M4maths Previous Puzzles

26 Apr 2012 INFINITE SEQUENCE

If 1 + x + x^2 + x^3 + ............upto infinite = 2
then x^3 + x^4 + x^5 + ............upto infinite = ?

OPtion

1) 1/2
2) 1
3) 1/4
4) 1/8
5) 1/16
6) 1/32
7) 1/10
8) 1/3
9) 1/6
10) none of these

Solution

for infinite multiplicative sequence (G. P.)
formula for getting sum = a/(1-r)
here a is first term and r is ratio of second and first term.
so on solving by formula x = 1/2
so ? = 2 - 1 - 1/2 - 1/4 = 1/4

Correct Option: 3 Best Solution (0)

25 Apr 2012 sign

The value of (x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(x-8)(x-9)(x-10) at x = 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5 are

OPtion

1) 4 positive, 6 negative values
2) 5 positive, 5 negative values
3) 4 positive, 5 negative and one zero value
4) all positive values
5) 8 positive, 2 negative values
6) 6 positive, 4 negative values
7) all negative values
8) all zeros
9) 9 positive and 1 negative
10)none of these

Solution

it will be + for 0.5 and - for 1.5 then it will be alternatively +, -
so 5 + ND 5 -

Correct Option: 2 Best Solution (12)

24 Apr 2012 Family

A father said to his son that his (father) age was 7 times his (son) age and his mothers age was 6 times his age 15 years before. If age of father is 5 years more than that of mother, then sum of their ages (all the three) at present will be

OPtion

1) 115
2) 125
3) 130
4) 100
5) 95
6) 90
7) 85
8) 105
9) 80
10) none of these

Solution

let age of father = x
that of mother = x-5
and that of son = y
now according to the given conditions
x-15 = 7(y-15) or x-7y = -90
x-5-15 = 6(y-15) or x-6y = -70
on solving we will get y = 20 and x = 50
so sum = 50 + 45 + 20 = 115

Correct Option: 1 Best Solution (0)

23 Apr 2012 sequence

1, 5, 15, 34, 65, 111, .......
next number of the sequence will be

OPtion

1) 164
2) 165
3) 166
4) 167
5) 168
6) 169
7) 170
8) 172
9) 174
10) none of these

Solution

The given sequence is
01
02+03
04+05+06
07+08+09+10
11+12+13+14+15
16+17+18+19+20+21
22+23+24+25+26+27+28

Correct Option: 10 Best Solution (23)

20 Apr 2012 non integers

x + (1/y) = 7/3
y + (1/x) = 7/2
x and y are non integer values
then x*y = ?

OPtion

1) 0.12
2) 0.125
3) 0.133
4) 0.14
5) 0.15
6) 0.16
7) 0.167
8) 0.2
9) 0.25
10) none of these

Solution

x + (1/y) = 7/3 or (xy+1)/y = 7/3 (1)
y + (1/x) = 7/2 or (xy+1)/x = 7/2 (2)
on dividing (2) by (1), we will get
x/y = 2/3
let x = 2k and y = 3k
then from (1) equation, [6(k^2)+1]/3k = 7/3
or k = 1 or 1/6
so x = 2 or 2/6 and y = 3 or 3/6
since x and y are non integers
so x = 2/6 = 1/3 and y = 3/6 = 1/2

Correct Option: 7 Best Solution (0)

19 Apr 2012 Positive integers

The sum of 4 positive integers is 60. If ratio of these integers is 1:2:3:4, then their product will be

OPtion

1) 31254
2) 34524
3) 31204
4) 31104
5) 34214
6) 30004
7) 31224
8) 30404
9) 30444
10) none of these

Solution

Let the numbers are x, 2x, 3x, 4x
so according to the given condition x+2x+3x+4x = 60 or x = 6
so numbers are 6, 12, 18, 24
product = 6*12*18*24 = 31104

Correct Option: 4 Best Solution (36)

18 Apr 2012 cost

Total cost of a book and a note book is 114 rupee. If cost of book is more than the maximum percentage which any student can obtain in an exam and cost of note book is more than the no. of months in a leap year, than how many outcomes are possible. Given that all the costs are in integers.

OPtion

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

Solution

possible cost of book = 101, 102, 103 ..............
possible cost of note book = 13, 14, 15 ............
the only possible pair will be 101, 13

Correct Option: 1 Best Solution (0)

17 Apr 2012 dozen

x dozen - x^2 peice = A perfect square number peice
how many positive (non zero) integral values are possible for x

OPtion

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

Solution

possible values are x = 6, x = 12

Correct Option: 2 Best Solution (2)

16 Apr 2012 sequence

1, 4/5, 2/3, 4/7, 1/2, 4/9 ..........
next number of the sequence will be

OPtion

1) 3/5
2) 4/5
3) 1/3
4) 4/11
5) 3/8
6) 0.1
7) 0.2
8) 0.3
9) 0.4
10) none of these

Solution

1, 4/5, 2/3, 4/7, 1/2, 4/9
this sequence can also be written as
4/4, 4/5, 4/6, 4/7, 4/8, 4/9, 4/10
so next number = 4/10 = 0.4

Correct Option: 9 Best Solution (12)

13 Apr 2012 triple x

x^(x^x) - (x^x)^x = y
for x = 3, y will be

OPtion

1) 3^9[(3^9)+1][(3^9)-1]
2) 3^9[(3^18)+1]
3) 3^18[(3^9)-1]
4) 3^9[(3^9)+1]
5) 3^18[(3^27)-1]
6) 3^9[(3^18)-(3^9)]
7) 3^18[(3^18)-1][(3^18)+1]
8) 3^9[(3^18)+(3^9)]
9) 3^18[(3^9)-1]
10) none of these

Solution

3^(3^3) - (3^3)^3 = 3^27 - 3^9
= 3^9[(3^18)-1]
= 3^9[(3^9)+1][(3^9)-1]

Correct Option: 1 Best Solution (4)