CAT4MBA

hi cat4mba...can u please post the answers to QBM012

We have plenty of time till CAT so don’t you think it is better to try the questions on your own and then ask for the answer/solution for a particular question. Answers/solutions are not given to all the questions just to make the site/forum more users interactive. You can check the forum, every day users are coming up with interesting questions and we try our best to provide the detail answers with minute details and with the basic fundamentals involved.

So, please try to solve the questions on your own, if possible publish your answer. If you have any query then put a comment here or in the forum. Some one will definitely answer.

138. boys = 63, girls = 70
139. 17
140. 11
142. 2
143. 82^3
144. M = 6, N= 4
145. 3
146. none
148. 1056
149. A = 3, B = 0
150. 12

Here are my answers...

M136. Find the value of 1.1! + 2.2! + 3.3! + ......+n.n!
Ans. 1+1.1!+2.2!+..+n.n! = (n+1) ! Thus 1.1!+2.2!+...+n.n! = (n+1)! -1 Ans.

M138. The ratio of boys to girls at a school disco is 9:10. An extra 17 boys arrive and the ratio changes to 8:7.How many girls are there at the disco?
Ans. B:G = 9:10. B+17:G=8:7 tehn 17/G+9/10 = 8/7 thus 17/G = 8/7-9/10 = 80-63/70=17/70 thus Girls =70 Ans.

M139. 4^61 + 4^62 +4^63 +4^64 is divisible by
a. 18 b. 17 c. 20 d. None
Ans. 4^61( 1+4+16+64) =4^61x 85 thus it is divisible by 17 ans.

M145. How many numbers are there between 200 and 400, which are divisible by 11 and 3, but not by 2?
Ans Factors of 33.Sum of odd = even thus common difference is 66 as odd+even =odd 231 , the last term is 231+(n-1)66 <=400
Here 400 -231 =169 then n= [169/66] +1 = 2+1 =3 Ans.

M147. If you had discs numbered 1 to 10, how would you separate the discs into the two bags such that no bag contains its double?
Ans. Sum of 1+2+3+4+5+..+10 = 55 Now x + y = 55 such Total possible cases = 56 cases case when 3x = 55 no possibility.
Thus the cases are 56 No. including zero in one bag or x varies from 0 to 55. And it is considered that bags are also different.

M150. If N = 2 x 4 x 6 x 8 . . . 100 How many zeros are there at the end of N?
Ans N = 2^50(50!) The no. of zero = 50/5+50/25 =10+2 =12 Ans.

can some one solve question no 137 of QMB012

already discussed

Chk the following post and rajorshi's comments

http://www.cat4mba.com/node/2515

M136. Find the value of 1.1! + 2.2! + 3.3! + ......+n.n!

sol: (n+1)!-1

M137. What will be the remainder when 25⁶²⁵ + 26 is divided by 247 ?

sol: 247=13*19

using euler function for each of them and finding reminder for 13 and 19 separatley..

i.e. (25^625+26)mod 13=12  and (25^625+26) mod 19=11

multiplying both 132 = (25^625+26)mod 247

M138. The ratio of boys to girls at a school disco is 9:10. An extra 17 boys arrive and the ratio changes to 8:7.How many girls are there at the disco?

sol: solving (9x+17)/10x=8/7 ans is 70.

M139. 4⁶¹ + 4⁶² +4⁶³ +4⁶⁴ is divisible by
a. 18 b. 17 c. 20 d. None

sol: 20 & 17 hence . d ........ as 4^61 (1+4+4^2+4^3)=4^61 *85

M140. If an n-digit natural number is added to a number made by putting the digits of the original number in reverse order the sum is always divisible by k where n is an even number, then k must be a multiple of
22 111 11 None

sol: 11

M141. Given that [n(n+1)(n+2)]² = 3039162537*6, find the value of *.

sol: since the given no. is square of product of 3 consecutive nos. hence will always be divisible by 36 and hence 3^2 and 2^2

so checking the divisibility by 9 and 4... for both these divisor the suitable no is 9.

M142. By what least number must 217800 be multiplied in order to make it a perfect square?

sol: 2

M143. What is the highest power of 82 contained in 83! - 82! ?

sol: 3

M144. What is the value of M and N respectively? If M39048458N is divisible by 8 & 11; Where M & N are single digit integers

sol: N=4 and M=6

M145. How many numbers are there between 200 and 400, which are divisible by 11 and 3, but not by 2?

sol: 10

M146. 3²ⁿ - 1 is divisible by 2ⁿ⁺³ for n = ? 2 , 3 , 4 or none

sol: none

(3²ⁿ-1)=(3ⁿ-1)(3ⁿ+1)

this being a product of 2 consecutive even nos so will allways be divisible by 2^2

but n+3 cannot be expressed as 2 so it cant be divisiblw by 2^(n+3)..check by substitution...

M147. If you had discs numbered 1 to 10, how would you separate the discs into the two bags such that no bag contains its double?

sol: it is 12C2-2=64

M148. What is the smallest 4 digit number which leaves the remainder 2 when divided by 6 or 7 but is exactly divisible by 11.

M149. A five digit number 3A25B is divisible by 19 and 7. Find A and B?

M150. If N = 2 x 4 x 6 x 8 . . . 100 How many zeroes are there at the end of N?

sol: 2^20 * 50!

hence 12 zeros

I know its coming.....and I know i can handle it the best....

(n+1)! -1

(n+1)! -1

(n+1)! -1