number systm

sweta · Joined: 01 Oct 2005 Posts: 5

1)remainder wen 6 to the power 45 + 6 to the power 3 is divided by 215
a)0 b)1 c)2 d) none of these
2)remainder wen 3 to the power 440 is divided by 15?
a)6 b)4 c)2 d)0
3)for any value of `P`prime number greater tan 3 ,p to the power 2 +17 divided by 24?
a)0 b)1 c)2 d) none of these

4)from the vertex A of a right angle triangle,a perpendicular is drwn to the hypotenuse BC,the bisectors of the angle B meets the perpendicular at R and meets AC at S tan whch of the follwin is true
a)triangle ARS is isoscles b)RS=AS c) both(a) and (b) d)neithr(a)nor(b)

shaji · Posted: Tue Oct 11, 2005 12:26 am Post subject: Re: number systm

shaji · Posted: Tue Oct 11, 2005 12:33 am Post subject:

Hi;
1)Remainder (6^3)^15+(6^3)/15=2
2)Rem(81^110)/15=Rem(36^55)/15=6^55/15=6
3)Rem (p^2+17)/24=18. Choice=d
4) If U draw the triangle and use the property of similar triangles, you will notice the choice is 'a'.

The answer choices makes life much easier as you can notice.

Regards;

nirav_21 · Joined: 10 Oct 2005 Posts: 5 Location: Bhavnagar,Gujarat

Remainder when 3^440 is divided by 15
Remember one easy technique to find the remainders: -
see u have to divide by 15, so u bring 3 to the power to that extent to which u know the table of 15.
For example dividing 3^3 (27)by 15 will leave a large remainder.
Think about 3^4(81) will leave remainder 6 when divided by 15.
This is a good choice.
Now 3^440 = (3^4)^110
= (6)^110 (Put the remainder in place of 3^4 =81)
= (6^2)^55 (The good possibility for 15 is 5^2=36, because it will leave the remainder again 6 on dividing by 15.)
= (6)^55
= (6^2)^27 X 6 (Again remainder 36/15 will be 6)
= (6)^27 X 6 (Now we take higher number 6^4 = 1296 will agin leave remainder 6 on dividig by 15)
= (6)^4)^6 X 6^3 X 6
= (6)^6 X 6^4
= 36^6 X 36^2 (REmainder when 36 ^6 is divided is

proceed like this and u can get y our anser easily it is a bit difficult to write on pc, otherwise by practice u can iimporve