M4maths Previous Puzzles

30 Aug 2017 Factors

How many factors of 878800000 are odd number?

OPtion

1) 8
2) 30
3) 18
4) 12
5) 25
6) 16
7) 36
8) 32
9) 48
10) None of these

Solution

878800000 = 2^7* 5^5 * 13^3

Any factor of this number should be of the form 2^a * 5^b * 13^c.

For the factor to be a odd number a should be 0

b can take values 0, 1, 2, 3, 4, 5
and c can take values 0, 1, 2, 3

Total number of odd factor = 6*4 = 24

Correct Option: 10 Best Solution (5)

29 Aug 2017 Distance

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 45° and 60° respectively. If the lighthouse is 222 m high, the distance between the two ships is:

OPtion

1) 350.17 m
2) 352.17 m
3) 353.17 m
4) 354.17 m
5) 355.17 m
6) 356.17 m
7) 357.17 m
8) 358.17 m
9) 359.17 m
10)None of these

Solution

Let AB be the lighthouse where A is the bottom point of light house and C and D be the positions of the ships.
Then, AB = 222 m, Angle ACB = 45° and angle ADB = 60°.
AB/AC = tan 45° = 1
=> AC = AB = 222

AB/AD = tan 60° = 3^(1/2)
=> AD = AB/3^(1/2) = 74*3^(1/2)

CD = (AC + AD) = 222+ 74*3^(1/2)
= 350.17
Option 1)

Correct Option: 1 Best Solution (15)

28 Aug 2017 Simple Interest

A sum fetched a total simple interest of Rs. 63 at the rate of 5% p.a. in 3 years. What is the sum?

OPtion

1) Rs 400
2) Rs 410
3) Rs 420
4) Rs 425
5) Rs 450
6) Rs 500
7) Rs 480
8) Rs 415
9) Rs 525
10) None of these

Solution

SI = PRT/100
P= SI*100/RT = 63*100/5*3 = 21*20 = 420
Option 3)

Correct Option: 3 Best Solution (33)

25 Aug 2017 Age

"A father said to his son, ""I was as old as you are at the present at the time of your birth"". If the father's age is
58 years now, what was the son's age seven years back?"

OPtion

1) 21
2) 20
3) 19
4) 18
5) 16
6) 17
7) 22
8) 23
9) 24
10) None of these

Solution

Let the sons current age be x
So fathers age x years back when son was born => 58-x = x
Solving we get x = 29
7 Years back son's age = 29-7 = 22 years

Correct Option: 7 Best Solution (5)

24 Aug 2017 Stocks & Shares

The market value of a 9.5% stock, in which an income of Rs. 900 is derived by investing Rs. 13500, brokerage being 1/4 %, is:

OPtion

1) 142.00
2) 142.50
3) 142.75
4) 141.75
5) 142.25
6) 143.00
7) 141.25
8) 141.50
9) 143.25
10) None of these

Solution

For an income of Rs. 900, investment = Rs. 13500

For an income of Rs. 9.5, investment = Rs. (13500/900) * 9.5 = 142.5
For a Rs. 100 stock, investment = Rs. 142.5

Market value of Rs. 100 stock = Rs. 142.5 - 0.25 = Rs. 142.25

Correct Option: 5 Best Solution (10)

23 Aug 2017 Speed and Distance

Manoranjan could either walk or drive to office. The time taken to walk to the office is 9 times the driving time. One day, his wife took the car making him walk to office. After walking 3 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) 27/4
2) 25/4
3) 23/4
4) 21/4
5) 19/4
6) 29/4
7) 17/7
8) 15/4
9) 13/7
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 – 3) km.
If he walks at a speed of y km/hr. Then his driving speed = 9y km/hour, as he is 9 times faster in car.

Then,
3/y + x/9y = (x – 3)/y
Or, 3 + x/9 = x – 3
or 8x/9 = 6
Or, x = 27/4
Finally, x – 3 = 27/4 - 3 = 15/4
Option 8)

Correct Option: 8 Best Solution (5)

22 Aug 2017 Mean, Median, & Mode

Find the product of mean, median and mode (i.e. you need to find mean*median*mode)for the following list of values?
23; 16; 45; 28; 18; 23; 36;

OPtion

1) 18009
2) 14283
3) 12528
4) 12006
5) 11683
6) 15548
7) 16767
8) 16646
9) 16146
10) None of these

Solution

Mean = Sum of nos. / Count of numbers = (23+16+45+28+18+23+36)/7 = 189/7 = 27
Median = Middle term when number are arranged in ascending order = 23
Mode = Number which is present maximum number of times =23
Product = 23*23*27 = 14283

Option 2)

Correct Option: 2 Best Solution (2)

21 Aug 2017 Profit and Loss

Rizwan buys an old scooter for Rs. 26750 and spends Rs. 2175 on its repairs. If he sells the scooter for Rs. 34600, his gain percent is:

OPtion

1) 19.58 %
2) 18.06 %
3) 17.48 %
4) 19.85 %
5) 19.90 %
6) 18.60 %
7) 18.80 %
8) 17.30 %
9) 19.62 %
10) None of these

Solution

Cost Price (C.P.) = Rs. (26750 + 2175) = Rs. 28925

Selling Price (S.P.) = Rs. 34600

Gain = (S.P.) - (C.P.) = Rs.(34600 - 28925) = Rs. 5675

Gain % = (5675/28925)*100 = 19.619 = ~19.62 %

Correct Option: 9 Best Solution (8)

18 Aug 2017 Root and Power

Find the value of:
(7)^1.35 * (13)^0.35 * (91)^0.65 = ?

OPtion

1) 633.34
2) 637.00
3) 631.57
4) 635.23
5) 634.91
6) 654.88
7) 630.57
8) 649.00
9) 632.00
10) None of these

Solution

(7)^1.35 * (13)^0.35 * (91)^0.65
=> (7)^1.35 * (13)^0.35 * (7*13)^0.65
=> [(7)^1.35 * (7)^0.65] * [(13)^0.35 * (13)^0.65]
= [7^2] * [13^1]
= 49*13
= 637

Correct Option: 2 Best Solution (9)

17 Aug 2017 Time and Work

P can do a work in 19.5 days. Q can do the same work in 13 days and R can do the same in 6.5 days. Q and R start the work and leave after 4 days. P finishes the remaining work in X days. What is the value of X?

OPtion

1) 2.5 days
2) 2.0 days
3) 1.75 days
4) 1.5 days
5) 2.25 days
6) 4.5 days
7) 5 days
8) 5.5 days
9) 6.0 days
10) None of these

Solution

Amount of work done by Q and R in 4 days = 4*(1/13 + 1/6.5) = 12/13

Amount of work remaining after 4 days = 1/13

Amount of work done by P in 1 day = 1/19.5
So for 1/19.5 work P takes 1 day
Hence for 1/13 work P would take (1/(1/19.5))*1/13 = 1.5 days

Correct Option: 4 Best Solution (7)