M4maths Previous Puzzles

18 Jul 2013 Problem

A person is walking with uniform speed and when he has completed half his journey he increased his speed 20% and arrives at his destination. Also last half part of his journey be complete 30 minutes earlier than first half part of journey. How long was he walking the first half.

OPtion

1) 1hour
2) 1hour 30 minute
3) 2hour
4) 3hour
5) 4hour
6) 4hour 30 minute
7) 6hour
8) 6hour minute
9) 7hour
10)None of these

Solution

Let v=speed in first half and t=time taken to cover first half
Distance = vt (i)
For the second half;
Speed=v+(20v/100)=6v/5
Time =(t-0.5)hrs
Distance =(6v/5)(t-1/2) (ii)
From (i) and (ii), we get vt = (6v/5)(t-0.5)
t=3 hour
option 4

Correct Option: 4 Best Solution (26)

17 Jul 2013 average

average of 5 non negative integers is 9. If sum of any 3 integers out of 5 is 36, then the possible product of other 2 will be

OPtion

1) 10
2) 28
3) 14
4) 8
5) 30
6) 12
7) 9
8) 15
9) 21
10) none of these

Solution

non negative means 0 is also a possible integer.
now grand sum of 5 integers = 45
sum of 3 integers = 36
so sum of other 2 = 9
possible cases are
0,9
1,8
2,7
3,6
4,5
now check

Correct Option: 3 Best Solution (0)

16 Jul 2013 AP

Find the sum of all odd integers between 2 and 100 which are divisible by 3.

OPtion

1) 767
2) 897
3) 867
4) 987
5) 768
6) 679
7) 785
8) 989
9) 877
10) None of these

Solution

Sequence 3,9,15,21,..........99
Clearly a=3; common difference = 6
An=99
a+(n-1)d = 99
3+(n-1)6=99
n=17
solve
867
option 3

Correct Option: 3 Best Solution (0)

15 Jul 2013 Sequence

What is the next number of the following sequence
3/7,5/21,7/43,9/73,11/111,.........

OPtion

1) 13/129
2) 15/137
3) 17/147
4) 13/157
5) 19/167
6) 13/149
7) 15/177
8) 17/153
9) 13/153
10)None of these

Solution

3/3^2-2 = 3/7
5/5^2-4 = 5/21
7/7^2-6 = 7/43
9/9^2-8 = 9/73
11/11^2-10 = 11/111
13/13^2-12 = 13/157

Correct Option: 4 Best Solution (0)

12 Jul 2013 Equation

Solve the equation for x:
9^(x+2)-6*3^(x+1)+1=0

OPtion

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

Solution

9^2*9^x-6*3*3^x+1=0
Solve
x=-2

Correct Option: 9 Best Solution (0)

11 Jul 2013 Problem

The power, in mega watts (MW), produced between midnight and noon in a nuclear power plant is given by P=4h^2-48h+744, where h is the hour of the day. At what times is the power 664 MW.

OPtion

1) 3 A.M and 9 A.M
2) 2 A.M and 10 A.M
3) 2 A.M and 8 A.M
4) 5 A.M and 10 A.M
5) 10 A.M and 11 A.M
6) 4 A.M and 8 A.M
7) 3 A.M and 10 A.M
8) 2 A.M and 9 A.M
9) 6 A.M and 8 A.M
10) None of these

Solution

Solve Equation
4h^2-48h+744=664
h=10,2
The power is 664 MW at 2 A.M and 10 A.M
option 2

Correct Option: 2 Best Solution (26)

10 Jul 2013 Problem

The taxi in a city comprise of a fixed charges together with the charge for the distance covered. For a journey of 10 km, the charges paid is Rs.75 and for a journey of 15 km, the charge paid is Rs.110 what will a person have to pay for traveling a distance of 25 km.

OPtion

1) 75
2) 120
3) 175
4) 180
5) 210
6) 235
7) 260
8) 300
9) 320
10) None of these

Solution

Let fixed charges of taxi be Rs.x and charges for covering distance be Rs.y per km.
Then according to question, we have
x+10y=75 (i)
x+15y=110 (ii)
Solve
we get x=5 and y=7
Person will have to pay for travelling a distance of 25 km.
x+25y=5+25*7=Rs.180
option 4

Correct Option: 4 Best Solution (7)

09 Jul 2013 Problem

One herd of camels was seen in the forest, twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels.

OPtion

1) 15
2) 16
3) 20
4) 25
5) 36
6) 40
7) 49
8) 52
9) 64
10) None of these

Solution

Let total number of camels = x
2.sqrt(x) are on the mountain and remaining camels are 15
x-2.sqrt(x)=15
x-15=2.sqrt(x) (Squaring both side)
solve we get
x = 9 and x = 25
x cannot be 9 because 15 are remaining
The total camels are 25
option 4

Correct Option: 4 Best Solution (14)

08 Jul 2013 Sequence

What is the next number of the following sequence
1,4,9,7,7,9,......

OPtion

1) 1
2) 4
3) 9
4) 10
5) 13
6) 16
7) 17
8) 19
9) 21
10)None of these

Solution

1^2=1=1+0=1
2^2=4=4+0=4
3^2=9=9+0=9
4^2=16=1+6=7
5^2=25=2+5=7
6^2=36=3+6=9
7^2=49=4+9=13
option 5

Correct Option: 5 Best Solution (10)

05 Jul 2013 Three digit

Sum of 3 digit of a three digit number is 17. On reversing the digits, the difference of new number & previous number is 297. If units place digit is 3 less then the sum of other two digits. Then product of the digits of the number is..

OPtion

1) 18
2) 63
3) 64
4) 72
5) 144
6) 162
7) 168
8) 180
9) 189
10) None of these

Solution

Let digits are x, y, (17-x-y)
number [100x+10y+(17-x-y)]
By the given condition
[100(17-x-y)+10y+x]-[100x+10y+(17-x-y)]=297
100(17-2x-y)-(17-2x-y)=297
99(17-2x-y)=297
17-2x-y=3
2x+y=14 (i)
17-x-y=x+y-3
2x+2y=20
x+y=10
4
6
7
option 7

Correct Option: 7 Best Solution (7)