Posted: Tue Jul 04, 2006 3:09 am Post subject: number system problems
1.which of the following is not a perfect square?
a) 1,00,856 b) 3,25,137 c) 9,45,729 d) all of these
2.some birds settled on the branches of a tree. Ffirst, they sat one to a branch and there was one bird too many. Next they sat two to a branch and there was one branch too many. How many branches were there?
a) 3 b) 4 c) 5 d) 6
3.the square of a number greater than 1000 that is not divisible by 3, wen divided by 3, leaves a remainder of
a) 1 always b) 2 always c) either 1 or 2 d)cant be said
4.if 2<x<4 and 1<y<3, then find the ratio of the upper limit for x+y and the lower limit of x-y
Posted: Mon Jul 10, 2006 1:09 pm Post subject: number system problems
Quote:
1.which of the following is not a perfect square?
a) 1,00,856 b) 3,25,137 c) 9,45,729 d) all of these
2.some birds settled on the branches of a tree. Ffirst, they sat one to a branch and there was one bird too many. Next they sat two to a branch and there was one branch too many. How many branches were there?
a) 3 b) 4 c) 5 d) 6
3.the square of a number greater than 1000 that is not divisible by 3, wen divided by 3, leaves a remainder of
a) 1 always b) 2 always c) either 1 or 2 d)cant be said
4.if 2<x<4 and 1<y<3, then find the ratio of the upper limit for x+y and the lower limit of x-y
a) 6 b) 7 c) 8 d) none of these
please explain methods also wid answers
1) A Necessary (not sufficient) condition for a number to be perfect square is that its DIGITAL root be 1, 4, 7, or 9. So (a) and (b) are definitely not the perfect squares but (c) may or may not be a perfect square. However (c) is also not a perfect square. Hence Ans. (d)
Posted: Thu Jul 13, 2006 5:52 pm Post subject: Re: number system problems
[quote="palagg"]1.which of the following is not a perfect square?
a) 1,00,856 b) 3,25,137 c) 9,45,729 d) all of these
2.some birds settled on the branches of a tree. Ffirst, they sat one to a branch and there was one bird too many. Next they sat two to a branch and there was one branch too many. How many branches were there?
a) 3 b) 4 c) 5 d) 6
3.the square of a number greater than 1000 that is not divisible by 3, wen divided by 3, leaves a remainder of
a) 1 always b) 2 always c) either 1 or 2 d)cant be said
4.if 2<x<4 and 1<y<3, then find the ratio of the upper limit for x+y and the lower limit of x-y
a) 6 b) 7 c) 8 d) none of these
please explain methods also wid answers[/quote]
q2) the answer is a) 3 branches
in this question the best way is to answer with options.
the option a says there are 3 branches.
that means from the first situation where each branch is occupied by one bird, the q says 1 bird is left. therefore, there are 4 birds.
now when there are 3 branches and 4 birds, when 2 birds sit on 1 branch, 1 branch is left unoccupied. since the ques also states that 1 branch is left unoccupied this is the answer.
q3) the answer is c) either one or two.
the logic is simple. let us take 1001 as the no. 1001 is not divisible by 3. the remainder when 1001*1001/3 = 2*2/3 (by remainder theorem). which is 4/3 which gives one.
next take 1003 which is not div by 3. 1003*1003/ 3 gives us 1*1/3 which is 1 (by remainder theroem).
therefore, the answer is 1 alsways. u need not check for more values as when a no is divided by 3 the remainder can be 1 or 2. both these options have been checked when we checked for 1001 and 1003.
hance answer a)
q4) none of these. since here there is no assumptions of the x and y being integers. therefore the ratio can be (3.9 + 2.9)/ (2.1-1.1) which is 6.8. hence answer is d) none of these
i hope i am correct. plz anyone correct me if i am wrong. and plllllzzzz explain the concept of digital roots.
Posted: Fri Jul 14, 2006 9:50 am Post subject: Number Systems
(3) Consider the numbers (3N+1) and (3N+2) > 1000, where N is integer. Remainder of square when divided by 3 is Rem {(1^2)/3} or Rem{(2^2)/3} = 1. Hence Answer a) 1 always
(4) Lower limit of x-y is negative. Hence Answer d) none of these
Posted: Fri Jul 14, 2006 10:25 am Post subject: DIGITAL ROOT
Sum the digits of the Number. Is sum is not the single digit number., Again sum the digits. Continue unti a single digit number(DIGITAL ROOT) is obtained. The number of additions required is called ADDITIVE PERSISTENCE of the number.
Posted: Fri Jul 14, 2006 7:51 pm Post subject: Re: DIGITAL ROOT
quote="CZ@@@H@@@R"]Sum the digits of the Number. Is sum is not the single digit number., Again sum the digits. Continue unti a single digit number(DIGITAL ROOT) is obtained. The number of additions required is called ADDITIVE PERSISTENCE of the number.
9,45,729, Sum = 36
36, Sum = 9
Digital Root = 9
Additive persistence = 2[/quote]
thanx for explaining the concept of digital roots. Is the concept of additive persistence useful. if yes, cud u plz cite a question where the concept of ap is used.
also since 945729 may be a perfect square, u suggest that we find out by actually factorizing it. Have i understood u correctly?
