Official Quant thread for CAT 2013

MBA CAT 2022
481
@nick_baba said:
buddy as i said k i don have an OA..so i wudn't mind a logical sentence...
by checking the symmetry. 1-9/10 = 1/10

put x =1-x
f(x) = 9^x/(3+9^x)
f(1-x) = 9^1-x/3+9^1-x
f(1-x)=9/9^x / 3.9^x+9 /9^x
f(1-x) = 9/3.9^x+9 = 3/3+9^x

adding
f(x) + f(1-x) = 1..
f(1/10)+f(9/10) = 1 so will be other four terms...
f(1/2) =1/2

so ans is 4+1/2 =9/2

482
@nick_baba said:
bhai f(x)+f(1-x)=1...ye property ko yahan kaise use kara..i mean ye to koi cyclicity pe depend karti hai..plz justify this..
Not sure about the cyclic order or not
Bt just tried putting x = 1 and x = 0
so got it .
Baad me yaad aya ki kaha ki pada tha but not able to recall where.. will tag you if i find anything

P.S : with this post, i am now certified pagal
483
@milestogo3 said:
by checking the symmetry. 1-9/10 = 1/10put x =1-xf(x) = 9^x/(3+9^x) f(1-x) = 9^1-x/3+9^1-xf(1-x)=9/9^x / 3.9^x+9 /9^xf(1-x) = 9/3.9^x+9 = 3/3+9^xadding f(x) + f(1-x) = 1..f(1/10)+f(9/10) = 1 so will be other four terms...f(1/2) =1/2so ans is 4+1/2 =9/2
@chandrakant.k said:
Not sure about the cyclic order or notBt just tried putting x = 1 and x = 0 so got it . Baad me yaad aya ki kaha ki pada tha but not able to recall where.. will tag you if i find anything P.S : with this post, i am now certified pagal
gr8...like minds think alike..

@chandrakant.k ..ye baat...level 5 completed..:clap:
484
@nick_baba said:
The numerical value of f(1/10) + f(2/10) + €Ś. + f(9/10), where f(x) = 9^x/(3+9^x) is(A) 10/3 (B) 4 (C) ˆš10 (D) 5 (E) 9/2No OA..discussions welcomed..


i got the same question in this year cat bt there was a slight difference in that

f(1/11) + f(2/11) +.....+ f(10/11) i got the ans. as 5, 16th october morning slot

P.S. i hope i am not violating NDA as this years cat window is long over:D:P


485
@busar005 said:
i got the same question in this year cat bt there was a slight difference in thatf(1/11) + f(2/11) +.....+ f(10/11) i got the ans. as 5, 16th october morning slotP.S. i hope i am not violating NDA as this years cat window is long over
buddy not sure of this year's CAT but this was in one of the previous papers as i remember....


486

what is the minimum value of 12x+14y,given that 12x+14Y>0

a)0 b)2 c)4 d)8
487
@Sandy0303 said:
what is the minimum value of 12x+14y,given that 12x+14Y>0a)0 b)2 c)4 d)8
2
x=-1 y=1

PS: 0 isiliye nahi liya coz question mein 12x+14y>0 diya hai nahi to 0 bhi aa sakta hai :)
488
@Sandy0303 said:
what is the minimum value of 12x+14y,given that 12x+14Y>0a)0 b)2 c)4 d)8
X=-1 y = 1
so 2
489
@sumeet1489 ,can't it be solve by AM>GM,how can it be 2?12x+14y/2>(12x*14y)~1/2
490
@Sandy0303 said:
@sumeet1489 ,can't it be solve by AM>GM,how can it be 2?12x+14y/2>(12x*14y)~1/2
we don't have value of xy
491
@Sandy0303 said:
@sumeet1489 ,can't it be solve by AM>GM,how can it be 2?12x+14y/2>(12x*14y)~1/2
i tried using the same at first but cudn't find a way out..coz there's no constraint given on the values of x and y..or even they are integers or not....so jus went by options in this case.
492
@Sandy0303 said:
what is the minimum value of 12x+14y,given that 12x+14Y>0a)0 b)2 c)4 d)8
2
2(6x + 7y)
6x+7y can have a min value of 1 ..so 2
493

consider a circle take a chord PQ of length r.take a point M diametric opposite to P.what is the length of QM.

a)r b)root 2 r c)r/2
494
@rkshtsurana thanks got it,
495
@Sandy0303 said:
consider a circle take a chord PQ of length r.take a point M diametric opposite to P.what is the length of QM.a)r b)root 2 r c)r/2
radius kya he r circle ka ??/
496
@rkshtsurana may be 1 or not given in quest.i forget
497
@Sandy0303 said:
consider a circle take a chord PQ of length r.take a point M diametric opposite to P.what is the length of QM.a)r b)root 2 r c)r/2
PM = 2r (assuming radius = r)
PQ = r
QM = rt(4r^2 - r^2) = root(3) r
498
Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyom €™s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Vyom (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?
a) 40
b) 50
c) 60
d) 80
e) None of these
499
@grkkrg said:
Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyom €™s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Vyom (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?a) 40b) 50c) 60d) 80e) None of these
e- escalator speed, s - no. of steps , x - shyama, vyom's speed

25/3x=(s-25)/e ---- (i)
20/2x=(s-20)/e ---- (ii)

dividing (i) by (ii)
=>5/6=(s-25)/(s-20)
=>5s-100=6s-150
=>s=50

b)50
500
@grkkrg said:
Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyom €™s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Vyom (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?a) 40b) 50c) 60d) 80e) None of these
50..

let the escalator move t steps in the time shayam moves 25 steps.

in the same time vyom would have moved 50/3 steps

so vyom would move (20-50/3) =10/3steps after shyam gets down/

if vyom takes 10/3 steps

in the same time escalator would have taken t/5 steps

so equating total no.of steps

25+t=20+t+t/5

t=25

total steps=50