@ScareCrow28 said:95*100/x = 105x = 1900/21
hw u made this equ,cn u explain it??
@sumit99 said:A cloth merchant says due to slump in the market, he sells the cloth at 5% loss, but he uses a fake metre scale and actually gains 5%. What is the length of the scale?A- 92.75 cmB-90.25 cmC-1900/21D-90.8
x-5+.05x = 5
1.05x = 10
x = 10/1.05 = 9.52
so 100-9.52 = 90.48?? ~ 90.25 (to match the options)
@sumit99 said:hw u made this equ,cn u explain it??
Sorry bro! 
Here's the explanation:
Let, 1m=Rs 100
5% loss means he sold it for Rs 95
Fake metre scale gains: 5% = He got Rs 105
5% loss means he sold it for Rs 95
Fake metre scale gains: 5% = He got Rs 105
So, 95*100/d = 105
Because he sold less metre for same amount
d = 1900/21 ?
@saurav205 said:Question :for how many prime nos. p is p^4+15p^2-1 a prime no.?P.S. : I do not have the OA...
prime number is always odd except 2 ,( odd^4 = odd )+ (15*odd^2=odd) , so finally odd+odd-1=even, vch will be never a prime !! so "0" values, check for p=2, its value is even 75 vch isn't prime
@saurav205 : i guess none becoz
P^4 -1 +15p^2 = always divisible
how :
when P is even = then P^4-1= ends with 5 + 60 = last digit 5 = hence not prime
when p= 5= then p^4-1 + 15*25= 999 = divisible
when p is odd considering cycilicity of 1 3 5 7 9 = last digit will be 1 = hence last digit of expression = 5 .. not prime
@sumit99 said:A cloth merchant says due to slump in the market, he sells the cloth at 5% loss, but he uses a fake metre scale and actually gains 5%. What is the length of the scale?A- 92.75 cmB-90.25 cmC-1900/21D-90.8
OA) C: 1900/21
@The_Loser : i guess none becoz = n^2+ n+ 1 is not a complete square root //..
it will be if u add n or make it a complete square root expression
@The_Loser said:perfect. explain
I did it more intuitively rather mathematically
n(n+1) + 1
n*(n+1) are 2 consecutive terms and co-prime they would have different factor(s) and +1 won't make it so that it gets to a perfect square...
or you can do it this way...
n^2+n+1 = k^2
4k^2 - (2n+1)^2 = 3
(2k+2n+1)(2k-2n11) = 3 = 3*1
2k+2n+1 = 3 and 2k-2n-1 = 1 (k=1 and n=0)
2k+2n+1 = 1 and 2k-2n-1 = 3 (k=1 and n=-1)
hence, only 2 such integer values exist
@saurav205 said:Question :for how many prime nos. p is p^4+15p^2-1 a prime no.?P.S. : I do not have the OA...
none:
for p=1=> 15
p=2=> 75
and for p=>3
it should take (6k+ -1) form w/c its not taking at all . hence NONE
for p=1=> 15
p=2=> 75
and for p=>3
it should take (6k+ -1) form w/c its not taking at all . hence NONE
now this 95% of cost of product : actually turns out to be : 105% of C.P /// becoz of fake scale
hence = 95/105*100= 1900/21
@swapnil4ever2u said:how many 3 digit numbers have their unit digit neither less than the hundred digit nor less than the tens digit ??
ans: 330
ans: 330
@sumit99 said:A cloth merchant says due to slump in the market, he sells the cloth at 5% loss, but he uses a fake metre scale and actually gains 5%. What is the length of the scale?A- 92.75 cmB-90.25 cmC-1900/21D-90.8
1/20 = (CP-SP1)/CP ......case 1 loss 5%
=>19CP=SP1....1
1/20 = (Sp2-CP)/CP.........case 2 gain 5%
=>21CP=sp2......2
divide both and multiply by 100.since we are finding how mch less he gives for every 100m.
1900/21??
=>19CP=SP1....1
1/20 = (Sp2-CP)/CP.........case 2 gain 5%
=>21CP=sp2......2
divide both and multiply by 100.since we are finding how mch less he gives for every 100m.
1900/21??
@The_Loser said:For how many natural numbers, N the expression N ˛ + N + 1 results in a perfect square?
none
n^2 + n + 1 = x^2
n^2 +n +1-x^2 = 0
taking discriminant
-1+_/4x^2+3/2
now _/4x^2+3 should be a natural number
4x^3+ 3 =y^2
(y+2x)(y-2x)=3
y+2x =3
y-2x=1
y = 2 x = 1/2
not possible for any integral natural x
so none
1900/21
@The_Loser said:For how many natural numbers, N the expression N ˛ + N + 1 results in a perfect square?
2 values
@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
bhai can u plz explain the part in bold.. ?
@viewpt said:bhai its the only option nearer to 1900/21=90.45
sir, i think u overlooked... option C 1900/21 hi h!!
@ChirpiBird said:sir, i think u overlooked... option C 1900/21 hi h!!
aisa hai kya..my bad..feeling sleepy
..now chk edited.
..now chk edited.@saurav205 said:Question :for how many prime nos. p is p^4+15p^2-1 a prime no.?P.S. : I do not have the OA...
my approach
as p is prime it is of the form 6k+-1
so its power 4 is ofv the form 6k+1
similarly power 2 is also of the form 6k+1
6k+1+ 90k + 15 - 1
6k + 3
which is never prime so 0