Number System

[bhars18]

If log 2, log (2x -1) and log (2x + 3) are in A.P, then x is equal to ?

Bhars.

[arcade79]

2.5

[bhars18]

Originally Posted by arcade79

2.5

Please add the steps followed also so that others can benefit

Bharathi.

[arcade79]

I m sorry for missing that out...

here are the steps....
For 3 no.s a,b,c in AP, we have 2b=a+c

Hence here we have 2log(2x-1)= log2+log(2x+3)

Removing Log we have
(2x-1)^2= (2)(2x+3)

or 4x^2-8x-5=0

Solving we have x = -0.5 or 2.5
If we use x=-0.5 then second number wont exist so we have x=2.5

Now see putting it, we have three no.s as 2,4,8

Taking log we hav log2, 2log2, 3log2 ie AP...

so also note that GP can become AP on taking log provided we hav progressive GP....

Hope thats clear to everyone...

[CatCrazy]

mite sound dumb but have completely forgotten whts a progressive GP

Cud u clarify

GP can become AP on taking log provided we hav progressive GP....

[arcade79]

simple when the common ratio is gr8r than 1 and the series terms are increasing continously...

and btw why wud that sound dumb... no one is born with all fundaes ....

[CatCrazy]

thanks for that info ..

[icarus]

Hi

Juz found some number related probs in CAT'99 Paper. Most of the questios are sitters. I dunno if this would help the Junta

1. The difference between the biggest and the smallest number formed by using 0, 1, 2, 3, 4 exactly once is :

(1) 28000 (2) 32591 (3) 27143 (4) 41976


2. If (AB) x (AB) = XYA, then X stands for :

(1) 3 (2) 1 (3) 6 (4) 9


3. A number divided by 899 gives remainder of 63. What will be the remainder when it is divided by 29 ?

(1) 5 (2) 7 (3) 9 (4) 15

4. How many numbers can be formed by using 8,7,5,3,2 such that they are divisible by 125 ? Digits to be used exactly once.

(1) 20 (2) 4 (3) 2 (4) 1


5. If n x n x n is odd, then which is true ?
(I) n x n is even
(II) n x n is odd
(III) n is odd

(1) (I) alone (2) (I) and (II) (3) (II) and (III) (4) (II) alone

6. The unit's digit in the expansion of 2 raised to power 51 is :

(1) 2 (2) 4 (3) 6 (4) 8

7. Take a 99 digit number. It is created by using first 54 natural numbers. The number thus is 1234567891011.....5354. This number is now divided by 8. The remainder is :

(1) 1 (2) 2 (3) 4 (4) 8


8. How many 5 digit numbers can be made using 1, 2, 3, 4, 5 such that the digit in the unit place is greater than the digit in the hundred's place ?

(1) 40 (2) 120 (3) 60 (4) 720

And one or two more similar, easy questions also appeared.

[icarus]

Hi

I juz happen to remember that CAT2000 had some really good question on numbers. You can find the questions in CAT2000 brochure if you have one.

Also you can juz log into PTINDIA @ http://ptindia.com/.

I found the user id and passwd some where in this forum to be

pgforum and pgforum respectively


let me know if you want me to copy paste those ques here !!!!!

Cheers
shyam

[morning_star]

Hi

Here's a question..I guess its quite simple...but then my maths is pathetic so never mind

Find the remainder if 30^40 is divided by 17.

Luv n Luk