M4maths Previous Puzzles

08 Oct 2019 Arithmetic

The sum of squares of three successive integers is 9749. Sum of these integers is?

OPtion

1) 161
2) 222
3) 191
4) 181
5) 361
6) 121
7) 171
8) 184
9) 154
10) None of these

Solution

(a-1)^2 + a^2 + (a+1)^2 = 9749
=> a^2 -2a + 1 + a^2 + a^2 + 2a + 1 = 9749
=> 3a^2 + 2 = 9749
=> a^2 = (20174-2)/3 = 3249
=> a = 57
So the 3 numbers are 56, 57 and 58 and their sum is 171

Correct Option: 7 Best Solution (3)

07 Oct 2019 RANK of the word

The rank of the word NAVARATRI in the dictionary of all the words formed by the letters of the word NAVARATRI is?

OPtion

1) 14550
2) 14540
3) 14530
4) 14545
5) 14535
6) 14525
7) 14549
8) 14544
9) 14520
10)None of these

Solution

Rank is 14550

Correct Option: 1 Best Solution (0)

04 Oct 2019 Heights and Distance

A helium balloon leaves the ground at a point A and rises vertically at uniform speed. At the end of 5 minutes, Raju finds the angular elevation of the balloon as 30°. If the point at which Raju is standing is 550 m away from point A, what is the speed of the balloon in m/s?

OPtion

1) 2.67
2) 2.17
3) 1.67
4) 1.067
5) 1.58
6) 2.058
7) 1.085
8) 2.076
9) 1.058
10) None of these

Solution

Let C be the position of Raju. Let A be the position at which balloon leaves the Ground and B be the position of the balloon after 5 minutes.

Given that CA = 550 m, angle BCA = 30°

tan 30° = 1/(3^1/2) = BA/CA
BA = CA/(√3) = 550/√3 m

time taken = 5 min = 5 × 60 = 300 seconds

Speed = Distance/Time
=> (550/√3)/300
= 1.058 meter/second

Option 9)

Correct Option: 9 Best Solution (3)

03 Oct 2019 Solve

The value of 216^(2/3) x (1296)^0.75 is

OPtion

1) 6^(24/5)
2) 6^(26/5)
3) 6^(19/4)
4) 6^(14/3)
5) 6^(21/4)
6) 6^(5/1)
7) 6^(36/7)
8) 6^(41/8)
9) 6^(27/6)
10) None of these

Solution

(6^3)^(2/3) x (6^4)^3/4
=> 6^(2) x (6^3)
=> 6^ (2 + 3)
=> 6 ^(5)
=> 7776

Correct Option: 6 Best Solution (1)

02 Oct 2019 Simple Interest

How much amount would a person receive at maturity if he invests a sum of Rs. 1947 at the rate of 10% of simple interest for 2 years in a bank.

OPtion

1) 389.40
2) 398.40
3) 389.04
4) 2,386.40
5) 2,363.40
6) 2,336.40
7) 2,336.04
8) 2,236.40
9) 309.40
10) None of these

Solution

SI = PRT/100 = 1947*2*10/100 = 389.40
A = 389.40 + 1947 = 2,336.40

Correct Option: 6 Best Solution (4)

01 Oct 2019 Probability

A man throws three dices simultaneously on the floor. What is the probability of getting three numbers whose product is even?

OPtion

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

Solution

Each dice could either have an even number or odd number.
Product would be odd only if all three numbers are odd.

Total number of possible outcomes in terms of even and odd results = 2*2*2 = 8

For product to be odd, total number of positive outcomes = 1 (considering all three dices should have an odd numbered result)

Probability of getting three numbers whose product is odd = 1/8

Probability of getting three numbers whose product is even= 1- 1/8 = 7/8

Correct Option: 9 Best Solution (0)

30 Sep 2019 Solve for x

45 * x = 17.5% of 5400.
then x = ?

OPtion

1) 15
2) 18
3) 21
4) 24
5) 27
6) 28
7) 11.5
8) 12
9) 16
10) None of these

Solution

x = 17.5*54/45 =21

Correct Option: 3 Best Solution (5)

27 Sep 2019 Solve

The tickets numbered from 1 to 30 are mixed up and then a ticket is drawn at random. What is the probability that the ticket has a number which is a multiple of 3 or 5?

OPtion

1) 9/20
2) 8/30
3) 8/30
4) 9/30
5) 8/15
6) 7/150
7) 14/30
8) 1/4
9) 1/2
10) None of these

Solution

The sample space, S= (1, 2, 3, 4, 5 ...28, 29, 30) or n(S) = 30

The event "E" of getting a multiple of 3 or 5 = (3, 6, 9, 12, 15, 18, 21, 24, 27, 5, 10, 20, 25, 30) or n (E) = 14

Probability = 14/30 = 7/15

Correct Option: 7 Best Solution (4)

26 Sep 2019 Solve

The HCF of 2/3, 8/9, 64/81, and 10/27 is:

OPtion

1) 2/27
2) 2/9
3) 3/49
4) 2/81
5) 5/49
6) 4/81
7) 4/27
8) 4/49
9) 2/243
10) None of these

Solution

HCF = HCF of Numerator/LCM of denominator

HCF of 2, 8, 64 and 10 = 2
LCM of 3, 9, 81, 27 = 81

Hence HCF = HCF/LCM = 2/81

Correct Option: 4 Best Solution (3)

25 Sep 2019 Solve

A train moving at speed of 180 km/hr crosses a pole in 7 seconds. Find the length of the train.

OPtion

1) 250
2) 300
3) 350
4) 175
5) 700
6) 150
7) 125
8) 375
9) 325
10) None of these

Solution

Length of the train is equal to the distance covered by train to cross the pole. So, we will find the distance traveled by the train in 7 seconds by applying the following formula:

Distance= Speed x Time

Speed is given in Km/hr so we will convert it into m/s as answers are given in meters.

Speed=180*5/18 = 50 m/s
Time = 7 seconds

Distance = 50 * 7= 350 meters

Correct Option: 3 Best Solution (0)