Official Quant thread for CAT 2013

MBA CAT 2024
30778
@hexagon said:
@naga25french thoda detail me explain karoge
What do you want me to explain now ? Atleast quote the part which needs explanation.
@junefever said:
Is it a typo error??
shouldn't it be
prob reduces to 33 / 13 . remainder is 7
Not typo error but carelessness
30779
Check your D.S.aBILITY :

In the line graph depicting sales of scooters, the sales values are plotted on the Y-axis and the years on the X-axis. The sale in year 2002 is point A and the sale in year 2008 is point B. In between these years, the sales are depicted by different points and these successive points are joined by straight line segments.

Information in which of the following statement/s is required to find the annual average growth rate in the sales of scooters over 2002-2008?

I. The scale of Y-axis is 1cm = 10,000 scooters and on the X-axis, each successive year is marked at a gap of 1 cm.

II. The straight line AB makes angle of 45 degrees with the positive X-axis, measured anti-clockwise.

a] Statement I alone
b] Statement II alone
c] Both statements I and II
d] cannot be found even by both statements
30780
@junefever said:
Find remainder when 33333333......86 times is divided by 13?
7 imo
30781
@floamiya said:
Check your D.S.aBILITY :In the line graph depicting sales of scooters, the sales values are plotted on the Y-axis and the years on the X-axis. The sale in year 2002 is point A and the sale in year 2008 is point B. In between these years, the sales are depicted by different points and these successive points are joined by straight line segments.Information in which of the following statement/s is required to find the annual average growth rate in the sales of scooters over 2002-2008?I. The scale of Y-axis is 1cm = 10,000 scooters and on the X-axis, each successive year is marked at a gap of 1 cm.II. The straight line AB makes angle of 45 degrees with the positive X-axis, measured anti-clockwise.a] Statement I aloneb] Statement II alonec] Both statements I and IId] cannot be found even by both statements
option d) we need to know the value of A imo.
30782
@zuloo said:
30 hai kya?
thoda detail karna bhai..
30783
@hexagon said:
@naga25french sorry for that Find remainder when 33333333......86 times is divided by 13?i didnot understand how to apply ferm thm to the above question as explained by you
according to fermat't theroem , 333... 12 times is divisble by 13.. so repeating this 7 times. we get 84 times 333.... divisble... now remains last 2 digits. 33... which gives remainder of 7 when divided by 13..
30784
x,y and z are positive reals. What is the maximum value of

[(x+y+z)^3−x^3−y^3−z^3]^2/[(x^2+y^2+z^2)^3−x^6−y^6−z^6]
30785
@floamiya said:
Check your D.S.aBILITY :In the line graph depicting sales of scooters, the sales values are plotted on the Y-axis and the years on the X-axis. The sale in year 2002 is point A and the sale in year 2008 is point B. In between these years, the sales are depicted by different points and these successive points are joined by straight line segments.Information in which of the following statement/s is required to find the annual average growth rate in the sales of scooters over 2002-2008?I. The scale of Y-axis is 1cm = 10,000 scooters and on the X-axis, each successive year is marked at a gap of 1 cm.II. The straight line AB makes angle of 45 degrees with the positive X-axis, measured anti-clockwise.a] Statement I aloneb] Statement II alonec] Both statements I and IId] cannot be found even by both statements
I think it is C
as tan45 will say
sale graph length/year graph length=1
we know year graph length=7 cm
so sale length will also be 7 cm
so total sale volume increase will be 7*10000
average growth will be 7*10000/7=10000/year
30786

