Official Quant thread for CAT 2013

@Faruq said:
3 different numbers A, B, C has 2, 3, 4 factors respectively. when A , B and C are multiplied a new number D is produced that has n number of factors. How many different values of n are possible ?
7 hai kya??

A=2 = a
B=3=b^2
C=4 = cd,e^3

now make pairs of A*B*C considering C=cd

possibilities :
1) (a)*(b^2)*(cd) =2*3*2*2=24(wen all different)
2)(a)*(b^2)*(ad) = a*2*b^2*d=18(wen C has 1 digit same as A)
3)(a)*(b^2)*(bd)= a*b^3*d=16(wen C has 1 digit same as B)
4)(a)*(a^2)*(cd)=a^3*c*d=16 (wen digit B is same as A)
5)(a)*(a^2)*(ad)=10

Consider C=e^3
possible pairs
6)a*b^2*e^3=24
7)a*b^2*a^3=15
8)a*b^2*b^3=12
9)a*a^2*a^3=7

so possible values are = 7,10,12,15,16,18,24

so 7 values possible??
@impluse said:
there are two numbers m and n. which of the following must be added to two numbers m and n such that their ratio becomes x:ya) mx+ny/y=xb)my+nx/y-xc)my-nx/x-yd)my+nx/y+xplease share the approach


let the number be z

(m+z)/(n+z) = x/y

my+zy=nx+zx

my-nx=z(x-y)

z=(my-nx)/(x-y)
@chevy thanks

Find the remainder when 3^3+(33)^3+(333)^3+....+(333....67 times)^3 is divided by 7???

a)0
b)1
c)2
d)6

Please provide the approach along with solutions.
To reach next floor of a building using an escalator moving upwards,a person takes 56 seconds and climbs 42 steps of an escalator.When the same person increases his speed,he can climb 94 steps in 30 seconds to reach the next floor.how many steps does the escalator have between the two floors?
a)112
b)124
c)144
d)154

Please provide the approach along with solutions.
@saurabhlumarrai said:
Find the remainder when 3^3+(33)^3+(333)^3+....+(333....67 times)^3 is divided by 7???a)0b)1c)2d)6Please provide the approach along with solutions.
2 ?
3^3 + (-2)^3 + (-3)^3 + 1^3 + (-1)^3 +(0)^3 +3^3 + (-2)^3 ...
= 11 (-1) + 27

Hence, = 2 ..
Edited
@saurabhlumarrai said:
Find the remainder when 3^3+(33)^3+(333)^3+....+(333....67 times)^3 is divided by 7???a)0b)1c)2d)6Please provide the approach along with solutions.
3^3+33^3+333^3+3333^3.......... mod 7
=3^3+5^3+4^3+1^3+6^3+0^3+3^3+5^3+4^3+.........3^3 mod 7
=11*(5^3) + 3^3 mod 7 (1^3+ 6^3 mod 7 =0, 3^3+4^3 mod 7 = 0)
=4*6+6 mod 7
=2 mod 7
@saurabhlumarrai said:
To reach next floor of a building using an escalator moving upwards,a person takes 56 seconds and climbs 42 steps of an escalator.When the same person increases his speed,he can climb 94 steps in 30 seconds to reach the next floor.how many steps does the escalator have between the two floors?a)112b)124c)144d)154

Please provide the approach along with solutions.
42+56e=94+30e
26e=52
e= 2
so total = 42+56*2=42+112=154
@saurabhlumarrai no. of steps is identical in both cases...the difference in the no. of steps he climbs (=52) is the equal to neg. diff in the no. of steps the elevator moves...ratio of distances moved by elevator in the two cases is 56:30...we get the actual values to be 112:60...so our answer is (112+42)=(94+60)=154
@saurabhlumarrai said:
To reach next floor of a building using an escalator moving upwards,a person takes 56 seconds and climbs 42 steps of an escalator.When the same person increases his speed,he can climb 94 steps in 30 seconds to reach the next floor.how many steps does the escalator have between the two floors?a)112b)124c)144d)154Please provide the approach along with solutions.
154 ?

42 + 56*x = 94 + 30*x
x = 2
no. of steps = 94 + 30*2 = 154

Q hritik draws a card frm well shuffled pack of cards . if the card is red king he is paid rs 39 while if it is a black honour , he is paid rs. 26 n all in other case he has to pay rs.13 . in the long run per draw of a card hritik makes an avg of ??

@saurabhlumarrai said:
Find the remainder when 3^3+(33)^3+(333)^3+....+(333....67 times)^3 is divided by 7???a)0b)1c)2d)6Please provide the approach along with solutions.
3/7 R=3
33/7 R = 5
333/7 R = 4
3333/7 R=1
33333/7 R=6
333333/7 R=0
the cycle repeats after this....
hence this will be for 11 terms...like 11*6+1 = 67...
last term will give a remainder of 3
(6+6+1+1+6+0)*11 + 6
226/7
R=2

mera ans bhi bata do koi

@Abir1103 said:
Q hritik draws a card frm well shuffled pack of cards . if the card is red king he is paid rs 39 while if it is a black honour , he is paid rs. 26 n all in other case he has to pay rs.13 . in the long run per draw of a card hritik makes an avg of ??
I guess he will make a loss of 9.5 man...
OA kya hai??
@saurabhlumarrai said:
Find the remainder when 3^3+(33)^3+(333)^3+....+(333....67 times)^3 is divided by 7???a)0b)1c)2d)6Please provide the approach along with solutions.
2?
[(-1)^3 + ( -1)^3 + ( 1)^3+(1)^3 + (-1)^3 + 0]mod 7 = -1 mod 7

dis pattern repeats after every 6 terms,,till 66 dere are 11 time 6 terms

so 11*-1 + 27

16 mod 7 = 2
@saurabhlumarrai said:
To reach next floor of a building using an escalator moving upwards,a person takes 56 seconds and climbs 42 steps of an escalator.When the same person increases his speed,he can climb 94 steps in 30 seconds to reach the next floor.how many steps does the escalator have between the two floors?a)112b)124c)144d)154Please provide the approach along with solutions.
154 steps??

let speed of escalator is a steps/sec

42+56a=94+30a

a=2

putting a in eqn above

42+56*2 = 154??
@impluse said:
there are two numbers m and n. which of the following must be added to two numbers m and n such that their ratio becomes x:ya) mx+ny/y=xb)my+nx/y-xc)my-nx/x-yd)my+nx/y+xplease share the approach
You can solve this question by assuming values....
m=1
n=2
add 2 to both
m+2/n+2 = 3/4
so x=3
and y=4
check the option that gives you value 2...

P.S. : Method will fail if more than one option gives you the same value...
Q hritik draws a card frm well shuffled pack of cards . if the card is red king he is paid rs 39 while if it is a black honour , he is paid rs. 26 n all in other case he has to pay rs.13 . in the long run per draw of a card hritik makes an avg of ??

need soln plz
@saurav205 loss of 5 hai
@Abir1103 said:
Q hritik draws a card frm well shuffled pack of cards . if the card is red king he is paid rs 39 while if it is a black honour , he is paid rs. 26 n all in other case he has to pay rs.13 . in the long run per draw of a card hritik makes an avg of ??
(2*39+10*26+40*13)/52= 16.5

:neutral: