Official Quant thread for CAT 2013

@Faruq said:
The average of 60 positive distinct integers all greater than 7 is equal to 41. What could be the maximum possible value of any one of these 60 integers?a. 277 b. 217 c. 210 d. 224
277
@vbhvgupta said:
At what % above CP must an article be marked so as to gain 17% after allowing a discount of 10%.
1cp, 1.17 gain ..this is 90%...
(1.17/.90) .. 1.30..
30%?
Q. Wht is the probability tht a quad eqn : ax^2 + bx + c= 0has equal roots if a,b n c are distinct n r taken frm {1,2,3,4,6,8,9} ?

options-> a) 1/35 b) 2/35 c) 1/105 d) 2/105

need soln plz.
@saurav205 said:
Y=5100....but then this was the CP for which the retailer bought at 15% discount...So the actual CP (for the person who sold it to the retailer) = .85a=5100a=6000hence the discount offered was 6000-5100=900
Oops..! Yeah..noted Thanx for correcting 😃
@Faruq said:
The average of 60 positive distinct integers all greater than 7 is equal to 41. What could be the maximum possible value of any one of these 60 integers?a. 277 b. 217 c. 210 d. 224
277

sum from (8 + 9+.. upto 66) + k = 41*60

k=2460-2183
@Abir1103 said:
Q. Wht is the probability tht a quad eqn : ax^2 + bx + c= 0has equal roots if a,b n c are distinct n r taken frm {1,2,3,4,6,8,9} ?options-> a) 1/35 b) 2/35 c) 1/105 d) 2/105need soln plz.
1/35 ?
@Abir1103 said:
Q. Wht is the probability tht a quad eqn : ax^2 + bx + c= 0has equal roots if a,b n c are distinct n r taken frm {1,2,3,4,6,8,9} ?options-> a) 1/35 b) 2/35 c) 1/105 d) 2/105need soln plz.
See for the roots to be equal we must have
b^2 = 4a*c
now (b^2)/4 =a*c------------------------(1)
b will take only even values 2,4,6,8

Now make pair
for b=2 (see equation 1)
a and c will have value as 2 ,2 but we need distinct digits. so this case discarded

for b=4
a ,c will have values 2 and 2 or 4, 1 but these are also not giving distinct values so discarded

for b=6
a , c will have 9, 1 so these give 2 values
either a= 9 or 1 or c = 9,1 so 2 ways

for b= 8
these are also not giving distinct values
so discarded (put value f b in equation 1 and solve for a n c by putting values from given set )

and also total ways for selecting values of b,a,c will be = 7*6*5

(2)/ (7*6*5)= 1/105
@Abir1103 what is OA?

1/105

is 31^11 greater 17^14 please share your approch


@Bigshu said:
is 31^11 greater 17^14 please share your approch
(17^3)^11=4913^11 compare this with 31^11 and decide for yourself which should be greater
@Bigshu said:
is 31^11 greater 17^14 please share your approch
17^14 is greater. but I am not getting a straight way other than using log tables
@iLoveTorres said:
(17^3)^11=4913^11 compare this with 31^11 and decide for yourself which should be greater
bhai (17^3)^11 = 17^33 hoga...not 17^14
@mailtoankit said:
bhai (17^3)^11 = 17^33 hoga...not 17^14
sab ke sab le lo meri 😞
@iLoveTorres said:
(17^3)^11=4913^11 compare this with 31^11 and decide for yourself which should be greater
@Bigshu (17^3)17^11=4913(17)^11 compare this with 31^11 and decide for yourself which should be greater.
Sorry had to edit it as i was wrong in my way of representation
@Bigshu said:
is 31^11 greater 17^14 please share your approch
17^14 will be greater
and another Simple solution - ese questions kisi b exam mai nahi aate


In a cyclic quadrilateral ABCD, if AB = 2, BC = 3, CD = 4 and DA = 5, what is the ratio of the lengths of the diagonals?

7:11

11:13

10:11

13:15
@sameersapre23 said:
In a cyclic quadrilateral ABCD, if AB = 2, BC = 3, CD = 4 and DA = 5, what is the ratio of the lengths of the diagonals?7:1111:1310:1113:15
11:13 ?
pq = ac+bd
p/q = ab+cd/ad+bc

where p and q are length of diagonals of given figure.

@mailtoankit said:
bhai (17^3)^11 = 17^33 hoga...not 17^14
Wese mai b aaj tak confuse rehta hoo ismai...........!! hahahahahahaha
@sameersapre23 said:
pq = ac+bdp/q = ab+cd/ad+bcwhere p and q are length of diagonals of given figure.
Ya, this is a standard formula