If n^3+100 is exactly divisible by n+10, where n is a positive integer find the maximum possible value of n.
a) 790
b) 780
c) 660
d) 890
e) 880
Everyone, please don't post so many posts to give the OA/Thank you/ Praises etc, a simple like is an acknowledgement by which one can know that the person is correct. Try to edit the same post as far as possible, it keeps the thread clean and maintains readability. A small request from my side 😃
@joyjitpal said:If a number system, the product of 44 and 11 is 1034. The number 3111 of this system, when converted to the decimal number system becomes(a) 406 (b) 1086 (c) 213 (d) 691
406?
The base is 5
@joyjitpal said:If a number system, the product of 44 and 11 is 1034. The number 3111 of this system, when converted to the decimal number system becomes(a) 406 (b) 1086 (c) 213 (d) 691
(4n+4)(n+1) = n^3 + 3n + 4
4n^2 + 8n + 4 = n^3 + 3n + 4
n^3 - 4n^2 - 5n = 0
n^2 - 4n - 5 = 0
(n-5)(n+1) = 0
n = 5
3111_5 = 406_10
4n^2 + 8n + 4 = n^3 + 3n + 4
n^3 - 4n^2 - 5n = 0
n^2 - 4n - 5 = 0
(n-5)(n+1) = 0
n = 5
3111_5 = 406_10
@joyjitpal said:If a number system, the product of 44 and 11 is 1034. The number 3111 of this system, when converted to the decimal number system becomes(a) 406 (b) 1086 (c) 213 (d) 691
The number system is base 5.
1 + 5 + 25 + 3*125 = 375 + 31 = 406.
How did I know the base was 5?
4*1 = 4, unit's place.
4*1 + 4*1 = 8, ten's place.
But the ten's place here is 3.
8mod5 = 3.
So, number system is of base 5.
1 + 5 + 25 + 3*125 = 375 + 31 = 406.
How did I know the base was 5?
4*1 = 4, unit's place.
4*1 + 4*1 = 8, ten's place.
But the ten's place here is 3.
8mod5 = 3.
So, number system is of base 5.
@joyjitpal said:If n^3+100 is exactly divisible by n+10, where n is a positive integer find the maximum possible value of n.a) 790 b) 780 c) 660 d) 890 e) 880
[n^3 + 100] = [n+10]^3 - 30n(n+10) - 900
Q = [n+10]^2 - 30n - [900/(n+10)] = Integer
Hence, n = 890
Q = [n+10]^2 - 30n - [900/(n+10)] = Integer
Hence, n = 890
@joyjitpal said:If n^3+100 is exactly divisible by n+10, where n is a positive integer find the maximum possible value of n.a) 790 b) 780 c) 660 d) 890 e) 880
Used the long division method to calculate the remainder
Got this equation in the end :
(n^3+100)/(n+10) = (n^2-10n+100) - 900/(n+10)
For the above equation to have integer values 900/(n+10) should be an integer.
Max possible value of n would be 890 IMO
Please correct me if i am wrong
An equilateral triangle ABC is inscribed in a circle.let P be a point on the circle opposite to point B i.e P is on the arc AC. Then which one is correct?
A)AP>BP+CP B)AP=2BP+CP
C)AP=BP+2CP D)AP=BP+CP.
A)AP>BP+CP B)AP=2BP+CP
C)AP=BP+2CP D)AP=BP+CP.
@ajeetaryans said:An equilateral triangle ABC is inscribed in a circle.let P be a point on the circle opposite to point B i.e P is on the arc AC. Then which one is correct?A)AP>BP+CP B)AP=2BP+CP C)AP=BP+2CP D)AP=BP+CP.
none?
min value of BP is side of the triangle.....max value of AP is side of the triangle....
min value of BP is side of the triangle.....max value of AP is side of the triangle....
@ajeetaryans said:An equilateral triangle ABC is inscribed in a circle.let P be a point on the circle opposite to point B i.e P is on the arc AC. Then which one is correct?A)AP>BP+CP B)AP=2BP+CP C)AP=BP+2CP D)AP=BP+CP.
BP can't be less than AP & CP.. none of the options follows this ??
@ajeetaryans said:An equilateral triangle ABC is inscribed in a circle.let P be a point on the circle opposite to point B i.e P is on the arc AC. Then which one is correct?A)AP>BP+CP B)AP=2BP+CP C)AP=BP+2CP D)AP=BP+CP.
not getting any of the four options.
Let side of triangle be x
Min. BP= x and Max. AP=x
so none follows as per the options.
x,y,z are 3 positive real nos. such that 2x+3y+4z=36. whats the max possible value of xy3z2?
1) 4096
2) 4913
3) 5484
4) 5832
5) 6436
No OA...
@manasvr said:x,y,z are 3 positive real nos. such that 2x+3y+4z=36. whats the max possible value of xy3z2?1) 40962) 49133) 54844) 58325) 6436No OA...
I am taking xy3z2 as xy^3z^2
2x/1= 3y/3 = 4z/2
use the above relation, and with the given equation,
2x+3y+4z=36
calculate the respective value, which will be,
x=3
y=6
z=3
ans= 5832
Three players A, B and C play the following game.
• There are three cards, each marked with a different single-digit positive numbers.
• In each round the cards are randomly dealt to the players and each receives the number of marbles equal to the integer on his card.
• Result after two or more rounds:
players A B C
total marbles 20 10 9
• In the last round the player B received the largest number of marbles.
• There are three cards, each marked with a different single-digit positive numbers.
• In each round the cards are randomly dealt to the players and each receives the number of marbles equal to the integer on his card.
• Result after two or more rounds:
players A B C
total marbles 20 10 9
• In the last round the player B received the largest number of marbles.
Ques. If cards are arranged according to descending order of the numbers written on them, who got the middlemost card in the first round????..plz explain.. (Ans. C)
@badwal.aman said:Three players A, B and C play the following game. • There are three cards, each marked with a different single-digit positive numbers. • In each round the cards are randomly dealt to the players and each receives the number of marbles equal to the integer on his card. • Result after two or more rounds:players A B Ctotal marbles 20 10 9 • In the last round the player B received the largest number of marbles.Ques. If cards are arranged according to descending order of the numbers written on them, who got the middlemost card in the first round????..plz explain.. (Ans. C)
8,4,1 .. so C got middlemost ??
@pulkitgurditta said:8,4,1 .. so C got middlemost ??
20 + 10 + 9 = 3a+ 3b + 3c .. so a+b+c=13 ... now make combinations.. so i got 8,4,1
and distributions were... A B C . 1 (8,1,4) , (8,1,4) (4,8,1)