M4maths Previous Puzzles

24 Jan 2019 Series

Find the next terms of the following sequence
4096, 2048, 2040, 1020, 1012, 506, ?, ?

OPtion

1) 500, 250
2) 496, 248
3) 498, 249
4) 502, 251
5) 504, 252
6) 498, 239
7) 496, 248
8) 500, 249
9) 598, 249
10) None of these

Solution

Answer: 498, 249

4096/2= 2048 , 2048-8=2040
2040/2 = 1020, 1020-8 = 1012
1012/2 = 506, 506 - 8 = 498
498/2 = 249

Correct Option: 3 Best Solution (5)

23 Jan 2019 Mixture

A mixture contains sugar solution and colored water in the ratio 4 : 3. If 14 liters of colored water is added to the mixture, the ratio becomes 2 : 5. Find the initial quantity of sugar solution in the given mixture (in liters).

OPtion

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

Solution

The initial ratio is 4 : 3.
Let ‘k’ be the common ratio.
=> Initial quantity of sugar solution = 4 k
=> Initial quantity of colored water = 3 k
=> Final quantity of sugar solution = 4 k
=> Final quantity of colored water = 3 k + 14
Final ratio = 4 k : 3 k + 14 = 2 : 5
=> 20 k = 6 k + 28
=> k = 2
Therefore, initial quantity of sugar solution in the given mixture (in liters) = 4 k = 8 liter

Correct Option: 7 Best Solution (5)

22 Jan 2019 Probability

What is the probability of getting all the 6 spoiled eggs from a supplier if the probability of one spoiled egg is 0.29?

OPtion

1) 0.0005918
2) 0.0005848
3) 0.0005048
4) 0.0005928
5) 0.0005908
6) 0.0005948
7) 0.0006948
8) 0.0005348
9) 0.0005998
10) None of these

Solution

Probability of one spoiled eggs = 0.29
Probability of six spoiled egg = (0.29)^6 = 0.000594823321 = ~0.0005948

Correct Option: 6 Best Solution (0)

21 Jan 2019 Direction

Majnu Bhai is facing northwest. He turns 90 degrees in the clockwise direction, then he turns 45 degrees in the anti-clockwise direction and finally he turns 135 degree in clockwise direction. Which direction is he facing now?

OPtion

1) Esst
2) North East
3) North West
4) West
5) South
6) North
7) South West
8) South East
9) North East or North West
10) None of these

Solution

Clockwise turns = 90+135 = 225
Anti-Clockwise turn = -45
Consolidated turn in clockwise direction = 225-45 = 180 degrees
Majnu bhai initially was facing north west direction, so on turning 180 degrees in clockwise the new direction would be south east

Correct Option: 8 Best Solution (2)

18 Jan 2019 Series

Fine the sixth term of the series:
1, 6, 21, 60, ...

OPtion

1) 155
2) 150
3) 165
4) 175
5) 145
6) 215
7) 230
8) 315
9) 135
10) None of these

Solution

nth term of Series is = n*(2^n - 1)
1st term = 1*(2^1 -1 ) = 1
4th term = 4*(2^4 -1 ) = 60
6th term = 6*(2^6 - 1 ) = 378

Correct Option: 10 Best Solution (0)

17 Jan 2019 Number

A number consists of 3 digits whose sum is 10. The middle digit is equal to the difference of the other two and the number will be increased by 99 if its digits are reversed. The square of the number is:

OPtion

1) 164036
2) 168100
3) 180625
4) 172225
5) 264196
6) 254016
7) 164025
8) 180616
9) 179776
10) None of these

Solution

let the digits of the No. be x. y & z
Hence, x+y+z=10.................(1)
z-x=y..............(2)

AS per the condition
(100z+10y+x)-(100x+10y+z)=99
=> z-x=1 -----(3)

Form (2) and (3), we deduce y=1

From equation (1) and (2)
we get,
x+z=9 and
z-x =1

Solving we get z= 5 and x = 4

So the number is 415 and its square is = 172225

Correct Option: 4 Best Solution (0)

16 Jan 2019 Population

The population of rodents in a house doubles every day. Every day 25 rodents are killed. How many rodents are there if after every four days, the number of rodents becomes same again?

OPtion

1) 20
2) 5
3) 15
4) 6
5) 24
6) 12
7) 25
8) 16
9) 8
10) None of these

Solution

1st day - x
2nd day - (2x-25)
3rd day - [2(2x-25)-25]
4th day - 2[2(2x-25)-25] - 25 = 8x - 7*25

After fourth day the value becomes equal to the first day so 8x - 7*25 = x
Solving, we get x = 25

Correct Option: 7 Best Solution (0)

15 Jan 2019 Profit & Loss

Lalu sold his watch and sunglasses at a loss of 5% and gain of 5% respectively for 3600 to Bhalu. Bhalu sold the same sun glasses and watch at a loss of 4% and gain of 4% respectively for 3800. The price of watch and sun glasses respectively to Lalu in rupees were.

OPtion

1) 2650, 950
2) 2550, 1050
3) 2750, 850
4) 2850, 850
5) 2450, 1250
6) 2950, 750
7) 2450, 1050
8) 2650, 1050
9) 2850, 950
10) None of these

Solution

Let the CP of watch be Rs x and sunglasses be Rs y.

Lalu sold his watch and sunglasses at a loss of 5% and gain of 5% :
3600=95x/100 + 105y/100

Bhalu sold the same sun glasses and watch at a loss of 4% and gain of 4% respectively :
3800= 104x/100 + 96y/100

On solving,
y=744.44
x=2966.67

Option 10)

Correct Option: 10 Best Solution (0)

14 Jan 2019 Simple Interest

Nirav took a loan of Rs. 201900 from PNB with simple interest for as many years as the rate of interest. If he was supposed to pay Rs. 395724 as interest at the end of the loan period, what was the rate of interest?

OPtion

1) 11
2) 10
3) 11.5
4) 12.5
5) 14.5
6) 15
7) 16
8) 14.0
9) 15.5
10) None of these

Solution

SI = PRT/100
=> 395724 = (201900 *R*T)/100
As R=T so => 395724 = (201900 *R*R)/100

R^2 = 395724 * 100/201900 = 196
=> R= 14

Option 8)

Correct Option: 8 Best Solution (0)

11 Jan 2019 Speed and Distance

Rahmatullah could either walk or drive to office. The time taken to walk to the office is 11 times the driving time. One day, his wife took the car making him walk to office. After walking 2.5 km, he reached a temple when his wife called to say that he can now take the car. Ramanujam figured that continuing to walk to the office will take as long as walking back home and then driving to the office. Calculate the distance between the temple and the office in KMs.

OPtion

1) 5/2
2) 5/3
3) 7/2
4) 7/3
5) 2.0
6) 2.5
7) 6/2
8) 3.5
9) 3.25
10)None of these

Solution

Suppose the distance between his home and office is x km. Then, distance between his office and temple is (x – 2.5) km.
If he walks at a speed of y km/hr. Then his driving speed = 11y km/hour, as he is 11 times faster in car.

Then,
2.5/y + x/11y = (x – 2.5)/y
Or, 2.5 + x/11 = x – 2.5
or 10x/11 = 5
Or, x = 11/2
Finally, x – 2.5 = 11/2-5/2 = 6/2 = 3
Option 7)

Correct Option: 7 Best Solution (4)