Official Quant thread for CAT 2013

MBA CAT 2024
21546

@saurav205 said:
21...
made a mistake...21 nai aayega...
21547
@Calvin4ever said:
The sum of the n terms of a series is n! + n^2 then the 6th term is . . ?? (n is a natural number)
611
@Calvin4ever said:
perfect power of 5 is x^5 and I took it as 5^x !!
same here
21548
(1/2)+(2^2/2^2)+(3^2/2^3)+(4^2/2^4)+(5^2/2^5)+.....=?
a) 4
b) 5
c) 6
d) 7
21549
@joyjitpal said:
(1/2)+(2^2/2^2)+(3^2/2^3)+(4^2/2^4)+(5^2/2^5)+.....=?a) 4b) 5 c) 6 d) 7
6 hai kya? 😛 koi method nai lagaya filhaal
21550
@ScareCrow28 said:
6 hai kya? koi method nai lagaya filhaal
explanation pls .
21551
@Calvin4ever said:
explanation pls .
I told you I didn't use any rigorous solution 😛 Just see.. its 0.5 + 1 + 1.1 + 1 + 0.8 + 0.5 ..
So roughly it will come to 6..Not feeling like doing maths now :(
21552
@joyjitpal said:
(1/2)+(2^2/2^2)+(3^2/2^3)+(4^2/2^4)+(5^2/2^5)+.....=?a) 4b) 5 c) 6 d) 7
is it 6..
calculated the 1st few terms...thoda estimate lagaya hai...
21553
@Calvin4ever said:
The sum of the n terms of a series is n! + n^2 then the 6th term is . . ?? (n is a natural number)
Tn term = Sn - Sn-1
T6 = n! + n^2 - ((n - 1)! + (n - 1)^2) = 6! + 6^2 - 5! - 5^2 = 756 - 145 = 611 ?
21554
A cuboid of dimensions 51, 85 , 102 cm is first painted by red colour then it is cut into minimum possible identical cubes.Now the total surface area of all those faces of cubes which are not red is :
21555
@Calvin4ever said:
The sum of the n terms of a series is n! + n^2 then the 6th term is . . ?? (n is a natural number)

611.. manually kiya..
@ScareCrow28 said:
6! + 6^2 - 5! - 5^2 = 600 + 11 = 611 ?
Scare crow, please do post the explanation...
21556
@joyjitpal said:
(1/2)+(2^2/2^2)+(3^2/2^3)+(4^2/2^4)+(5^2/2^5)+.....=?a) 4b) 5 c) 6 d) 7
c?
21557
@kambarish said:
611.. manually kiya.. Scare crow, please do post the explanation...
See, Nth term in any series can also be written as = Sum till Nth term - Sum till (n-1)th term
Take any series for ex,
a, b, c, d, e
Now e = a+b+c+d+e - (a+b+c+d)
Same has been done!
21558
@joyjitpal said:
(1/2)+(2^2/2^2)+(3^2/2^3)+(4^2/2^4)+(5^2/2^5)+.....=?a) 4b) 5 c) 6 d) 7
S = (1/2)+(2^2/2^2)+(3^2/2^3)+(4^2/2^4)+(5^2/2^5)+.....(1)
S/2 = (1/2^2)+(2^2/2^3)+(3^2/2^4)+(4^2/2^5)+(5^2/2^6)+.....(2)
EQ (1)-(2)
S/2= (1/2)+(3/2^2)+(5/2^3)+(7/2^4)+(9/2^5)+.....
S = (1)+(3/2)+(5/2^2)+(7/2^3)+(9/2^4)+.....
S-(5/2) = (5/2^2)+(7/2^3)+(9/2^4)+.....
S/4 = (1/2^2)+(3/2^3)+(5/2^4)+(7/2^5)+(9/2^6)+.....
S-(5/2)-S/4 = (4/2^2)+ (4/2^3) + (4/2^4) + ....
(3S/4)-(5/2)= (4/2^2)+ (4/2^3) + (4/2^4) + ....
 multiplying by 2
(3S/2)-5 = (4/2) + (4/2^2) + (4/2^3) + ....
(3S/2)-5 = 4 * [(1/2)/1-(1/2)]
(3S/2)-5 = 4
3S/2 = 9
S = 6

P.S This is the first time i have done anything conventionally.. Though the best method will be to add a few terms and answer the question and move on. After all CAT doesnt have STEP MARKS :P
I would also thank @scrabbler . Off late being under his guidance maths doesnt seem to be so terrorising :)
21559
@iLoveTorres said:
S = (1/2)+(2^2/2^2)+(3^2/2^3)+(4^2/2^4)+(5^2/2^5)+.....(1) S/2 = (1/2^2)+(2^2/2^3)+(3^2/2^4)+(4^2/2^5)+(5^2/2^6)+.....(2)EQ (1)-(2) S/2= (1/2)+(3/2^2)+(5/2^3)+(7/2^4)+(9/2^5)+..... S = (1)+(3/2)+(5/2^2)+(7/2^3)+(9/2^4)+..... S-(5/2) = (5/2^2)+(7/2^3)+(9/2^4)+..... S/4 = (1/2^2)+(3/2^3)+(5/2^4)+(7/2^5)+(9/2^6)+..... S-(5/2)-S/4 = (4/2^2)+ (4/2^3) + (4/2^4) + .... (3S/4)-(5/2)= (4/2^2)+ (4/2^3) + (4/2^4) + .... multiplying by 2 (3S/2)-5 = (4/2) + (4/2^2) + (4/2^3) + ....(3S/2)-5 = 4 * [(1/2)/1-(1/2)](3S/2)-5 = 4 3S/2 = 9 S = 6
21560
@Calvin4ever said:
A cuboid of dimensions 51, 85 , 102 cm is first painted by red colour then it is cut into minimum possible identical cubes.Now the total surface area of all those faces of cubes which are not red is :
=(6*17*17*90) - ( 2*((51*85)+(51*102)+(85*102)))
=17^2((540)-(2*62))
=289*416
21561
@Dexian said:
=(6*17*17*90) - ( 2*((51*85)+(51*102)+(85*102)))=17^2((540)-(2*62))=289*424
Almost . . calculation mistake. . It shud be 17^2((540)-(2*63))=289*414
21562
@Dexian said:
=(6*17*17*90) - ( 2*((51*85)+(51*102)+(85*102)))=17^2((540)-(2*62))=289*424
63 I think...and 414 X 289

regards
scrabbler
21563
@Calvin4ever said:
Almost . . calculation mistake. . It shud be 17^2((540)-(2*63))=289*414
sorry....... almost asleep..............
21564
A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 20% impurities to the product. Find the net profit percentage of the dealer?
21565
@amresh_maverick said:
A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 20% impurities to the product. Find the net profit percentage of the dealer?
50 % ??