Number System - Questions & Discussions

arnab3112 · May 22, 2012, 5:30am

{(34 + 4)^16!}^1777 / 17

{(4)^16!}^1777 / 17

((16)^(16!/2)}^1777 / 17

(17 - 1)^(16!/2)^1777 / 17

(- 1)^(16!/2) ^1777

16! /2 = positive and even value

and we know any power of even value wud only result in even no.

so,remainder should be 1.:)

Thanks a lot bro.. Can u give me an idea as to where to get the concepts for these kind of questions..

ankitsharma1 · May 22, 2012, 7:37am

(1+2*2!+3*3!+4*4!+.......+12*12!)
What will be the remainder when the above expression is divided by 13?

rakeshkr579 · May 22, 2012, 7:41am

(1+2*2!+3*3!+4*4!+.......+12*12!)
What will be the remainder when the above expression is divided by 13?

THIS HAS ALREADY BEEN DISCUSSED.

CHECK IT HERE:

http://www.pagalguy.com/discussions/official-quant-thread-for-cat-2012-part-3-25080436

ankitsharma1 · May 22, 2012, 7:48am

Thanks for the quick reply Rakesh.
What should I be looking at in the above link, the same question or a similar type of question?

rakeshkr579 · May 22, 2012, 7:50am

Thanks for the quick reply Rakesh.
What should I be looking at in the above link, the same question or a similar type of question?

same question!!

cat_aspirant_25631794 · May 22, 2012, 10:56am

THIS HAS ALREADY BEEN DISCUSSED.

CHECK IT HERE:

http://www.pagalguy.com/discussions/official-quant-thread-for-cat-2012-part-3-25080436

Hi Rakesh,

Can't find the same question on the link.. Dunno what i am missing.

rakeshkr579 · May 22, 2012, 11:31am

Hi Rakesh,

Can't find the same question on the link.. Dunno what i am missing.

OK SORRY FOR THE INCONVENIENCE!!

ACTUALLY I USE THE 40 POST PER PAGE DISPLAY.

THAT'S Y POSTED THAT LINK.

ANYWAYS,HERE IS THE ACTUAL ONE FOR YOU:

http://www.pagalguy.com/discussions/official-quant-thread-for-cat-2012-part-3-25080436

P.S-EDITED THE POST TOO!!

enceladus · May 22, 2012, 7:00pm

find the remainder when (38^16!)^1777 is divided by 17

a. 1
b. 16
c. 8
d. 13

The answer is one.. Can someone explain how??

E(17) = 16.
16!^1777 mod 16 = 0.
=> 30^0 mod 17 = 1.

cat_2011_26016534 · May 24, 2012, 8:44am

Between 100 and 200 hw many nos r dere in which one digit is the avg of the other two??

11
12
10
8
9

can any1 pls suggest me shrtcuts??

rakeshkr579 · May 24, 2012, 10:21am

between 100 and 200 hw many nos r dere in which one digit is the avg of the other two??

11
12
10
8
9

can any1 pls suggest me shrtcuts??

is the answer for this is 9??????

estallar12 · May 24, 2012, 1:57pm

Between 100 and 200 hw many nos r dere in which one digit is the avg of the other two??

11
12
10
8
9

can any1 pls suggest me shrtcuts??

I am getting it as 11 numbers.
Approach :
See, we have the Range from 101 to 199.

The Hundred's digit will always be ''1'' here.
Hence let the number be 1XY.
Now, Possibility is : (X+Y)/ 2 = 1;
This is possible if X = Y =1 or if X=0 and Y=2 or if X=2 and Y=0.
Thus we have, 111, 102 and 120.

Likewise we can 8 more numbers.

The 11 numbers will be : (102, 120), 111, (123, 132), (135, 153), (147, 174), (159 and 195).

cat_2011_26016534 · May 24, 2012, 7:10pm

no..its 11....

cat_2011_26016534 · May 24, 2012, 7:13pm

I am getting it as 11 numbers.
Approach :
See, we have the Range from 101 to 199.

The Hundred's digit will always be ''1'' here.
Hence let the number be 1XY.
Now, Possibility is : (X+Y)/ 2 = 1;
This is possible if X = Y =1 or if X=0 and Y=2 or if X=2 and Y=0.
Thus we have, 111, 102 and 120.

Likewise we can 8 more numbers.

The 11 numbers will be : (102, 120), 111, (123, 132), (135, 153), (147, 174), (159 and 195).

hm its d correct ans....thanks a lot 4 sharin d approach....

rakeshkr579 · May 24, 2012, 7:53pm

cat 2011 Says
hm its d correct ans....thanks a lot 4 sharin d approach....

ok got it ,i was misinng the first two nos.---102 and 120.

cat_2011_26016534 · May 25, 2012, 7:02pm

1) a teacher ws tryin 2 form grps of students s.t every grp has equal no.of students & dat nno should b a prime no.She tried 4 first 5 prime nos,bt on each occasion exactly one student ws left behind.how many diff possibl solutions r dere 4 d total no.of students,if d total no.of students is in 4 digits.

a)0 b)2 c)3 d)4 e)5

2)what vll b d last digit of 2^3^4^5 - 2^3^5^4 ???

a)0 b)2 c)4 d)6 e)none of dese

cat_aspirant_25631794 · May 26, 2012, 10:21am

1) a teacher ws tryin 2 form grps of students s.t every grp has equal no.of students & dat nno should b a prime no.She tried 4 first 5 prime nos,bt on each occasion exactly one student ws left behind.how many diff possibl solutions r dere 4 d total no.of students,if d total no.of students is in 4 digits.

a)0 b)2 c)3 d)4 e)5

2)what vll b d last digit of 2^3^4^5 - 2^3^5^4 ???

a)0 b)2 c)4 d)6 e)none of dese

I am not really sure that i am clear with the first question

. Here is the answer to second question.

2. c(4)?

cat_aspirant_25631794 · May 26, 2012, 12:01pm

Q1. If (sqrt(3) +1)^5 = I + F, where I is an integer and F is a proper Fraction, then the value of F.(I+F) is

A. (SQRT(3))^5
B. 1.99^5
C. 32
D. 31.232

Q2. When product of 'r' consecutive positive integers is divided by r!, then the quotient is
A. any natural number
B. a perfect square
C. a proper fraction
D. either A or B

enceladus · May 26, 2012, 2:27pm

Q2. When product of 'r' consecutive positive integers is divided by r!, then the quotient is
A. any natural number
B. a perfect square
C. a proper fraction
D. either A or B

My take is option D.

Lets take examples.
1*2*3/3! = 1 (which is a perfect square).
4*5*6/3! = 20 (which is a natural number).

cat_2011_26016534 · May 26, 2012, 6:17pm

hmmm 2nd is d correct ...can u pls tell me d approach...

pankaj1986 · May 26, 2012, 7:07pm

What is the remainder when 128^1000 is divide by 153 ?
a. 103
b. 145
c. 118
d. 52