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Heldensheld

Member

Registered: 2006-07-01

Posts: 25

ARgh, math is nightmare, Nightmare is Bad...Some one free me from this

These questions are hard...and I can't get them !

Q1 Pete takes 3 days to dig a well at a copnstant rate. Matt takes 5 days to dig the same sized well, in the same soil, also working at a constant rate. If they both work together to dig the well, each working at the same rate as before, how long will they take to dig the well?

Q2 How many 6-Digit numbers such as 612543 can be written using the digits 1,2,3,4,5 and 6 once only in any order?

Q3 John said, "Write down any 3-digit integer of different digits, and write down the number obtained by reversing the digiots. Find the difference between these two numbers. Repear the process with your answer but this time add the two numbers. The result is always 1089."

If you helped, thanks !

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: ARgh, math is nightmare, Nightmare is Bad...Some one free me from this

Q2:- Well..6 x 5 x 4 x 3 x 2 x 1 , that is 6! or 720.

Q3:- John was right! Let the three digit number be 100x+10y+z. The number obtained by reversing the digits would be x+10y+100z.The difference between the two is 99(x-z) and this would certainly be divisible by 1089 since the number 1089 is divisible by 99. (99x11)

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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.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: ARgh, math is nightmare, Nightmare is Bad...Some one free me from this

Q1: Look at their daily rates (how much they dig in a day): Pete's rate is 1/3 of a well a day, Matts is 1/5 of a well a day. Together their well-digging rate is (1/3+1/5) = 8/15 of a well a day (a little better than half a well a day). So it should take them 15/8 days to dig the well (a little less than 2 days).

But personally I think they would get in each others way - there isn't much space in a well.

Q3: Add Two Numbers and the Answer is Always 1089 (the repeating is not always necessary, only if it doesn't work the first time)

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Heldensheld

Member

Registered: 2006-07-01

Posts: 25

Re: ARgh, math is nightmare, Nightmare is Bad...Some one free me from this

Lol...you're funny!!!!

Thanks anyway!

Pi Man

Guest

Re: ARgh, math is nightmare, Nightmare is Bad...Some one free me from this

Here's how I read Q3.

853 - 358 = 495     Now, reverse the result and add the 2 together:   495 + 594 = 1089

912 - 219 = 693     693 + 396 = 1089.

321-123 = 198       198 + 891 = 1089

When you subtract ZYX from XYZ, let's call the answer ABC.   

   XYZ
-  ZYX
=====
   ABC

Since we're subtracting the smaller number from the bigger number:  Z < X.   So C = 10+Z-X, i.e. you have to borrow one from the 10's column.   

Now in the 10's column, you had to borrow one so you have (Y - 1) - Y.   So you have to borrow one from the 100's column.   (10 + Y - 1) - Y = 9.   The middle digit B  is always 9.

In the 100's column you had to borrow one also so A = (X - 1) - Z.

That gives us A = X-Z-1, B = 9, and C = 10+Z-X.     

XYZ - ZYX = 100(X-Z-1) + 10(9) + 1(10+Z-X).   

Reverse your result and add them:

100(X-Z-1)    + 90 + (10+Z-X)
100(10+Z-X) + 90 + (X-Z-1)
=====================
100(10-1) + 180 + 9   = 1089

mathishard!!!

Guest

Re: ARgh, math is nightmare, Nightmare is Bad...Some one free me from this

Q1:well, I Thinkthat It Would Take Them At Least 4 Days If They Work Together Because It Would Take One Of Them 5 Days And The Other 3 So The # Inbetween Those Two #s Is 4.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: ARgh, math is nightmare, Nightmare is Bad...Some one free me from this

But if 2 people work together, don't they finish a lot faster?

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Patrick

Real Member

Registered: 2006-02-24

Posts: 1,005

Re: ARgh, math is nightmare, Nightmare is Bad...Some one free me from this

MathsIsFun - You say there isn't much space in a well, but that depends on the size I guess? And digging a well in 3 or 5 days is very unlikely btw ^^

I do however agree with you. The logical way to work around the problem is to find out how much they dig each day. Good job

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