Official Quant thread for CAT 2013

MBA CAT 2022
1361
@ASHISH_mantra said:
@chandrakant.k Please solve this Puzzle I found It difficult please solve iwillanswer.in/1633/solve-this...
i5+3+2 = 151022
9+2+4 = 183652
8+6+3 = 482466
5+4+5 = 202541
THEN ;
7+2+5 =?

it is 143547
first two digit 7 x2
next two digit 7 x5
last two digit 7x(2+5) -2
1362
@krum that happens to everyone. :P
1363
What is the minimum value of 2^sinx + 2^cosx
a) 2^(2_/2 - 2)
b) _/2^(2 - _/2)
c) 2^(_/2 - 1)
d) _/2^( 1 - _/2/2)

phew!!
1364
@sowmyanarayanan
MY TECHNIQUE WAS DIFFERENT. refer attachement
just wanted to know is the formula, u posted, general or specific to this question
1365
@sowmyanarayanan said:
What is the minimum value of 2^sinx + 2^cosx
_/2^(_/2-1)

EDITED

1366
@sowmyanarayanan options?

1367
@techsurge said:
@sowmyanarayananMY TECHNIQUE WAS DIFFERENT. refer attachementjust wanted to know is the formula, u posted, general or specific to this question
this one is neat :)
1368
@techsurge said:
@sowmyanarayananMY TECHNIQUE WAS DIFFERENT. refer attachementjust wanted to know is the formula, u posted, general or specific to this question
i am just splitting the octagon in to most basic figures. no general formula for this question.
1369
@techsurge bhai yeh wala bahut aasan laga mujhe .......
sidha ek rectangle ban jayega
3root2 *root2=6
baki 4 triangle ka 4*1=4
aur baki square ka 2(2)=4
sahi hai yeh
6+4+4=14
1370
@sowmyanarayanan said:
What is the minimum value of 2^sinx + 2^cosxa) 2^(2_/2 - 2)b) _/2^(2 - _/2)c) 2^(_/2 - 1)d) _/2^( 1 - _/2/2)phew!!
c?
1371
@sowmyanarayanan said:
What is the minimum value of 2^sinx + 2^cosxa) 2^(2_/2 - 2)b) _/2^(2 - _/2)c) 2^(_/2 - 1)d) _/2^( 1 - _/2/2)phew!!
b

when sinx=cosx =-1/_/2
1372
@sowmyanarayanan said:
What is the minimum value of 2^sinx + 2^cosxa) 2^(2_/2 - 2)b) _/2^(2 - _/2)c) 2^(_/2 - 1)d) _/2^( 1 - _/2/2)phew!!

differentating
cosx 2^sinx - sinx 2^cos x = 0
cosx 2^sinx = sinx 2^cos x
2^sinx-cosx = tanx
x = pie/4 ...........it ll be min at x = pie/4
2* 2*1/rt2
2^ 1 + rt/2

x = 5pie/4 pe hga -ve..perodicity hgi yaha

option b


1373
@Anivesh90 said:
c?
OA says b)
share your approach. let us try coming to the answer from there
1374
@sowmyanarayanan is it d? because sin and cos value never bigger than 1 all three are rejected because gretare than 1
1375
@sowmyanarayanan said:
What is the minimum value of 2^sinx + 2^cosxa) 2^(2_/2 - 2)b) _/2^(2 - _/2)c) 2^(_/2 - 1)d) _/2^( 1 - _/2/2)phew!!
min at 225

=>2^(-1/root)+2^(-1/root2)
=>2/2^(1/root2)
=>2^(1-1/root2)
=>2^(root2*root2-1*root2)/2
=>_/2^(2 - _/2)
1376
@krum said:
2^(_/2 - 1)
its b,


2* 2^(sinx+cosx)/2 => 2* 2^(sin225+cos225)/2 =>b
1377
@catter2011 bhai dekh har option mein sinx aur cosx ki value greater than 1 de rakhi hai n sin never as value gretare than 1 toh is hisab se option d ni hoga
1378
@techsurge said:
bwhen sinx=cosx =-1/_/2
agree sinx+cosx max is _/2 and min is -_/2 at 45 and 225 respectively.. unfortunately i took min as 1 , in my fst attempt..
1379
@krum
@sauravd2001
@rkshtsurana
@techsurge

Solution says y = 2^sinx + 2^cosx
From symmetry, y would have minimum value when sin x = cos x = -1/_/2

so b)

Can anyone explain what the bold line means?
1380
@sauravd2001 said:
@catter2011 bhai dekh har option mein sinx aur cosx ki value greater than 1 de rakhi hai n sin never as value gretare than 1 toh is hisab se option d ni hoga
cant get u properly..

apply AM>GM and u ll end up lyk this

2* 2^(sinx+cosx)/2 => 2* 2^(sin225+cos225)/2 =>b