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Questions from tg book of number system
by dr naina singh - Monday, 11 August 2008, 07:09 PM
  1. In 1836, my age was equal to the last two digits of my birth year. My grandfather said that it was true for him also. then, the sum of my age and my grandpa's age in 1936 was
a) 84    b)  86   c) 90    d) 94

2.N is the sum of the squares of 3 consecutive odd numbers such that all the digits of n are the same . If N is a four digit number, then the value of N is
a) 3333  b)5555  c)7777   d)9999

3.  S=(104 +324)(224 +324)(344 +324)(464 +324)(584 +324) / (44 +324)(164 +324)(284 +324)(404 +324)(524 +324).then the value of S is
 a)373   b) 256  c)504  d)588

4.If N =(63)1!+2!+3!+4!+5!+6!+.......+63!  +(18)1!+2!+3!+4!+....+18!!! +(37)1!+2!+3!+4!+....+37 , then unit digit of N is
  a)2   b) 4  c)6   d)8

5.In 19th  century  a person was X years old in th year X. how old was he in 1884 ?
a)43   b)58   c) 68   d) 78

6.
What  is the sum of the coefficients of all the terms of (1 + 2x + 3x2- 4x3)10
When in expanded form ?
a) 16  b) 256  c) 512  d) 1024

Please post the approach
Re: Questions from tg book of number system
by Deepak Kumar - Tuesday, 12 August 2008, 11:46 AM
  1. In 1836, my age was equal to the last two digits of my birth year. My grandfather said that it was true for him also. then, the sum of my age and my grandpa's age in 1936 was
a) 84    b)  86   c) 90    d) 94

Ans: for boy: 1836-1800-10x-y=10x+y, 10x+y=18
for Grandfather: 1836-1700-10x-y=10x+y, 10x+y=68
sum=86

2.N is the sum of the squares of 3 consecutive odd numbers such that all the digits of n are the same . If N is a four digit number, then the value of N is
a) 3333  b)5555  c)7777   d)9999

Ans: we can squares as 4n+1 so for three numbers 3(4n+1); number should be divisible by 3 and leave remainder 3 with 4 so answer is a 9999

3.  S=(104 +324)(224 +324)(344 +324)(464 +324)(584 +324)
/ (44 +324)(164 +324)(284 +324)(404 +324)(524 +324).then the value of S is
 a)373   b) 256  c)504  d)588

Ans: try to make a form of a2 - b2

4.If N =(63)1!+2!+3!+4!+5!+6!+.......+63!  +(18)1!+2!+3!+4!+....+18!!!+ (37)1!+2!+3!+4!+....+37 , then unit digit of N is
  a)2   b) 4  c)6   d)8

Ans: after 4! all will have at least one zero in the end and will be divisible by 4 so taking into account only first four
(3)4k+33+ (8)4k+33 +(7)4k+33 =3+8+7=18 so unit digit is 8

5.In 19th  century  a person was X years old in the year X. how old was he in 1884 ?
a)43   b)58   c) 68   d) 78

Ans: check out for all square from 1800 to 1899 there is only one square that is  1849= 432 so he is 43 hear old in 1849; born in 1806 so he is 78 yr in 1884.


Re: Questions from tg book of number system
by CATastrophic . - Tuesday, 12 August 2008, 12:06 PM
  6: put x = 1
Re: Questions from tg book of number system
by dr naina singh - Wednesday, 13 August 2008, 02:27 PM
  thanks guys u rock on.
Re: Questions from tg book of number system
by vamsi krishna - Wednesday, 13 August 2008, 07:28 PM
 

Mr. Deepak,

thanks for ur prompt response..

I have som doubts heree.

1> i am not comfortable wid this question becoz grand father's age can also be calcuated using 1600( instead of 1700 tat u have used). which give GF's age 118 ?

2> i dnt u_stand ur solution completely

LET numbers be x y and z, their squares can be represented as 4l+1, 4m+1, 4n+1, then we get sum of squares as 4x+3, not necessarily of 3(4n+1);

 

regards

 

VaMsI

Re: Questions from tg book of number system
by dr naina singh - Wednesday, 13 August 2008, 08:41 PM
  Abhijeet Singh can u explain why we take x=1 not anything else .
Re: Questions from tg book of number system
by Robin uthappa - Thursday, 14 August 2008, 09:19 AM
 

Tho' I am not asked to reply but yet I'd wish to try

Following are the reasons, I cud think of:

1) Since its an algebric expression it'd have several number of terms in it. Now, in order to count, just the constant numeric values, we've to keep the value of x=1.

By taking any other value for x, We'd not be able to account for the correct summation of all the constant values.

 

2) Taking a number other than 1 would not give a value which would match any of the options.

 

 

Hope the above helps!

 

Best

Re: Questions from tg book of number system
by dr naina singh - Thursday, 14 August 2008, 04:24 PM
  thanks robin
Re: Questions from tg book of number system
by Deepak Kumar - Thursday, 21 August 2008, 01:47 PM
  Hi Vamsi,
for q 1. How can two single digit numbers can form a number greater than 99??

Re: Questions from tg book of number system
by vamsi krishna - Thursday, 21 August 2008, 03:19 PM
  OH ...Got da Point...Thnks...
Re: Questions from tg book of number system
by rashi agarwal - Saturday, 23 August 2008, 10:58 PM
 

hello doctor,

my answers are

2.a

3.256

4.d

5.d

please post the answers and the soilution to the remaining questions

Re: Questions from tg book of number system
by ark d - Monday, 25 August 2008, 06:59 AM
  hi naina..
Qs no 2. ans is B) 5555
say the nos are a-2, a, a+2
now, (a-2)^2+a^2+(a+2)^2=N
0r, a^2= (N-8)/3
now a no is divisible by 3 if sum of all digits of the no is div by 3.
hence ans B) 5555
the odd nos are 41, 43, 45..
Re: Questions from tg book of number system
by Damini Sarin - Saturday, 30 April 2016, 11:17 AM
  Hi Deepak Sir,

My problem pertains to Ques:1

In the solution you mentioned that both the age of boy and grandfather to be xy. How did we reach such conclusion?