3 3) 1 : 44) 1 : 5
3) 1:4

a/(4a + 6d) = 1/10
10a = 4a + 6d
6a = 6d

T1/T4 = a/(a+3d) = 1/4
7233
@htomar said:
If Sn denotes the sum of the first n terms in an Arithmetic Progression and S1 : S4 = 1 : 10 then the ratio of first term to fourth term is1) 1 : 3 2) 2 : 3 3) 1 : 44) 1 : 5
a/(4a+6d)=1/10
=>6a=6d
=>d=a

a/4a = 1/4
7234
@htomar said:
If Sn denotes the sum of the first n terms in an Arithmetic Progression and S1 : S4 = 1 : 10 then the ratio of first term to fourth term is1) 1 : 3 2) 2 : 3 3) 1 : 44) 1 : 5
1/4?
7235
If x + y + z = 1 and x, y, z are positive real numbers, then the least value of ((1/x) - 1) ((1/y) - 1) ((1/z) - 1) is
1) 4
2) 8
3) 16
4) None of the above
7236
@htomar said:
If x + y + z = 1 and x, y, z are positive real numbers, then the least value of ((1/x) - 1) ((1/y) - 1) ((1/z) - 1) is 1) 4 2) 8 3) 164) None of the above
Should be 8.

(1/x - 1)*(1/y - 1)*(1/z - 1)

= (xy + yz + xz)/xyz - 1 ----(A)

Now AM >= GM

So, xy+yz+xz >= 3*(xyz)^(2/3)

So, Put in (A)

(1/x - 1)*(1/y - 1)*(1/z - 1) >= 3*1/(xyz)^(1/3) - 1

(1/x - 1)*(1/y - 1)*(1/z - 1) >= ( 3/(1/3) - 1) >= 8

So Least Value should be 8.


7237
@htomar said:
If x + y + z = 1 and x, y, z are positive real numbers, then the least value of ((1/x) - 1) ((1/y) - 1) ((1/z) - 1) is 1) 4 2) 8 3) 164) None of the above
8?
7238
@htomar

simplify ((1/x) - 1) ((1/y) - 1) ((1/z) - 1)

we will get (1/x+1/y+1/z)-1

now ap>=hp

therefore (x+y+z)/3>= 3/(1/x+1/y+1/z)

on solving: (1/x+1/y+1/z)-1>=8

so min value =8
7239
@htomar said:
If x + y + z = 1 and x, y, z are positive real numbers, then the least value of ((1/x) - 1) ((1/y) - 1) ((1/z) - 1) is 1) 4 2) 8 3) 164) None of the above
At, x=y=z=1/3, (1/x-1)(1/y-1)(1/z-1) attains a value of 8.
It is easy to see, any other value of the expression (1/x-1)(1/z-1)(1/z-1) is greater than 8.
So, 8 is the minimum value.

7240
@htomar said:
If x + y + z = 1 and x, y, z are positive real numbers, then the least value of ((1/x) - 1) ((1/y) - 1) ((1/z) - 1) is 1) 4 2) 8 3) 164) None of the above
1/x -1 = (x+y+z)/x - 1 = (y+z)/x
similarly 1/y -1 = (x+z)/y and (1/z-1) = (x+y)/z

hence the given expression equals (x+y)(y+z)(z+x)/(xyz)

we know (x+y) >= 2rt(xy) [AM>= GM]

=>(x+y)(y+z)(z+x) >= 2rt(xy)*2rt(yz)*2rt(xz)

=>(x+y)(y+z)(z+x)/(xyz) >= 8

ATDH.