M4maths Previous Puzzles

16 Aug 2012 operations

If [K+2]/[K+3] = K/9
then which of the following operations between the values of K will give an integer as answer.

OPtion

1) addition only
2) subtraction only
3) multiplication only
4) division only
5) addition and subtraction
6) multiplication and division
7) addition and multiplication
8) subtraction and multiplication
9) division and addition
10) none of these

Solution

[K+2]/[K+3] = K/9
so K^2-6K-18 = 0
on solving we get K = 3+3sqrt(3) and 3-3sqrt(3)
so addition and multiplication will give integer.

Correct Option: 7 Best Solution (0)

15 Aug 2012 cards

In a pack of 52 cards, 2 cards are drawn at random one by one with replacement. What will be the probability to get 2 ace of diamond.

OPtion

1) 1/2674
2) 1/2704
3) 1/676
4) 1/650
5) 1/2652
6) 1/1974
7) 1/3240
8) 1/3654
9) 1/980
10) none of these

Solution

probability = 1/52 * 1/52 = 1/2704

Correct Option: 2 Best Solution (0)

14 Aug 2012 solve

x + y^2 = 13
y + x^2 = 13
x and y are integers
then x.y will be

OPtion

1) -6
2) -8
3) -10
4) -12
5) -14
6) -15
7) -18
8) -20
9) -21
10) none of these

Solution

on subtracting the two equations we get
(x-y)-(x^2-y^2)= 0
or (x-y)[1-(x+y)] = 0
so x=y or x+y=1
x=y will not provide integral solution so x+y = 1
now add the equations we get (x+y)+(x^2+y^2)=26
so (x+y)+[(x+y)^2-2x.y]=26
or 1+[1-2x.y]=26
or 2-2x.y = 26
or 2x.y = -24
or x.y = -12

Correct Option: 4 Best Solution (0)

13 Aug 2012 sequence

Next number of the sequence
1, 3, 7, 13, 21, ............ will be

OPtion

1) 28
2) 30
3) 31
4) 33
5) 37
6) 39
7) 40
8) 41
9) 43
10) none of these

Solution

1 = 0^2 + 1
3 = 1^2 + 2
7 = 2^2 + 3
13 = 3^2 + 4
21 = 4^2 + 5
31 = 5^2 + 6

Correct Option: 3 Best Solution (0)

10 Aug 2012 solve

value of 1/[2+{3/(4+(5/6))}] will be

OPtion

1) 29/76
2) 25/73
3) 12/95
4) 65/67
5) 45/46
6) 12/49
7) 36/97
8) 23/85
9) 28/91
10) none of these

Solution

1/[2+{3/(4+(5/6))}]
= 1/[2+{3/(29/6)}]
= 1/[2+{18/29}]
= 1/[76/29]
= 29/76

Correct Option: 1 Best Solution (0)

09 Aug 2012 Rank

Rank of the word THING in the dictionary of words formed by letters of the word THING.

OPtion

1) 97
2) 99
3) 101
4) 102
5) 105
6) 106
7) 109
8) 110
9) 111
10) none of these

Solution

On arranging the letters in order we get
G, H, I, N, T
T is 5th letter
then G, H, I, N
H is 2nd letter
then G, I, N
I is 2nd letter
then G, N
N is 2nd letter
then G
total no. of words = 5*4*3*2*1 = 120
so rank = (120/5)*4+(24/4)*1+(6/3)*1+(2/2)*1+1
= 96+6+2+1+1 = 106

Correct Option: 6 Best Solution (0)

08 Aug 2012 light8

The sun light comes in 500 sec. to the earth. If light speed is 3 * 10^8 m/s, then distance between earth and sun in million kms will be

OPtion

1) 1.5
2) 15
3) 150
4) 1400
5) 1.6
6) 160
7) 18
8) 180
9) 1.8
10)none of these

Solution

distance = velocity * time = 3 * 10^8 * 500 = 15 * 10^10 m
= 15 * 10^7 km
= 150 million km

Correct Option: 3 Best Solution (38)

07 Aug 2012 interest

If a man invests 2,00,000 rupee in a fixed deposit at an interest rate of 9.25 % yearly then output after 3 years will be

OPtion

1) 260792
2) 254657
3) 243912
4) 286574
5) 263456
6) 245360
7) 273489
8) 234542
9) 261519
10) none of these

Solution

200000*1.0925*1.0925*1.0925 = 260792

Correct Option: 1 Best Solution (0)

06 Aug 2012 sequence

36, 5, 16, 3, 4, ..........
what will be the next number

OPtion

1) 6
2) 8
3) 15
4) 22
5) 1
6) 2
7) 30
8) 27
9) 25
10) none of these

Solution

36 = 6^2
5 = 5^1
16 = 4^2
3 = 3^1
4 = 2^2
1 = 1^1

Correct Option: 5 Best Solution (0)

03 Aug 2012 Tank

A tank can be filled by a tap A in 10 hours, whereas it can be emptied by tap B and tap C in 6 hours and 12 hours one by one. If all the 3 taps work together, then total time taken for making a fully filled tank empty will be (in hours)

OPtion

1) 5
2) 4
3) 3
4) 2
5) 4.5
6) 3.5
7) 6.67
8) 7.5
9) 6.25
10) none of these

Solution

total tank filled by tap A in 1 hour = 1/10 part
similarly water drained by tap B in 1 hour = 1/6 part
and by tap C = 1/12 part
so total drained water in 1 hour = 1/6 + 1/12 - 1/10 = 3/20
so total time taken = 20/3 hours

Correct Option: 7 Best Solution (19)