Official Quant thread for CAT 2013

scarecrow28 · February 24, 2013, 7:19pm

@jain4444 said:
A group of workers was put on a job. From the second day onwards, oneworker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group wouldhave finished the job in two thirds the time. How many workers were there inthe group

Incoming - 3

mani0303 · February 24, 2013, 7:26pm

@jain4444 said:
A group of workers was put on a job. From the second day onwards, oneworker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group wouldhave finished the job in two thirds the time. How many workers were there inthe group

n + (n-1) + (n-2) +... + 1 = n*(2/3)*n

So, n = 3

___________/|\______________,Jain bhai:)

jain4444 · February 24, 2013, 7:45pm

@mani0303 said:
n + (n-1) + (n-2) +... + 1 = n*(2/3)*n So, n = 3___________/|\______________,Jain bhai

kya baat hai mani anna ____/\___

find all (p,q) such that GCD (p,q) =1 and p not equal to q with p/q = [p^2 +60]/[q^2 +60]

ilovetorres · February 24, 2013, 7:50pm

@jain4444 said:
kya baat hai mani anna ____/\___ find all (p,q) such that GCD (p,q) =1 and p not equal to q with p/q = [p^2 +60]/[q^2 +60]

(1,60)(60,1)(4,15)(15,4)(3,20)(20,3)?

mani0303 · February 24, 2013, 7:56pm

@jain4444 said:
kya baat hai mani anna ____/\___ find all (p,q) such that GCD (p,q) =1 and p not equal to q with p/q = [p^2 +60]/[q^2 +60]

60(P - Q) = PQ(P - Q)

=>PQ = 60

So,ordered paairs of (P,Q) are (1,60)(3,20),(4,15),(5,12),(12,5),(15,5),(20,3),(60,1)

@jain4444 @Estallar12 - what's the formula to find number of ways to write a number as a product of two numbers which are co-prime to each other?

chirpibird · February 24, 2013, 8:05pm

Find the next number in the series.. 1,8,11,69,88,96,101,111,181..
OA tomo.

chirpibird · February 24, 2013, 8:06pm

Find the next number in the series.. 1,8,11,69,88,96,101,111,181..
OA tomo.

scrabbler · February 24, 2013, 8:08pm

@mani0303 said:
60(P - Q) = PQ(P - Q)=>PQ = 60So,ordered paairs of (P,Q) are (1,60)(3,20),(4,15),(5,12),(12,5),(15,5),(20,3),(60,1)@jain4444 @Estallar12 - what's the formula to find number of ways to write a number as a product of two numbers which are co-prime to each other?

Find number of distinct prime factors = n, then number of ways = 2^(n-1).

If ordered ways then 2^n.

regards
scrabbler

scrabbler · February 24, 2013, 8:11pm

@ChirpiBird said:
Find the next number in the series.. 1,8,11,69,88,96,101,111,181..OA tomo.

609?

regards
scrabbler

scarecrow28 · February 24, 2013, 8:21pm

@ChirpiBird said:
Find the next number in the series.. 1,8,11,69,88,96,101,111,181..OA tomo.

609

Strobogrammatic number

ilovetorres · February 24, 2013, 9:15pm

@scrabbler said:
609?regardsscrabbler

bhai yeh kaise aaya? n mujhe wo 4 set venn diagram ka logic bikul galat laga.. do you mind to spend sometime to crack the logic

scrabbler · February 24, 2013, 9:19pm

@iLoveTorres said:
bhai yeh kaise aaya? n mujhe wo 4 set venn diagram ka logic bikul galat laga.. do you mind to spend sometime to crack the logic

Aaj nahin dost, kal office jaana hai...

As for the 609 maine isiliye logic post nahin kiya ki log thoda banghead kare...worth thinking over laga mujhe...

Hint deta hoon...it is a lateral thinking question so try looking at it from different angles...;)

regards
scrabbler

mailtoankit · February 24, 2013, 9:28pm

@ChirpiBird said:
Find the next number in the series.. 1,8,11,69,88,96,101,111,181..OA tomo.

609 ?

rotate karo 180 deg...number same aayega..

kaafi sochne ke baad dimaag chala...

the_loser · February 25, 2013, 3:09am

D1 + D2 +D3 +D4 = 17

D represents dice

Find number of ways. ?

jain4444 · February 25, 2013, 4:10am

For how many positive integers n ‰¤ 1000, is the digit root of n^2 + n + 1 equal to 3?

P.S - The digit root of a number is a single digit value obtained by iterative digit sums. For example, the digit root of 31^2 + 31 + 1 = 993 would be 3 since 9 + 9 + 3 = 21 , 2 + 1 = 3.

hesse · February 25, 2013, 4:14am

@The_Loser D1 + D2 +D3 +D4 = 17D represents dice
Find number of ways. ?

d1 d2 d3 d4

6 6 4 1

6 6 3 2

6 5 4 2

6 5 5 1

6 5 3 3

5 5 5 2

5 5 4 3

5 4 4 4

=> 4!/2 + 4!/2 + 4! + 4!/2 + 4!/2 + 4!/3! +4!/2 +4!/3

= 3*24 + 4 + 12 = 16 + 72 =88

rkshtsurana · February 25, 2013, 4:29am

@The_Loser said:
D1 + D2 +D3 +D4 = 17D represents diceFind number of ways. ?

1so D1 + D2 + D3+ D4 = 13 where D>= now

now 13+ 4 - 1 C 4-1 = 16C3
now if D >= 7 so
ley D1` = D1+ 7
D1` + D2+ D3+ D4 = 6
so 6+4-1 C 4-1 = 9c3
so 16c3 - 4* 9c3
= 560 - 336 = 224 ?

the_loser · February 25, 2013, 4:30am

@hesse said:
@The_LoserD1 + D2 +D3 +D4 = 17D represents diceFind number of ways. ?d1 d2 d3 d46 6 4 16 6 3 26 5 4 26 5 5 16 5 3 35 5 5 25 5 4 35 4 4 4=> 4!/2 + 4!/2 + 4! + 4!/2 + 4!/2 + 4!/3! +4!/2 +4!/3= 3*24 + 4 + 12 = 16 + 72 =88

could you rectify this. ?

a+b+c+d = 17

a'+b'+c'+d' = 13

now 16c3 - 4 * 10c3 = 80

the_loser · February 25, 2013, 4:33am

@rkshtsurana said:
1so D1 + D2 + D3+ D4 = 13 where D>= nownow 13+ 4 - 1 C 4-1 = 16C3 now if D >= 7 soley D1` = D1+ 7D1` + D2+ D3+ D4 = 6 so 6+4-1 C 4-1 = 9c3so 16c3 - 4* 9c3= 560 - 336 = 224 ?

whn you have already districuted 1,1,1,1 to D1,D2,D3,D4.

than in final subtraction should not it be like give 6 to any one as one it already entails.

so subtracted 7+4-1c4-1 = 10c3. ??

Just a doubt need to clarify that. :-)

rkshtsurana · February 25, 2013, 4:36am

@The_Loser said:
whn you have already districuted 1,1,1,1 to D1,D2,D3,D4.than in final subtraction should not it be like give 6 to any one as one it already entails.so subtracted 7+4-1c4-1 = 10c3. ??Just a doubt need to clarify that.

ya correct...when i distributed one ..limit changed to 0so we ll take d` = d+6 where d>=0
so 7+4-1 C 4-1 = 10c3