[shreyans_nitt]

Originally Posted by target_iim_a

Which of the following represents the sum of a certtain no. of consecutive natural numbers starting from 1?
1)206
2)439
3)805
4)1125
5)1275

options*2 shud be nearest to a square.....thats an easy way to check.....rest the solution has already come 1275....

[GildroY]

Originally Posted by shreyans_nitt

options*2 shud be nearest to a square.....thats an easy way to check.....rest the solution has already come 1275....

I did it the same way for initial approx. estimation of the answer, but didn't mentioned it ...
A few things are trade secrets.

[amit2ibm]

f(94) - f(93)= 94^2 - 93^2
f(92) - f(90)= 92^2 - 91^2
|| || || ||
|| || || ||
f(20) - f(1= 20^2 - 19^2
-------------------------- adding all these equations we get
f(94) - f(1 = (94^2 -93^2) + (92^2 - 91^2) +................+ (20^2 - 19^2)
f(94) - f(1 = 187 + 183 + 179 + ................ + 39 (sum of an AP whose first term
is 39, common diff is 4 and last
term is 187)
f(94) - f(1 = 4294
f(94) - {19^2 - f(19)} = 4294
f(94) - 361 + f(19) = 4294
f(94) + f(19) = 4655
2* f(94) = 4655
f(94) = 2327.5

hope dis z rite? plz tel me..

[GildroY]

Answer this question:

[1] What is the remainder, when 16! is divided by 17?

[shreyans_nitt]

(p-1)!+1 is multiple of p, where p is a prime.{Wilson's theorem}

so 16! will leave a remainder of 16 when divided by 17......

[kanu09]

Solve these...

(a) Let F(x)=x^2+3x+2 and let S be the set of integers {0,1,2,.......25}. Find the number of membersofs of S such that F(s) has a remainder of zero when divided by six

(b) Let N be the largest integer divisible by all positive integers less than its cube root. The number of divisors of N are

(a) 16 (b) 24 (c) 18 (d) none of the foregoing

[shreyans_nitt]

Originally Posted by kanu09

Solve these...

(a) Let F(x)=x^2+3x+2 and let S be the set of integers {0,1,2,.......25}. Find the number of membersofs of S such that F(s) has a remainder of zero when divided by six

x^2+3x+2 = (x+2) (x+1)

either (x+2) shud be a multiple of 3 or (x+1) shud be a multiple of 3...the other one will definitely be even in that case...so the whole will be divisible by 6..

(x+2) = 1,4,7,10.....25
(x+1) = 2,5,8.........22

so in total 17 numbers.....

[shreyans_nitt]

Originally Posted by kanu09

Solve these...


(b) Let N be the largest integer divisible by all positive integers less than its cube root. The number of divisors of N are

(a) 16 (b) 24 (c) 18 (d) none of the foregoing

Not the best approach but here i am:

cube root of 8 = 2 ....8 is divisible by 1
cube root of 26 <3....26 is divisible by 2,1
cube root of 60 <4...60 is divisible by 3,2,1

so we need to choose the largest number in such a way that it is a multiple of
3*2 for numbers less than 64
3*4 for numbers less than 125 & greater than 64
3*4*5 for numbers less than 216 and greater than 125
3*4*5 for numbers less than 343 & >216
3*4*5*7 for numbers less than 512 & >343
3*8*5*7 for numbers less than 729 & >512

but it is not possible as 3*8*5*7 = 840 > 729....

so largets number will be below 512...it will be 420 as 3*4*5*7 is 420

N = 420 = factors = 24.....

[ABhishek009]

Well guys I am havin a few questions of Time speed and Distance will someone plz help me with them ?

Q.1. A thief is running @ speed of 10 m/sec , a policeman who is 5000 m starts chasing the thief @ speed of 20 m / sec, a ferocious dog comes in between the thief and chases the thief @ speed of 30 m/sec. The dog has a typical habbit of biting the thief until the Police catches him.

i. Find the total distance travelled by the dog ?

ii. Find how many times did the dog bit the thief ?

iii. The total distance travelled by the dog in forward direction ?

Q.2. A train travelling @ 37 minutes late finds an accident in its route , after tarvelling 70 kms , reduces its spped by 3/4th of its original speed.

HAd the accident occered after travelling 85 kms in its route the train would hav been 25 mins late.

Find the original speed of the train.

Q.3. Ramu is given Rs 382 in one-rupee coins. He has been asked to allocate them into a number of bags such that any amount required between Re 1 and Rs 382 can be given by just handling out a certain number of bags without opening any of them. What is the minimum number of bags possible?
a) 15 b) 13 c) 11 d) 17


Would b of great help if someone explains the solution too in brief.

[subash_r]

Originally Posted by ABhishek009

Well guys I am havin a few questions of Time speed and Distance will someone plz help me with them ?

Q.1. A thief is running @ speed of 10 m/sec , a policeman who is 5000 m starts chasing the thief @ speed of 20 m / sec, a ferocious dog comes in between the thief and chases the thief @ speed of 30 m/sec. The dog has a typical habbit of biting the thief until the Police catches him.

i. Find the total distance travelled by the dog ?

ii. Find how many times did the dog bit the thief ?

iii. The total distance travelled by the dog in forward direction ?

Q.2. A train travelling @ 37 minutes late finds an accident in its route , after tarvelling 70 kms , reduces its spped by 3/4th of its original speed.

HAd the accident occered after travelling 85 kms in its route the train would hav been 25 mins late.

Find the original speed of the train.

Would b of great help if someone explains the solution too in brief.

Q1.
i. Well i and iii are the same questions i think.. .. am a bit confused..

Anyway

Let's say the cop catches the thief in 'x' meters from theif's starting point..
So,
(5000+x)/20 = x/10
We get x = 5000
So, cop covers total distance of 5000m

ii. The dog starts in between, ie 2500 metres behind theif..
Let the dog catch the thief at 'y' meters away from the starting postition of the thief
So, (2500+y)/30 = y/10
ie y = 3750
Thus dog covers 3750 m

I dont know how to find how many times dog bit. but let's say.. dog bites the theif once in every meter.. covered..
So that would be 5000-1250 = 3750 again

iii. Same as first question i think.. .....

Will try solvin the second one and will post if i succeed