Official Quant thread for CAT 2013

@dreamz007 said:
FIND THE UNIT DIGIT OF : 888^9235! + 222^9235! + 666^2359! + 999^9999! a> 1 b>7 c>9 d>3
6+6+6+1=9

9235! last digit is 00..it is disible by 4

888^4=6
222^4=6
666^4=6
999^4=1
sara joined facebook . She has 5 friends . each of her friends has twenty five friends . it is found that at least two of sara's friends are connected with each other . on her birthday , sara decides to invite her friends and the friends of her friends . How many people did she invite for her birthday party ?
A)>=105
B)C)>100 AND D)
E>=105 AND =
@Anuj07 said:
sara joined facebook . She has 5 friends . each of her friends has twenty five friends . it is found that at least two of sara's friends are connected with each other . on her birthday , sara decides to invite her friends and the friends of her friends . How many people did she invite for her birthday party ? A)>=105B)100 AND E>=105 AND =
B
@mbajamesbond said:
B
Solution ?

why not e ?
@Anuj07 said:
Solution ? why not e ?
OA kya hai...If B then solution batata hoon.
@mbajamesbond said:
OA kya hai...If B then solution batata hoon.
Yeh xat 2013 ka question hai sum keys are suggesting b and some are suggesting e !!

I feel e
@Anuj07 said:
Yeh xat 2013 ka question hai sum keys are suggesting b and some are suggesting e !!I feel e
See sara's 5 friends got 25 friends each= 125

Now out of them 2 friends are connected.Since they are already friends sara will call 125- 2= 123 friends on her birthday...

@mbajamesbond said:
See sara's 5 friends got 25 friends each= 125Now out of them 2 friends are connected.Since they are already friends sara will call 125- 2= 123 friends on her birthday...
and minumum friends is that it has to invite 125 - 5+ (5+4+3+2+1)
@Anuj07 said:
and minumum friends is that it has to invite 125 - 5+ (5+4+3+2+1)
whats the logic??

A builds a wall in 50 days. B demolishes in 60 days. Both work alternative days. The day when the wall will be first complete?

@veertamizhan said:
A builds a wall in 50 days. B demolishes in 60 days. Both work alternative days. The day when the wall will be first complete?
148 days ...
natural no of solution a+b+c =
@The_Loser 454??
@insane.vodka said:
its -ab (how can you negate terms like a^2b
yes...it will be -ab
@ravi.theja said:
@The_Loser 454??
ans -12C3
a+b+c ===> a+b+c= 12 ,a+b+c =11 , ........a+b+c=1 ===> so its (12+3-1)c(3-1)= 14c2 similarly 13c2 for a+b+c =11..and so on till 3c2 and 1 sol for a+b+c = 0.

==> 14c2 +13c2 +12c2+.........3c2+1 = 455?? wats d flaw in this @The_Loser
@dreamz007

@dreamz007 said:
FIND THE UNIT DIGIT OF : 888^9235! + 222^9235! + 666^2359! + 999^9999! a> 1 b>7 c>9 d>3
6+6+6+1 = 19 😃 so 9 is the units digit
@ravi.theja said:
a+b+c = a+b+c= 12 ,a+b+c =11 , ........a+b+c=1 ===> so its (12+3-1)c(3-1)= 14c2 similarly 13c2 for a+b+c =11..and so on till 3c2 and 1 sol for a+b+c = 0.==> 14c2 +13c2 +12c2+.........3c2+1 = 455?? wats d flaw in this @The_Loser
No flaw i wud say, bcz i did d same. May b ans given s nt correct.

Q=2 in hw many ways 8 ple can sit in d given fig.
@vbhvgupta said:
find remainder when 21^3 + 23^3 + 25^3 + 27^3 is divided by 96.
since 21,23,25,27 are in a.p and sum of all the terms is 96 which is xatly divisible by 96 here in this case rem=0

P.S :- a^n +b^n + c^n........+ n terms / ( a+b +c+...n terms ) rem =0 if a,b,c........ are in arthimetic progression
There are 4 people Erick, Helena, Johny and David and they have 9 seats available to sit on. Now Johny and Helena don €™t like each other and that €™s why they always need to have one blank seat in between them and others can sit on any seat but no one can sit on the blank seat between Johny and Helena.

First, the seats are arranged in a linear fashion and then the number of different linear arrangements possible are found to be M.Then the seats are arranged in circular fashion after which the number of different arrangements possible are found to be N. Then M + N is found to be
OPTIONS

1) 270
2) 450
3) 480
4) None of these
pls explain the solution