Official Quant thread for CAT 2013

MBA CAT 2024
21666
@raopradeep said:
a box contains five sets of balls while there are three balls in each set . each set of balls has one colour which is different from every other set . what is the least number of balls need to be removed from the box so as to assure that a pair of same coloured balls has been removed67911
6
21667
@Subhashdec2 oa is 11

21668
@iLoveTorres said:
If p > 4 is a prime number, then 24 divides p2 - 1 without remainder (A) never (B) sometimes only (C) always (D) only if p = 5 (E) none of these
OA C)ALWAYS
21669
@joyjitpal oa is 11 how to approach these questions ?

21670
@raopradeep said:
a box contains five sets of balls while there are three balls in each set . each set of balls has one colour which is different from every other set . what is the least number of balls need to be removed from the box so as to assure that a pair of same coloured balls has been removed67911

5 all different have to be removed first 5

then lets say we ahve 10 balls left
lets make pairs of 2 haveing same color
so 5 different colors are there
5+5+1=11


Box 1=1 6 8
Box 2=2 7 9
Box 3=3 8 10
Box 4=4 7 9
Box 5=5 6 10


21671
@Subhashdec2 said:
5 all different have to be removed first 5then lets say we ahve 10 balls left lets make pairs of 2 haveing same colorso 5 different colors are there5+5+1=11Box 1=1 6 8 Box 2=2 7 9Box 3=3 8 10Box 4=4 7 9Box 5=5 6 10
yaar need little more explanation samaj nahi aaraha hai
21672

Q:If both the roots of the quadratic equation ax^2+bx+c=0 lie in the interval (0,3) then a lies in
(1,3),(-1,-3),(-1,3),none of these

21673
@raopradeep said:
yaar need little more explanation samaj nahi aaraha hai
let the balls 1 2 3 4 5 be of different color
now 10 balls are left
let them be of 5 different colors and 2 of each color are there
these pairs of two are shared between different boxes (for me it is balls no 6 7 8 9 and 10)

now pick up 1-5=5 balls
den pick up one each of 6-10=5 balls
then the next one will ensure a pair
11
21674
@Subhashdec2 said:
let the balls 1 2 3 4 5 be of different colornow 10 balls are leftlet them be of 5 different colors and 2 of each color are therethese pairs of two are shared between different boxes (for me it is balls no 6 7 8 9 and 10)now pick up 1-5=5 ballsden pick up one each of 6-10=5 ballsthen the next one will ensure a pair11
bhai ye clear nahi ho rahaa hai ki after picking of 1-5 balls =5 balls
next any ball will generate pair from 6-10 balls i think plz correct me where i went wrong
21675
@pakkapagal said:
Q:If both the roots of the quadratic equation ax^2+bx+c=0 lie in the interval (0,3) then a lies in (1,3),(-1,-3),(-1,3),none of these
(1,3) i guess

21676

@Subhashdec2 i have a doubt.....question states that what is the least number of balls need to be removed from the box so as to assure that a pair of same coloured balls has been removed...

we have to stop when we have a pair of same colored balls...

so, even if the first 5 balls are of different color...then also from the 6th ball we will get a pair...

Please let me know if i missed sumthing here....

21677
@raopradeep said:
bhai ye clear nahi ho rahaa hai ki after picking of 1-5 balls =5 balls next any ball will generate pair from 6-10 balls i think plz correct me where i went wrong

1-10 are ball no's of different colors
bhai 10 balls h

1-5 only 1 ball
6-10 2 balls each
1-5 pick kiya pehle=5
6-10 ki ek ek ball pick ki=5
next ab 6-10 se hee pick karoge
any pickings will ensure a pairing of any of the balls of 6-10
hence 5+5+1
21678
@joyjitpal

@raopradeep

can u please tell what does lie in interval (0,3) means..???

21679
@Sufi0469 said:
@joyjitpal@raopradeepcan u please tell what does lie in interval (0,3) means..???
means interval between 0 and 3

0 , 3 are excluded :)
21680
@pakkapagal said:
Q:If both the roots of the quadratic equation ax^2+bx+c=0 lie in the interval (0,3) then a lies in (1,3),(-1,-3),(-1,3),none of these
is it (1,3) as the eqn will be (x-r1)(x-r2)=0 where r1 and r2 lie in(0,3)
and from this eqn , the coeff of x2 i.e a cant be a negative no..
21681
@Sufi0469 said:
@Subhashdec2 i have a doubt.....question states that what is the least number of balls need to be removed from the box so as to assure that a pair of same coloured balls has been removed...we have to stop when we have a pair of same colored balls...so, even if the first 5 balls are of different color...then also from the 6th ball we will get a pair...Please let me know if i missed sumthing here....
how can u be sure that 6th ball will ensure a pair

first 5 are one of a kind
they dont have any pairs at all
6th will automatically be different

21682
@raopradeep said:
(1,3) i guess
@cat_virus said:
is it (1,3) as the eqn will be (x-r1)(x-r2)=0 where r1 and r2 lie in(0,3)and from this eqn , the coeff of x2 i.e a cant be a negative no..
@joyjitpal said:
means interval between 0 and 30 , 3 are excluded
Yar ans none of these likha hai...arun sharma ka hai...
21683

@Subhashdec2 let me explain....

suppose we have 15 balls for which we have 5 sets...

like

3 white

3 blue

3 red

3 green

3 pink

now in these knid of questions we have to find the worse case scenario...

there can b a case like his 1st & 2nd pick both comes out to be white..

so we have got a pair..

but as per worse case scenario.....we will assume that he picks all diff colors in his first 5 picks...

now then at his 6th pick any balls he picks it will always make a pair with any of the 5 balls he have already picked...

this is what i have understood from the question....

21684
@Sufi0469 said:
@Subhashdec2 let me explain....suppose we have 15 balls for which we have 5 sets...like3 white 3 blue3 red3 green3 pinknow in these knid of questions we have to find the worse case scenario...there can b a case like his 1st & 2nd pick both comes out to be white..so we have got a pair..but as per worse case scenario.....we will assume that he picks all diff colors in his first 5 picks...now then at his 6th pick any balls he picks it will always make a pair with any of the 5 balls he have already picked...this is what i have understood from the question....
dude read the question properly
21685
@pakkapagal this is for sure that a cant be -ve....but how wud we find the range of a