Official Quant thread for CAT 2013

MBA CAT 2024
29606

brass in an alloy of copper and zinc. bronze is an alloy containing 80% of copper, 4% of zinc and 16% of tin. A fused mass of brass and bronze is found to contain 74% of copper, 16% of zinc and 10% of tin . The ratio of copper to zinc in brass is

29607
@YouMadFellow said:
N = 10^20000Divisor = 10^200 + 7Remainder = (7)^10010^20000 = Q*(10^200 + 7) + (7^100)Q*(10^200 + 7) = 10^20000 - 7^100Last digit of RHS = last digit of (10^20000 - 7^100) = [10- 1] = 9Last digit of LHS = 0 + Last digit of (Q * 7 )=> Last digit of Q = 7 ?
hey hw u got this remainder can u explain
29608
@ishu1991 said:
hey hw u got this remainder can u explain
Using remainder theorem:

Remainder of f(x) divided by (x-a) is given by f(a)

Here x = 10^200 , f(x) = (10^200)^100 = x^100
and a = (- 7)

=> Remainder = f(a) = (-7)^100 = 7^100
29609
@vbhvgupta said:
brass in an alloy of copper and zinc. bronze is an alloy containing 80% of copper, 4% of zinc and 16% of tin. A fused mass of brass and bronze is found to contain 74% of copper, 16% of zinc and 10% of tin . The ratio of copper to zinc in brass is
The Tin has come in the alloy has come only from the bronze i.e 10% from the 16% in bronze. LCM of 10 and 16 = 80 so let the weight of the alloy be 800 grams. (easy for calculation)

copper is = 74/100*800 = 592 grams
Zinc = 16*8 = 128 grams
Tin = 10* 8 = 80 grams.

From the bronze we will find the contribution of each metal -
Tin = 16 * 5 = 80 grams
Copper = 80* 5 = 400 grams
Zinc = 4*5 = 20 grams.

The residue has come from Brass: -
Copper = 592 - 400 = 192 grams
Zinc = 128 - 20 = 108 Grams

Copper : zinc = 192:108 = 64 : 36 = 16: 9 Ans

29610
@vbhvgupta said:
brass in an alloy of copper and zinc. bronze is an alloy containing 80% of copper, 4% of zinc and 16% of tin. A fused mass of brass and bronze is found to contain 74% of copper, 16% of zinc and 10% of tin . The ratio of copper to zinc in brass is
80:4:16
x:y
----------
74:16:10..
taking Bronze as 100 kg.s 16=10%....totl mass=160 kg.s
Brass used=60 kg.s
x:y=38.4/21.6=16:9
29611
@shattereddream said:
A = {179, 180, 181, €Ś..,360}. B is a subset of A such that sum of no two elements of B is divisible by 9. The number of elements in B cannot exceed
OA - 82
29612
@vbhvgupta said:
brass in an alloy of copper and zinc. bronze is an alloy containing 80% of copper, 4% of zinc and 16% of tin. A fused mass of brass and bronze is found to contain 74% of copper, 16% of zinc and 10% of tin . The ratio of copper to zinc in brass is
16:9 ?

quantity of tin in bronze = quantity of tin in fused mass
now let total quantity of bronze be 100
so tin = 16/100*100 = 16
zinc = 4/100*100 = 4
copper = 80/100*100 = 80

now quantity of tin in fused mass = 10/100*x = 16----> x = 160 (total quantity of fused mass)
so quantity of copper = 74/100*160 = 118.4
quantity of zinc = 16/100*160 = 25.6

therefore quantity of copper in brass = 118.4 - 80 = 38.4
quantity of zinc = 25.6 - 4 = 21.6

ratio = 38.4/21.6 = 16/9
29613
@vbhvgupta said:
brass in an alloy of copper and zinc. bronze is an alloy containing 80% of copper, 4% of zinc and 16% of tin. A fused mass of brass and bronze is found to contain 74% of copper, 16% of zinc and 10% of tin . The ratio of copper to zinc in brass is
is it 16:9?????/
29614
@vbhvgupta said:
brass in an alloy of copper and zinc. bronze is an alloy containing 80% of copper, 4% of zinc and 16% of tin. A fused mass of brass and bronze is found to contain 74% of copper, 16% of zinc and 10% of tin . The ratio of copper to zinc in brass is
64 : 36 i.e. 16 : 9

Trying to do orally:

look at copper : zinc : tin

80 : 4 : 16
gives
74 : 16 : 10
when mixed with
C : Z : 0

Tin (16 - 10 - 0) tells us that 16 - 10 : 10 - 0 = 3 : 5 is the ratio. Others too must change in same ratio 80 - 74 - C => C is 64 and similarly 4 : 16 : Z => Z is 36.

regards
scrabbler
29615
@vbhvgupta said:
brass in an alloy of copper and zinc. bronze is an alloy containing 80% of copper, 4% of zinc and 16% of tin. A fused mass of brass and bronze is found to contain 74% of copper, 16% of zinc and 10% of tin . The ratio of copper to zinc in brass is
let a be volume of brass and b be of bronze

0.16a/a+b=0.1
a:b=3:5
for copper
x*3+0.8*5=8*0.74
x=.64
so 64/100-64 = 16:9
29616
@vbhvgupta said:
brass in an alloy of copper and zinc. bronze is an alloy containing 80% of copper, 4% of zinc and 16% of tin. A fused mass of brass and bronze is found to contain 74% of copper, 16% of zinc and 10% of tin . The ratio of copper to zinc in brass is
New Alloy: C:Z:T = 74:16:10 = Lets say 100kg
Bronze = 80%C + 4%Z + 16%T
Brass = a%C + b%Z + 0%T

T = 16%Bronze = 10kg
Bronze = 125/2 Kg

Z = 4%125/2 Bronze + b% Brass= 16 = 2.5 + b% Brass
b%Brass = 13.5
Similarly, a%Brass = 74 - 50 = 24

a:b = 24:13.5 = 48:27 = 16:9
29617
@scrabbler said:
3030 when q is perpendicular to p, close to 90 when q is almost parallel to p...Damn, 3-D visualisation is confusing regardsscrabbler
The OA is 30
But can you please tell me how did you arrive at this : "30 when q is perpendicular to p, close to 90 when q is almost parallel to p..."
Having a tough time visualising it.
29618

N is an 8 digit no and s(N) denotes the sum of its digits. IF N +S(N) = 100000000 Find ten's digit of N.

29619

A two digit no is 18 less than the square of the sum of its digits. How many such no exists?

29620
@vbhvgupta said:
A to digit no is 18 less than the square of the sum of its digits. How many such no exists?
__/\__

Whats the OA sir??
m getting 2..
63 and 82..
29621
@vbhvgupta cant get ur quest.. is it a two digit no.??


29622
@varathawins said:
@vbhvgupta cant get ur quest.. is it a two digit no.??
YES..:)
29623
@saurav205 said:
__/\__Whats the OA sir??m getting 2..63 and 82..
___/\___ sahi hai bhai.
29624
@varathawins said:
@vbhvgupta cant get ur quest.. is it a two digit no.??
@saurav205
2(two) digit no...
29625
@vbhvgupta said:
___/\___ sahi hai bhai.
Tab approach daal deta hoon....
Its a bit unconventional...but still worked ....
first assumed the number to be 10a+b

and then assumed a+b = 6(just random)
so, 10a+b = 36 - 18= 18
and a+b = 6
solving the two ...we see 9a = 12....
so to get the desired result 9a = 9M...(as a has to be a whole number)..
check till the values where 9a also a+b so check for a+b = 5,6,7,8,9,10...