M4maths Previous Puzzles

10 May 2017 Trains

A train travelling at a speed of 76 mph enters a tunnel 9/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

OPtion

OPTION
1) 3 minutes 75 seconds
2) 3 minutes 40 seconds
3) 3.45 minutes
4) 3.70 minutes
5) 3 minutes 55 seconds
6) 3 minutes 35 seconds
7) 3 minutes 30 seconds
8) 3 minutes 25 seconds
9) 3 minutes 45 seconds
10) None of these

Solution

Total Distance covered = 9/2 + 1/4 = 19/4
Time Taken = Distance/Speed = (19/4)*(1/76) = 3.75 min = 3 min 45 seconds
Option 9)

Correct Option: 9 Best Solution (10)

09 May 2017 Root and Power

If 6^(n + 5) - 6^(n + 3) = 7560, What is the value of n?

OPtion

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

Solution

6^(n + 5) - 6^(n + 3) = 7560

=> 6^(n + 3 + 2) - 6^(n + 3) = 7560

=> 6^(n + 3) × 6^(2) - 6^(n + 3) = 7560

=> 6^(n + 3)[6^(2) - 1] = 7560

=> 6^(n + 3) × (35) = 7560

=> 6^(n + 3) = 216

=> 6^(n + 3) = 6^3

=> n + 3 = 3
=> n = 0

Correct Option: 10 Best Solution (14)

08 May 2017 Series

What is the sixth term of following series:
2+2i, 5+3i, 10+5i, 17+7i, 26+11i, ......

OPtion

1) 36+17i
2) 36+15i
3) 36+13i
4) 35+13i
5) 37+13i
6) 37+15i
7) 37+17i
8) 36+19i
9) 35+15i
10) None of these

Solution

Lets represent each term of series x+iy
x and y are two different series as described below:
x = Square of natural numbers + 1 = (1+1), (4+1), (9+1), (16+1), (25+1), (36+1)
y= Prime numbers Series = 2, 3, 5, 7, 11, 13

So the 6th term is = [(6^2+1) + (6th Prime number)i = 37+13i

Correct Option: 5 Best Solution (15)

05 May 2017 Area

An error 3% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

OPtion

1) 4.04 %
2) 4.14 %
3) 5.25 %
4) 5.00 %
5) 5.75 %
6) 6.00 %
7) 6.09 %
8) 6.25 %
9) 9%
10) None of these

Solution

Lets assume side is 100 cm
100 cm is read as 103 cm.

A1 = (100 x 100) cm2 and A2 = (103 x 103) cm2.

Difference in Area:
(A2^2 - A1^2) = [(103)2 - (100)2]
= (103 + 100) x (103 - 100)
= 203*3
= 609

Percentage error = (609x100)/(100*100) = 6.09%

Correct Option: 7 Best Solution (11)

04 May 2017 Rank of the word

Rank of the word RANKING in the dictionary of words formed by the letters of the word RANKING

OPtion

1) 2208
2) 2209
3) 2210
4) 2212
5) 2214
6) 2211
7) 2206
8) 2204
9) 2202
10) None of these

Solution

Lets arrange the letters of RANKING alphabetically
AGIKNNR
Please note that only N is repeated twice

Words starting with letter A = 6!/2! = 360
Words starting with letter G = 6!/2! = 360
Words starting with letter I = 6!/2! = 360
Words starting with letter K = 6!/2! = 360
Words starting with letter N = 6! = 720

Words starting with letter RAG = 4!/2! = 12
Words starting with letter RAI = 4!/2! = 12
Words starting with letter RAK = 4!/2! = 12

Words starting with letter RANG = 3! = 6
Words starting with letter RANI = 3! = 6

Words starting with letter RANKG = 2! = 2

Words starting with letter RANKIG = 1 = 1

And next word is RANKING, so + 1 = 1

Sum of all = 4*360 + 720 + 3*12 + 2*6 + 2 + 1 +1 = 2212

Option 4)

Correct Option: 4 Best Solution (5)

03 May 2017 Age

The present ages of two persons differ by 16 years. 3 years ago, the elder one was 3 times as old as the younger one. What is the present age of the elder person?

OPtion

1) 37 years
2) 35.5 Years
3) 25 years
4) 29 years
5) 27.5 years
6) 31 years
7) 23 years
8) 24 years
9) 29 years
10) None of these

Solution

Let the present age of elder one be x and younger one be y
So x-y = 16 ----(i)
3 year ago
(x-3) =3(y-3)
=> x = 3y - 6

Putting x value in (i)
3y - 6 - y = 16
=>2y = 22
=> y = 11
and x = 11+ 16 = 27
Hence Option 10)

Correct Option: 10 Best Solution (18)

02 May 2017 Profit and Loss

96 oranges are bought for Rs. 300 and sold at the rate of Rs. 24 per half dozen. The percentage of profit or loss is:

OPtion

1) 28% Loss
2) 23% Loss
3) 27% Loss
4) 30% Loss
5) 25% Loss
6) 28% Profit
7) 23% Profit
8) 27% Profit
9) 30% Profit
10) 25% Profit

Solution

Cost of 1 orange = 300/96 = 3.125
Selling price of 1 orange = 24/6 = Rs. 4

As SP > CP so its profit
So Profit % = (4 - 3.125)*100/3.125 = 28%

Correct Option: 6 Best Solution (28)

01 May 2017 Simple Interest

A sum fetched a total simple interest of Rs. 78.6 at the rate of 5% p.a. in 2 years. What is the sum?

OPtion

1) Rs 393
2) Rs 786
3) Rs 1572
4) Rs 7860
5) Rs 3930
6) Rs 157.2
7) Rs 800
8) Rs 700
9) Rs 900
10) None of these

Solution

SI = PRT/100
=> 78.6 = P *5*2/100
=> P = 78.6*10 = 786

Correct Option: 2 Best Solution (13)

28 Apr 2017 Probability

A number is randomly picked from following list 2, 3, 4, 5, 6, 7, 8, 9 and so on till 18.
What is the probability that its a prime number?

OPtion

1) 7/17
2) 7/18
3) 6/17
4) 6/18
5) 8/17
6) 8/18
7) 7/16
8) 8/16
9) 6/16
10) None of these

Solution

Count of total number betweeen 2 to 18 = 17

List of Prime numbers between 2 to 18:
2, 3, 5, 7, 11, 13, 17
Count of (2, 3, 5, 7, 11, 13, 17) = 7

Probability of selecting prime number from numbers between 2 to 18 = 7/17

Correct Option: 1 Best Solution (15)

27 Apr 2017 Time and Work

P can do a work in 12 days. Q can do the same work in 6 days and R can do the same in 8 days. Q and R start the work and leave after 2 days. P finishes the remaining work in X days. What is the value of X?

OPtion

1) 2 days
2) 2.5 days
3) 3 days
4) 3.5 days
5) 4 days
6) 4.5 days
7) 5 days
8) 5.5 days
9) 6.0 days
10) 10 days

Solution

Amount of work done by Q and R in 2 days = 2*(1/6 + 1/8) = 7*2/24 = 7/12

Amount of work remianing after 3 days = 5/12

Amount of work done by P in 1 day = 1/12
So for 1/12 work P takes 1 day
Hence for 5/12 work P would take (1/(1/12))*5/12 = 5 days

Correct Option: 7 Best Solution (14)