Official Quant thread for CAT 2013

mailtoankit · December 2, 2012, 6:19pm

@catter2011 said:
Find the sum of co-primes less thn 14

42?

catter2011 · December 2, 2012, 6:21pm

@mailtoankit hmm rt.. approach ?

deedeedudu · December 2, 2012, 6:21pm

@catter2011 said:
Find the sum of co-primes less thn 14

42
Euler(14)*14/2

mailtoankit · December 2, 2012, 6:23pm

@catter2011 said:
@mailtoankit hmm rt.. approach ?

E(14)=14(1-1/2)(1-1/7)=6

sum=6*14/2=42

karan20 · December 2, 2012, 6:45pm

@catter2011 said:
Find the sum of co-primes less thn 14

Sum of co prime : Euler ( N ) x N/2 => E (14 ) X 14/2 = 6 X 7 === 42..

kleptomaniac_20 · December 2, 2012, 7:14pm

@deedeedudu @bullseyes said:Find area of square if 2x -3y + 7 = 0 and 6x - 9y + 8 = 0 represent 2 sides of square
13/9

If I approach it like this :-

6x - 9y + 8 = 0

6x- 9y + 21 = 0

distance between them : 13/root 117 , hence area = 169/117 .

Where am I going wrong ?

bullseyes · December 2, 2012, 7:19pm

@kleptomaniac_20 said:
@deedeedudu@bullseyes said:Find area of square if 2x -3y + 7 = 0 and 6x - 9y + 8 = 0 represent 2 sides of square13/9If I approach it like this :-6x - 9y + 8 = 06x- 9y + 21 = 0distance between them : 13/root 117 , hence area = 169/117 .Where am I going wrong ?

no where.. answer is 13/9 urs is 169/117

19rsb · December 2, 2012, 7:44pm

@kleptomaniac_20 said:
@deedeedudu@bullseyes said:Find area of square if 2x -3y + 7 = 0 and 6x - 9y + 8 = 0 represent 2 sides of square13/9If I approach it like this :-6x - 9y + 8 = 06x- 9y + 21 = 0distance between them : 13/root 117 , hence area = 169/117 .Where am I going wrong ?

take out 13 common from Nr and Dr then 169/117 will get reduce to 13/9

cat.aspirant123 · December 3, 2012, 2:17am

what is unit digit of number N

1) unit digit of N = unit digit of N^8
2)unit digit of N/2 is a prime number, with no digits after decimal points

A, B, Either,neither

krum · December 3, 2012, 2:35am

@Cat.Aspirant123 said:
what is unit digit of number N1) unit digit of N = unit digit of N^82)unit digit of N/2 is a prime number, with no digits after decimal pointsA, B, Either,neither

both?

sujamait · December 3, 2012, 2:36am

@Cat.Aspirant123 said:
what is unit digit of number N1) unit digit of N = unit digit of N^82)unit digit of N/2 is a prime number, with no digits after decimal pointsA, B, Either,neither

both..5

angadbir · December 3, 2012, 2:51am

@Cat.Aspirant123 said:
what is unit digit of number N1) unit digit of N = unit digit of N^82)unit digit of N/2 is a prime number, with no digits after decimal pointsA, B, Either,neither

Take N = 30 or 26

Both the numbers follow both conditions.

Hence, none alone or together is sufficient to determine the answer.

grkkrg · December 3, 2012, 3:45am

@Cat.Aspirant123 said:
what is unit digit of number N1) unit digit of N = unit digit of N^82)unit digit of N/2 is a prime number, with no digits after decimal pointsA, B, Either,neither

From 1:
units digit = 0,1,5,6

From 2:
units digit = 2*2, 2*3, 2*5

From 1 and 2:
Units digit = 6 or 0

Question cannot be answered even with both the statements together.

maddy2807 · December 3, 2012, 3:51am

@Cat.Aspirant123 said:
what is unit digit of number N1) unit digit of N = unit digit of N^82)unit digit of N/2 is a prime number, with no digits after decimal pointsA, B, Either,neither

neither

kleptomaniac_20 · December 3, 2012, 3:53am

@19rsb Yeah got it ! Silly me :P

torque024 · December 3, 2012, 4:44am

Gm friends. :)
The points P, Q, R lie on a line in that order with PQ=9, QR=21. Let O be a point not on PR such that PO=RO and the distances PO and QO are integral.
Then sum of all possible perimeters of triangle PRO is
(a) 320 (b) 350 (c) 380 (d) 410

bullseyes · December 3, 2012, 5:04am

@Torque024 said:
Gm friends. The points P, Q, R lie on a line in that order with PQ=9, QR=21. Let O be a point not on PR such that PO=RO and the distances PO and QO are integral. Then sum of all possible perimeters of triangle PRO is (a) 320 (b) 350 (c) 380 (d) 410

380??

maddy2807 · December 3, 2012, 5:13am

@Torque024 said:
Gm friends. The points P, Q, R lie on a line in that order with PQ=9, QR=21. Let O be a point not on PR such that PO=RO and the distances PO and QO are integral. Then sum of all possible perimeters of triangle PRO is (a) 320 (b) 350 (c) 380 (d) 410

Let the distance between PO be x and that between OQ be y

From O drop a perpendicular to PR, which intersect PR at M,

Now PM is common in both the triangles, PMO and QMO,

THerefore,

x^2- 225= y^2-36

=> x^2-y^2=189

=> (x+y)(x-y)=189

factors of 189= 7*3^3

possible cases

1) (x+y)(x-y)= 63*3

x=33 and y=30

Perimeter= 2*33+30=96

2) (x+y)(x-y)=189*1

x= 95 and y=94

Perimeter= 220

3) (x+y)(x-y)=27*7

x= 17 and y= 10

Perimeter= 64

Rest all cases can be ignored as it is mentioned that O cannot lie on line PR and (x+y)

Required perimeter sum= 96+220+64=380

krum · December 3, 2012, 6:17am

@Torque024 said:
Gm friends. The points P, Q, R lie on a line in that order with PQ=9, QR=21. Let O be a point not on PR such that PO=RO and the distances PO and QO are integral. Then sum of all possible perimeters of triangle PRO is (a) 320 (b) 350 (c) 380 (d) 410

as sum of any two sides is > than third side

15
QO^2 = h^2+6^2
h = PO^2-15^2

=>QO^2 = PO^2-189
=>(PO+QO)*(PO-QO) = 189*1=27*7=21*9=63*3

==>QO=94 / 10 / 6 / 30

but PO = 15 won't give a triangle

perimeter = (30+190) / (30+34) / (30+66)

sum = 220+64+96 = 380

jain4444 · December 3, 2012, 6:26am

In how many ways can 12 people be arranged around a hexagonal table with successive sides being of length a metres, b metres, c metres, a metres, b metres and c metres respectively, if people can sit on chairs placed at corners and the centres of sides?
1) 36 — 12!/2^6
2) 6! — 12!/2^6
3) 12!/2^6
4) None of these