@jain4444 said:
x,y and z are positive reals. What is the maximum value of[(x+y+z)^3−x^3−y^3−z^3]^2/[(x^2+y^2+z^2)^3−x^6−y^6−z^6]
24???
30787
@zuloo said:
option d) we need to know the value of A imo.
I don't think we need the value of A
we need to know the value of (B-A) which is 7*10000=70000
so average growth will be 70000/7=10000
30788
How many ordered quadruples of distinct positive integers (a,b,c,d) are there such that 1/a + 1/b + 1/c + 1/d = 1 ?
30789
@pratskool said:
24???
@hexagon said:
@jain4444 is it ans 24
Approach plz :)
30790
100! when expanded, ends in exactly 24 zeroes in decimal system. In how many other number systems, when converted, 100! still ends in exactly 24 zeroes?
(For example, 5! = 120 has one zero when expanded in decimal system and it becomes 71 after conversion in base-7 and has no zeroes at end.)
30791
@hexagon said:
my approach (0001) (0022)(3330 ) (4444) each has 4! for the first three and for the last one 1
whats about (0 2 3 6)? and distinct ???
30792
@Asfakul said:
100! when expanded, ends in exactly 24 zeroes in decimal system. In how many other number systems, when converted, 100! still ends in exactly 24 zeroes?(For example, 5! = 120 has one zero when expanded in decimal system and it becomes 71 after conversion in base-7 and has no zeroes at end.)
Will it be 1?
in base 5 system..
30793
@hexagon said:
my approach (0001) (0022)(3330 ) (4444) each has 4! for the first three and for the last one 1
0 is not a positive integer?

Also, 0001 can be arranged in 4 ways not 4!

regards
scrabbler
30794
@jain4444 said:
How many ordered quadruples of distinct positive integers (a,b,c,d) are there such that 1/a + 1/b + 1/c + 1/d = 1 ?
my approach
factors of 100 = 1,2,4,5,10,20,25,50,100
find facors of hundred whose sum is hundred
100 = 5 +25 + 20 +50
1 = 1/20 +1/4 +1/5 +1/2
ony one way
hence 4! = 24 ways
30795
@psk.becks said:
my approach factors of 100 = 1,2,4,5,10,20,25,50,100find facors of hundred whose sum is hundred100 = 5 +25 + 20 +50 1 = 1/20 +1/4 +1/5 +1/2ony one way hence 4! = 24 ways
Why 100?

Besides, there could be other answers too. Did little trial and error, found 2, 3, 9, 18 works too.

regards
scrabbler
30796
@scrabbler said:
Why 100?Besides, there could be other answers too. Did little trial and error, found 2, 3, 9, 18 works too.regardsscrabbler
(6662) (8842) (12,12,3,2) as well
30797
@jain4444 said:
How many ordered quadruples of distinct positive integers (a,b,c,d) are there such that 1/a + 1/b + 1/c + 1/d = 1 ?
Lets say that a > b > c > d, then

1/a + 1/b + 1/c + 1/d

4/d > 1
d

So, possible values of d are 2 and 3, as d can not be 1

When d = 2
1/a + 1/b + 1/c = 1/2
1/a + 1/b + 1/c
3/c > 1/2
c

c = 3
1/a + 1/b = 1/6
(a - 6)(b - 6) = 36
(b, a) = (7, 42), (8, 24), (9, 18), (10, 15)

c = 4
1/a + 1/b = 1/4
(a - 4)(b - 4) = 16
(b, a) = (5, 20), (6, 12)

c = 5
1/a + 1/b = 3/10
(3a - 10)(3b - 10) = 100
(a, b) = (20, 4), (10, 5) ....(not possible as b should be greater than 5)

When d = 3
1/a + 1/b + 1/c = 2/3
1/a + 1/b + 1/c 3/c > 2/3
c
c = 4
1/a + 1/b = 5/12
(5a - 12)(5b - 12) = 144
(a, b) = (12, 3), (6, 4) (not possible as b should be greater than 4)

So, possible solutions are (2, 3, 7, 42), (2, 3, 8, 24), (2, 3, 9, 18), (2, 3, 10, 15), (2, 4, 5, 20), (2, 4, 6, 12) and permutations

So, 6*4! = 144 ordered quadruplets