M4maths Previous Puzzles

18 Feb 2011 dictionary

what would be the 146th word in the dictionary of words formed by the letters of the word "SECRET"

OPtion

1) ECTSER
2) ECTESR
3) ECRTSE
4) ESRCTE
5) ESRTCE
6) ESRCET
7) ERESCT
8) ERETCS
9) ERECST
10) ERESTC

Solution

This question can be solved by equidistribution of words from every letter symmetrically.
on arranging these 6 letters in english alphabetic order we get
C(1 to 60) E(61 to 120) E(121 to 180) similarly .........
so 146th word would be start from E
next step for next letter
C(61 to 84) E(85 to 108) R(109 to 132) S(133 to 156)similarly .......
so next letter would be S
next step
C(133 to 138) E(139 to 144) R(145 to 150) similarly ...........
so next letter would be R
next step
C(145-146) E(147-148) T(149-150)
so next letter would be C
next step
E(145) T(146)
so next letter would be T
and last letter is E

Correct Option: 4 Best Solution (0)

17 Feb 2011 Tasty Fruit

How many methods are possible for distributing 6 mangos among 4 children if 1 mango would be provided to every child necessarily

OPtion

1) 10
2) 14
3) 15
4) 18
5) 24
6) 32
7) 38
8) 45
9) 60
10) 72

Solution

since 1 mango would be provided to every child necessarily, so we have to distribute remaining 2 mangos to the 4 children. Methods are
1) give both the mango to any 1 child for which there are 4 methods
2) give 1-1 to any 2 children for which there are 6 methods

Correct Option: 1 Best Solution (3)

16 Feb 2011 percentage

50 % of 80 % of 100 - 20 % of 60 % of 100 - 32 % of 25 % of 100 - 1/6 of 36 % of 100 = 12
What should be added in the right hand size to make the equation correct

OPtion

1) 10
2) 9
3) 8
4) 7
5) 6
6) 5
7) 4
8) 3
9) 2
10) 1

Solution

On solving
50 % of 80 % of 100 - 20 % of 60 % of 100 - 32 % of 25 % of 100 - 1/6 of 36 % of 100 = 40 - 12 - 8 - 6 = 14
but RHS is given as 12 so 2 should be added in RHS

Correct Option: 9 Best Solution (9)

15 Feb 2011 unit\'s place

integer in the units place of 63^63 is

OPtion

1) 0
2) 1
3) 2
4) 3
5) 4
6) 5
7) 6
8) 7
9) 8
10) 9

Solution

63*63*63*63 = ........1
so every pair of four 63 has 1 in unit's place.
Finally , we have three 63 and 63*63*63 = ......7
Hence the result

Correct Option: 8 Best Solution (7)

14 Feb 2011 potato and onion

The cost of 3 kg potato and 2 kg onion is 72 rupee and that of 4 kg potato and 3 kg onion is 104 rupee.H.C.F. of the cost of 1 kg potato and 1 kg onion is

OPtion

1) 6
2) 4
3) 5
4) 8
5) 3
6) 9
7) 12
8) 10
9) 2
10) 16

Solution

on solving the conditions , costs of the two are 8, 24 rupee
so H.C.F. is 8

Correct Option: 4 Best Solution (7)

11 Feb 2011 Rank in dictionary

Rank of the word KUNDAN in the dictionary of words formed by the letters of the word KUNDAN

OPtion

1) 171
2) 148
3) 158
4) 177
5) 150
6) 168
7) 162
8) 186
9) 198
10) 145

Solution

Total number of the words by the letters of the word
KUNDAN = 6*5*4*3*2*1/2*1=360
Denominator is due to the revision of N twice.
The correct order of these letters in English alphabets is A, D, K, N, N, and U
So rank of KUNDAN = (360/6)*2 + (60/5)*4 + (12/4)*2 + (6/3)*1 + (2/2)*0 + 1
= 120 + 48 + 6 + 2 + 0 +1
= 177

Correct Option: 4 Best Solution (0)

10 Feb 2011 How many letters are possible

How many words can be formed by the letters of the word "TUESDAY"?
If all the vowels used in the word have to be taken in the order as these letters come in English alphabets.

OPtion

1) 1240
2) 780
3) 560
4) 480
5) 840
6) 1440
7) 5040
8) 720
9) 90
10) 16

Solution

TUESDAY, total numbers of letters in the word TUESDAY are 7
So numbers of methods to form word are 7*6*5*4*3*2*1/3*2*1 = 840
The denominator is due to the restriction given in the question

Correct Option: 5 Best Solution (6)

09 Feb 2011 Find the value

(x^x)^x - x^(x^x) = 0
How many positive integral values of x are possible?

OPtion

1) 4
2) 3
3) 2
4) 5
5) 6
6) 7
7) 8
8) 9
9) 0
10) 1

Solution

Possible answers are 1 and 2.

Correct Option: 3 Best Solution (1)

08 Feb 2011 How many methods?

How many methods are possible for arranging 5 boys and 4 girls in a round table in such a way that no 2 girls could sit together?

OPtion

1. 12500
2. 1750
3. 14400
4. 2880
5. 256
6. 1440
7. 12232456
8. 12
9. 9
10. 20

Solution

Methods for the arrangement of 5 boys = 1*4*3*2*1 = 24, between the boys there are 5 places so methods for the arrangement of 4 girls = 5*4*3*2 = 120
Hence total number of methods = 24 * 120 = 2880

Correct Option: 4 Best Solution (0)

07 Feb 2011 Next number?

1,2,6,42,?

OPtion

1) 48
2) 1806
3) 186
4) 1764
5) 1987
6) 2087
7) 1842
8) 286
9) 1942
10) 142

Solution

series is like
1
1+1^2=2
2+2^2=6
6+6^2=42
42+42^2=1806

Correct Option: 2 Best Solution (16)