M4maths Previous Puzzles

16 Sep 2011 word

How many words can be formed by using any 5 letters from the word CALCUTTA

OPtion

1) 120
2) 56
3) 7
4) 210
5) 90
6) 420
7) 300
8) 180
9) 390
10) none of these

Solution

Distribution of letters of the word CALCUTTA is A 2 times, C 2 times, L 1 time, T 2 times, U 1 time
Total 5 letter words having all letters different = 5*4*3*2*1 = 120
Total 5 letter words having 1 letter repeated = 3*(5*4*3*2*1)/2 = 180
Total 5 letter words having 2 letters repeated = 3*(5*4*3*2*1)/2*2 = 90
so total words are 390

Correct Option: 9 Best Solution (0)

15 Sep 2011 banana

The cost of n dozen banana is x rupee more than 100 rupee and the cost of 6n dozen banana is 14x rupee less than 700 rupee. Which of the following is the cost of 1 dozen banana (Given that n and x are positive integers)

OPtion

1) 25
2) 30
3) 35
4) 40
5) 45
6) 50
7) 55
8) 60
9) 65
10) none of these

Solution

let the cost of 1 dozen banana is y rupee
then n*y = 100+x
and 6n*y = 700-14x
take n*y = 100+x from first equation in the second equation, we will get
6(100+x) = 700-14x
or 600+6x = 700-14x
or 20x = 100
or x = 5
on putting x=5, n*y = 100+5 = 105

Correct Option: 3 Best Solution (5)

14 Sep 2011 sum

The sum of 2 numbers is 12, and sum of reciprocals of these numbers is 35th part of the sum of these numbers. Positive difference of the numbers will be

OPtion

1) 1
2) 2
3) 3
4) 4
5) 5
6) 6
7) 7
8) data are wrong
9) data are not sufficient to give answer
10) none of these

Solution

x+y=12
and (1/x)+(1/y)=12/35
on solving numbers will be 7 and 5

Correct Option: 2 Best Solution (0)

13 Sep 2011 Next number

Next number of the sequence
5,6,9,18,13,54,17,162,21,....will be

OPtion

1) 25
2) 38
3) 92
4) 178
5) 324
6) 486
7) 528
8) 978
9) 1097
10) none of these

Solution

This sequence is a combination of two sequences
1) A.P.
2) G.P.
5,9,13,17,21
6,18,54,162,...

Correct Option: 6 Best Solution (7)

12 Sep 2011 sequence

2,9,28,65,126,......
next number will be

OPtion

1) 195
2) 198
3) 200
4) 208
5) 210
6) 215
7) 217
8) 256
9) 299
10) none of these

Solution

2 = 1^3 + 1
9 = 2^3 + 1
28 = 3^3 + 1
similarly

Correct Option: 7 Best Solution (14)

09 Sep 2011 examination

In an exam total 15 questions are asked. You have to give answer of any 12 questions. Questions are divided in 3 sections. Each section contains 5 questions. You have to solve at least 3 questions from each section. How many methods are possible to give answers of all 12 questions.

OPtion

1) 256
2) 260
3) 275
4) 294
5) 308
6) 340
7) 395
8) 425
9) 505
10) none of these

Solution

Two cases arise
1) solve 3,4 and 5 questions from sections
total methods = 6*(5*4/2*1)*(5/1)*(1)= 300
2) sole 4 from each section
total methods = 5*5*5 =125
so answer = 300+125 = 425

Correct Option: 8 Best Solution (4)

08 Sep 2011 inequities

Given that x+y>z, x,y,z are positive integers
then
1) x>z
2) y>z
3) x-y>z
4) xy>=z
5) x/y>
How many of these 5 conditions are definitely true for all values of x,y and z

OPtion

1) 1
2) 2
3) 3
4) 4
5) 5
6) 6
7) 7
8) 8
9) 9
10) none of these

Solution

only xy>=z is true always on the basis of given conditions

Correct Option: 1 Best Solution (10)

07 Sep 2011 series

1,3,5,7,9,11,....... 50 terms
2,5,8,11,14,........ 50 terms
How many terms are same in these two series.

OPtion

1) 9
2) 10
3) 11
4) 12
5) 14
6) 16
7) 18
8) 21
9) 24
5) none of these

Solution

common terms are 5,11,17,23,29,....................,95
total no of terms = 16

Correct Option: 6 Best Solution (0)

06 Sep 2011 reference price

1 dozen orange weights 1200 gram. If cost of orange in dozen is 60 Rs/Dozen and that in Kg. is 50 Rs/Kg, then profit in purchasing 5 Kg orange taking the price in Dozen as reference price will be

OPtion

1) 50
2) 60
3) 100
4) 120
5) 30
6) 40
7) 10
8) 0
9) 150
10) none of these

Solution

price of 1 dozen = 1200 gms is 60 rupee
so that of 1 kg will be 60*1000/1200 = 50 rupee
so both price are same hence no profit

Correct Option: 8 Best Solution (9)

05 Sep 2011 prime

how many numbers between 1 and 50 are prime

OPtion

1) 25
2) 19
3) 17
4) 14
5) 12
6) 10
7) 9
8) 7
9) 6
10) none of these

Solution

total prime = 15

Correct Option: 10 Best Solution (14)