Official Quant thread for CAT 2013

MBA CAT 2024
21
@vijay_chandola said:
On buying a camera, the shopkeeper gives three rolls of film free. On buying a camera and six rolls of film, the shopkeeper gives additional four rolls of film free. If the equivalent discount is the same in both cases, then how many rolls will be equal in value to a camera? 12, 15, 18, 24@chandrakant.k : Thanks for starting the thread! @ All: __/\__
18 ?

3R/(C+3R) = 4R/(C+10R)

Solving to get C = 18R

PS: Aah... new season begins already 😃
22
@vijay_chandola said:
On buying a camera, the shopkeeper gives three rolls of film free. On buying a camera and six rolls of film, the shopkeeper gives additional four rolls of film free. If the equivalent discount is the same in both cases, then how many rolls will be equal in value to a camera? 12, 15, 18, 24@chandrakant.k : Thanks for starting the thread! @ All: __/\__
18 Can solve by options.
23

@vijay_chandola said:
On buying a camera, the shopkeeper gives three rolls of film free. On buying a camera and six rolls of film, the shopkeeper gives additional four rolls of film free. If the equivalent discount is the same in both cases, then how many rolls will be equal in value to a camera? 12, 15, 18, 24@chandrakant.k : Thanks for starting the thread! @ All: __/\__
18
24
@krum said:
4ltr-A, 1ltr-Bcost=600weight=40+12=52both are atleast 25% , how is it 51, @Estallar12 sir samjaiye
Its closer to 51 than 54..we both missed this point!
25
@krum said:
4ltr-A, 1ltr-Bcost=600weight=40+12=52both are atleast 25% , how is it 51, @Estallar12 sir samjaiye
even i used this tat is why i posted this question



@YouMadFellow : good solution
26
@billuisback said:
Its closer to 51 than 54..we both missed this point!
actually sir its not 25% , 12/52*100
27
@krum said:
actually sir its not 25% , 12/52*100
hmmm..Den we are right. No pen ..so might be some mistakes..
28
A function f is defined as f(n) = 6^n + 8^n for all integers n. Find the remainder when f(83) is divided by 49.
29
@chandrakant.k said:
take ths for example.. 472+559 = 1031 all conditions are statisified... A mixture comprises two chemicals A and B. The price of A is Rs. 100/- per litre and that of B is Rs.200/- per litre. We can spend a maximum of Rs. 600/- for making the mixture. The densities of A andB are 10 kg/litre and 12 kg/litre respectively. The mixture must contain each of the chemicals to theextent of at least 25% by weight. The maximum weight of the mixture that can be made is closestto:a. 60 kg b. 51 kg c. 54 kg d. 48 kg
let x ltrs of a be taken with Y ltrs of B.

Total Wt, W = 10x+12y .... (1)
Total Cost, 600 = 100x+200y...(2)

Solve 1 and 2
==> 8y=60-w and 4x = w-36

Using options,

for w=60, y=0 condition of 25% voilated.
for w=54, y=3/4, x=9/2 Wts = 3/4*12, 9/2*10 = 9 of y, 45 of x
ratio of y = 1/6 and again 25% voilated.

for w=48, y=3/2, x=3, wts = 3/2*12, 3*10 = 18,30 ratio of y = 18/48 = 3/8 > 36%

So wt has to between 54 and 48... only value satisfying is 51.
30
White balls, each of radius 6.5 cm, are floating in blue paint. While floating, the top of each ball is 4 cm above the paint surface. Now, if the paint is in a cuboid shaped vessel with base dimensions as 100 cm — 10 cm and height 10 cm; and there are 2 balls floating in this vessel, the total area in blue that a bird flying exactly above the vessel sees is:
OPTIONS

1)
2)
3)
4)
31
@vijay_chandola said:
A function f is defined as f(n) = 6^n + 8^n for all integers n. Find the remainder when f(83) is divided by 49.
35 hai kya?
32
@vijay_chandola said:
A function f is defined as f(n) = 6^n + 8^n for all integers n. Find the remainder when f(83) is divided by 49.
too complicated method.. hence ended up with wrong answer.. has to be 35

EDITED
33
@vijay_chandola said:
A function f is defined as f(n) = 6^n + 8^n for all integers n. Find the remainder when f(83) is divided by 49.
35?

((7-1)^83+(7+1)*83)mod49
=(83*7+83*7)mod49
=1162mod49
=35
34
@vijay_chandola said:
A function f is defined as f(n) = 6^n + 8^n for all integers n. Find the remainder when f(83) is divided by 49.
f(n) = (7-1)^n + (7+1)^n

n = 83 -> f(83) = 2* 83C1(7) + higher terms (terms containing 49)

f(83) mod 49 = 35
35
@krum said:
White balls, each of radius 6.5 cm, are floating in blue paint. While floating, the top of each ball is 4 cm above the paint surface. Now, if the paint is in a cuboid shaped vessel with base dimensions as 100 cm — 10 cm and height 10 cm; and there are 2 balls floating in this vessel, the total area in blue that a bird flying exactly above the vessel sees is:OPTIONS1) 2) 3) 4)
3rd Option?
36
@krum said:
White balls, each of radius 6.5 cm, are floating in blue paint. While floating, the top of each ball is 4 cm above the paint surface. Now, if the paint is in a cuboid shaped vessel with base dimensions as 100 cm — 10 cm and height 10 cm; and there are 2 balls floating in this vessel, the total area in blue that a bird flying exactly above the vessel sees is:OPTIONS1) 2) 3) 4)
radius of the white surface portion=sqrt(6.5^2-2.5^2)=6
=> area of two white balls (that can be seen from the top)=2*6^2*Pi=72*pi

==> Total area in blue=1000-72*pi
37
@vijay_chandola said:
A function f is defined as f(n) = 6^n + 8^n for all integers n. Find the remainder when f(83) is divided by 49.
35
38
@vijay_chandola said:
radius of the white surface portion=sqrt(6.5^2-2.5^2)=6=> area of two white balls (that can be seen from the top)=2*6^2*Pi=72*pi==> Total area in blue=1000-72*pi
We can do the same by Jugaad. area of two Balls will be 83 pi. Since they are 4 inches above, only some part will be submersed. Nearest value. 72 pi!
39
Let P0(x) = x^3 + 313x^2 – 77x – 8.

For integers n ≥1, define Pn(x) = Pn-1(x – n). Find the coefficient of x in P20(x)?
OPTIONS

1) 673
2) 763
3) 457
4) 856
5) None of these
40
@vijay_chandola said:
A function f is defined as f(n) = 6^n + 8^n for all integers n. Find the remainder when f(83) is divided by 49.
R(6^84/49) = R(6^83/49)*R(6/49) ----> 1= x* 6 -----> 41
R(8^84/49) = R(8^83/49) *R(8/49) ----> 1= y* 8------> 43

Therefore, R{(41+43)/49} = 35.