Official Quant thread for CAT 2013

MBA CAT 2024
24928
@Logrhythm got it...understood
24929
@Logrhythm said:
1) 42) 29 Not sure though...
iska approach??
24930
@bodhi_vriksha said:
one from my side: Find the largest number which cannot be written as 3x + 5y + 7z where x, y, z are non-negative integers.one more on similar lines: Find the largest number which cannot be written as 13x + 5y + 17z where x, y, z are non-negative integers.Team BV - Kamal Lohia
well here
in first
3x + 5y +7z
3x will goive all numbers of the form 3k
3x+ 5y will give all numbers of the form 3k+ 2 after 5
3x+ 7z will give all numbner of the form 3k + 1 after 7
so 4 will be the answer here as it is not possible

for second
13x+ 5y + 17z
here all 5k numbers are possible
13x + 5y will giver all numbers of the form 5k + 3 after 13
17z+ 5y will give all the numbers of the form 5k+ 2 after 17
13*2 +5y will give all the numbers of form 5k+1 after 26
17*2 + 5y will give all the numbers of form 5k+ 4 after 34
so as seen 29 will be the answer here clearly which is largest numbert not possible.
24931
@Dexian said:
iska approach??
1) 3x+5y+7z = (4k-1)x + (4k+1)y + (4k+3)z
so all numbers possible > 4

2) 13x+5y+17z
ye thoda tricky hai...
5k all possible (5,10,15,20,25,....) [5k form]
13k all possible (13,26,39....) [5k+3 form]
17k all possible (17,34,.....) [5k+2 form]

so the number had to be between 26 and 34

but 2(5k+3) = 5k+1 form and (5k+1) + (5k+3) = 5k+4
and 2(5k+2) = 5k+4
so smallest 5k+4 form number is 34

hence 34-5 = 29 is our number...

@bodhi_vriksha - Kamal sir, I know this problem is based on Frobenius number (Coin problem)...but do we have a direct formula for this?? just curious
24932
@MANJULNEOGI said:
If n is an integer from 1 to 96, what is the probability for n*(n+1)*(n+2) being divisible by 8?
1/2.! All even numbers from 1 to 96 will work..
24933
@sbharadwaj said:
1/2.! All even numbers from 1 to 96 will work..
you missed the case for odd numbers starting from 7 with common difference of 8....hence 12 terms ...
total : 50+12
P=62/100=0.62
24934
@heylady said:
you missed the case for odd numbers starting from 7 with common difference of 8....hence 12 terms ...total : 50+12P=62/100=0.62
Oops..! yeah.. Missed it thanks for correcting..!
24935
@heylady said:
you missed the case for odd numbers starting from 7 with common difference of 8....hence 12 terms ...total : 50+12P=62/100=0.62
this should be 96 na
24936
@iLoveTorres said:
this should be 96 na
yes man...my bad....then P= 60/96=5/8???
24937
IN a factory there are equal number of women and children. women work for 4 hours and children work for 4 hours a day . during festival times the work load goes up by 50 % . the govt rule does not allow children to work for more than 6 hours a day if they are equally efficient and the extra work done by women then extra hours of work put in by women everyday are
24938
@jain4444 said:
IN a factory there are equal number of women and children. women work for 4 hours and children work for 4 hours a day . during festival times the work load goes up by 50 % . the govt rule does not allow children to work for more than 6 hours a day if they are equally efficient and the extra work done by women then extra hours of work put in by women everyday are
2 hours..??
24939
@jain4444 said:
IN a factory there are equal number of women and children. women work for 4 hours and children work for 4 hours a day . during festival times the work load goes up by 50 % . the govt rule does not allow children to work for more than 6 hours a day if they are equally efficient and the extra work done by women then extra hours of work put in by women everyday are
2 hours?
24940
@Logrhythm said:
1) 3x+5y+7z = (4k-1)x + (4k+1)y + (4k+3)z so all numbers possible > 42) 13x+5y+17zye thoda tricky hai...5k all possible (5,10,15,20,25,....) [5k form]13k all possible (13,26,39....) [5k+3 form]17k all possible (17,34,.....) [5k+2 form]so the number had to be between 26 and 34but 2(5k+3) = 5k+1 form and (5k+1) + (5k+3) = 5k+4and 2(5k+2) = 5k+4 so smallest 5k+4 form number is 34hence 34-5 = 29 is our number...@bodhi_vriksha - Kamal sir, I know this problem is based on Frobenius number (Coin problem)...but do we have a direct formula for this?? just curious


Your answers are right . We have a grid approach to this .
for 13x+5y+17z....

1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
and so on ...

now see which no's cant be formed . we know 5 can be formed if y=1 and x=z=0...
so nos in the column of y can be formed..so now we wont check column of 5.. similarly 13 can be formed ...so all nos lying beneath 13 in that column wont be checked. same goes for 22 in first column and 17 in second column.. the largest no that we get is 29 bcuz beneath 29, we have 34 which can be formed ..hence all nos beneath it can also be formed ..
so highest no obtained is 29 😃 hope u guys got it 😃 cheers :)

Team BV----Pratik Gauri

24941
@jain4444 said:
IN a factory there are equal number of women and children. women work for 4 hours and children work for 4 hours a day . during festival times the work load goes up by 50 % . the govt rule does not allow children to work for more than 6 hours a day if they are equally efficient and the extra work done by women then extra hours of work put in by women everyday are
Let number of women and children be x
Total man hour required in a day= 4x+4x=8x
Increase in man hour due to festival = 1.5 * 8x = 12x
Children work=6x
Man hour to be done by women=12x-6x=6x
Extra hour by women = 6-4=2 hrs
24942

Q:Sonia ghandi wants to elect a president for the congress .there are 313 candidate for this post . sonia will follow foll0wing strategies :

a) She asked all the candidate to be in a single row from 1 to 313.
b) Firstly she deduct every person that are on alternate position but start from 2 (i.e. remove 2,4,6)

c) at the instance when she reach at the extreme right end then she start the same process in the same order as left 313 and start to deduct from 311 to on and on .

q) IF sonia wants that manmohan singh will become the presindent then on which position manmohan singh have to be stand.



puys please solve it it stuck ...
24943

An intelligence agency forms two digit code consisting of distinct digits selected from 0 through 9 such that first digit is not 0. Some codes, when hand written on slip, can however potentially create confusion when read upside down- for example 61 may appear as 19. Find the number of codes for which there is no confusion.

a)73 b)70 c)71 d)67
No OA
24944

for geometry freaks

Q:) there is a isosceles triangle : base =6 c.m., altitude = 1 c.m.
find the area of maximum square that can be extracted from this triangle...

24945
@uditultimate said:
Q:Sonia ghandi wants to elect a president for the congress .there are 313 candidate for this post . sonia will follow foll0wing strategies :a) She asked all the candidate to be in a single row from 1 to 313.b) Firstly she deduct every person that are on alternate position but start from 2 (i.e. remove 2,4,6)c) at the instance when she reach at the extreme right end then she start the same process in the same order as left 313 and start to deduct from 311 to on and on .q) IF sonia wants that manmohan singh will become the presindent then on which position manmohan singh have to be stand.puys please solve it it stuck ...
121
24946
@uditultimate said:
for geometry freaksQ there is a isosceles triangle : base =6 c.m., altitude = 1 c.m.find the area of maximum square that can be extracted from this triangle...
36/49 sq
24947

@pankaj1988 bro please describe the solution