Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,365

irspow's solution to Problem # k + 59 is correct. I shall wait for some more time before posting the solutions to unanswered problems.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,365

Problem # k + 86

Out of the total 390 students studying in a college of Arts and Science, boys and girls are in the ratio of 7 : 6 respectively and the number of students studying Arts and Science are in the ratio of 3 : 7 respectively. The boys and girls studying Arts are in the ratio of 4 : 5 respectively. How many boys are studying Science?

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,365

Excellent, irspow's solution to problem # k + 48 is correct too!

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**irspow****Member**- Registered: 2005-11-24
- Posts: 1,055

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

Offline

**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,365

Well done, irspow

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,365

Problem # k + 87

Prove that there exists atleast one multiple of 5 between 10^k and 10^k+1 where k is a Natural number.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

Offline

**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,365

I made a mistake while posting problem # k + 87.

The problem should have read 'Prove that there exists atleast one **power** of 5 between 10^k and 10^k+1 where k is a Natural number.

Problem # k + 88

Show that the sum of any number of terms of the series

1/1*2, 1/2*3, 1/3*4, 1/4*5, 1/5*6,................ is less than 1.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,365

Problem # k + 89

In a bolt factory, machines A, B, and C manufacture respectively 25%, 35% and 40% of the total bolts. Of their output, 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random. If the bolt drawn is found to be defective, what is the probability that it is manufactured by machine B?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

**igloo** **myrtilles** **fourmis**

Offline

**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

ganesh wrote:

I made a mistake while posting problem # k + 87.

The problem should have read 'Prove that there exists atleast onepowerof 5 between 10^k and 10^k+1 where k is a Natural number.

Ah. That makes more sense. I thought there was a mistake somewhere because as it was, the proof was really obvious, so it didn't seem sensible.

I've got a vague idea for k+88, but I'll wait for it to mature a bit more before posting it.

Why did the vector cross the road?

It wanted to be normal.

Offline

**irspow****Member**- Registered: 2005-11-24
- Posts: 1,055

*Last edited by irspow (2006-02-15 11:49:14)*

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

Offline

**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

I think my and irspow's methods are pretty much the same, just worded differently. We get the same answer, anyway.

Why did the vector cross the road?

It wanted to be normal.

Offline

**irspow****Member**- Registered: 2005-11-24
- Posts: 1,055

Sorry, I didn't mean to jump in your spot. The wording of this problem is what had me scratching though. I wasn't sure if ganesh wanted the over-all probability of drawing a defective bolt from B or the probability that I (or should I say we?) calculated.

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

Offline

**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Don't worry, you're in your own spot. Our spots just happen to look similar.

Anyway, I think we're right. Ganesh told us that the bolt was defective, and wanted to know tha probability of it being from B.

Why did the vector cross the road?

It wanted to be normal.

Offline

**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,365

Both mathsyperson and irspow are correct. Well done.

Problem # k + 90

Find the formula for sum of n terms of

(1*2*3), (2*3*4), (3*4*5), (4*5*6),................. Prove that the formula is correct by Mathematical Induction.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

k+90's formula is:

Anybody want to try their hand at an induction proof, or should I?

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

Offline

**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,365

Ricky is correct. I shall wait for someone to post a proof.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,365

Problem # k + 91

Find three consecutive terms in Geometric Progression such that their sum is 21 and the sum of their squares is 189.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Why did the vector cross the road?

It wanted to be normal.

Offline

**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,365

mathsyperson's solution to problem # k + 91 is correct. I shall post the method if none of the others are able to give a proper solution with the steps.

Problem # k + 92

If x=9 + 4√5, find the value of √x - 1/√x.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

I have the induction proof written up on paper, but I'm a bit too lazy to type it all up now. Maybe later tonight.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

Offline

**irspow****Member**- Registered: 2005-11-24
- Posts: 1,055

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

Offline

**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,365

Ricky and irspow are correct!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,365

Problem # k + 93

A right ciruclar cone is cut by two planes parallel to the base, trisecting the altitude. What is the ratio of the volumes of the three parts, the top, middle and the bottom respectively?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline