M4maths Previous Puzzles

20 Aug 2020 Number

A = (126a^2 + 113a + 11)/a; where A belongs to integer. How many integral solutions of A are possible?

OPtion

1) 2
2) 3
3) 6
4) 9
5) 8
6) 7
7) 10
8) 12
9) 4
10) None of these

Solution

(126a^2 + 133a +11)/a = 126a + 133 + 11/a

Now we can see that whatever the value of ‘a’, 126a + 133 will always give an integral value.
So, it now depends upon 11/a only

=> a can have any integral value, which is a factor of 11.
The integers, which will satisfy this condition are ±1, ±11. Thus, in total,a can take 4 values.

Correct Option: 9 Best Solution (0)

19 Aug 2020 Mensuration

A rope is 89 cm long. It is cut into 3 pieces. The longest piece is 3 times as long as the middle-sized piece &

the shortest piece is 44 cm shorter than the longest piece. Find the length of the shortest piece (in cm).

OPtion

1) 12
2) 19
3) 13
4) 9
5) 18
6) 15
7) 10
8) 21
9) 4
10) None of these

Solution

Let the middle be x CM

Longest piece = 3x cm
Smallest piece = 3x - 44

x+3x+3x-44 = 89
7x = 133
x= 19
shortest piece = 3*19-44 = 13 cm

Correct Option: 3 Best Solution (5)

18 Aug 2020 Numbers

The product of two numbers is 39375 and the quotient, when the larger one is divided by the smaller, is 7. The sum of the numbers is :

OPtion

1) 800
2) 500
3) 600
4) 840
5) 640
6) 540
7) 480
8) 700
9) 750
10) None of these

Solution

Let the numbers be x and y.
Then, xy = 39375 and x/y = 7.
(xyxy//)=39375/7
=>y2 =5625
=> y = 75
=> x = 7y = 7 x 75 = 525.
Sum of the numbers = 525 + 75 = 600.

Correct Option: 3 Best Solution (6)

17 Aug 2020 Numbers

Three numbers are in the ratio 3 : 6 : 9 and their average is 66. The largest number is :

OPtion

1) 72
2) 81
3) 90
4) 99
5) 60
6) 66
7) 100
8) 110
9) 144
10) None of these

Solution

Let the numbers be 3x, 6x and 9x, Then, (3x + 6x + 9x ) / 3 = 66

=> 6x = 66

=> x = 11.

Largest = 11x = 11*9 = 99

Correct Option: 4 Best Solution (4)

14 Aug 2020 Permutation

A five-digit number is formed using digits 1, 3, 5, 8 and 9 without repeating any one of them. What is the sum of all such possible numbers?

OPtion

1) 6666600
2) 6666680
3) 6606600
4) 6066600
5) 6931264
6) 6933264
7) 6932264
8) 6934264
9) 6935264
10) None of these

Solution

If we fix 1 at the unit’s place, the other digits can be arranged in 4! = 24 ways.

So, there are 24 numbers which have 1 at the unit’s place and sum of these numbers is 24.

Similarly, there will be 24 numbers each with 3, 5, 8 and 9 at the unit’s place.

So, the sum of all the numbers at the unit’s place will be:

24 + 24 × 3 + 24 × 5 + 24 × 8 + 24 × 9 = 624

Similarly, the sum of the digits at the ten’s place, hundred’s place,

thousand’s place and ten thousand’s place will be 624.

So, the sum of all numbers = 624 (1 + 10 +100 +1,000 +10,000) = 6933264

Correct Option: 6 Best Solution (5)

13 Aug 2020 Race

In a mile race, Yuvraj can be given a start of 128 m by Virat. If Virat can give Rohit a start of 4 m in a 100 m dash, then who out of Yuvraj and Rohit will win a race of one and half miles, and what will be the final lead given by the winner to the loser? One mile is 1,600 m.

OPtion

1) Yuvraj, 10 m
2) Rohit, 10 m
3) Yuvraj, 25 m
4) Rohit, 25 m
5) Yuvraj, 50 m
6) Rohit, 50 m
7) Yuvraj, 80 m
8) Rohit, 80 m
9) Rohit, 100 m
10) None of these

Solution

In a mile race, Yuvraj can be given a start of 128 m by Virat. This means that Virat can afford to start after Yuvraj has traveled 128 m and still complete one mile with him. In other words, Virat can travel one mile, i.e. 1,600 m in the same time as Yuvraj can travel (1600 – 128) = 1,472 m. Hence, the ratio of the speeds of Virat and Yuvraj = Ratio of the distances traveled by them in the same time = 1600/1472 = 25 : 23.

Virat can give Rohit a start of 4 miles. This means that in the time Virat runs 100 m, Rohit only runs 96 m. So the ratio of the speeds of Virat and Rohit = 96 : 100 = 25 : 24.

Hence, we have B : A = 25 : 23 and B : C = 25 : 24. So A : B : C = 23 : 25 : 24. This means that in the time Rohit covers 24 m, Yuvraj only covers 23 m. In other words, Rohit is faster than Yuvraj. So if they race for 1.5 miles = 2,400 m, Rohit will complete the race first and by this time Yuvraj would only complete 2,300 m. In other words, Rohit would beat Yuvraj by 100 m

Correct Option: 9 Best Solution (1)

12 Aug 2020 Probability

A letter is randomly picked from the word:
INDEPENDENCE

What is the Probability that it would be a vowel?

OPtion

1) 1/2
2) 2/3
3) 5/11
4) 1/3
5) 5/12
6) 4/11
7) 5/13
8) 1/4
9) 1/3
10) None of these

Solution

Total letters in INDEPENDENCE = 12

Total Vowels =5
E=4
I=1

Probability = 5/12

Correct Option: 5 Best Solution (1)

11 Aug 2020 Simple Interest

At what rate percent per annum will a sum of money double in 6 years.

OPtion

1) 20%
2) 15%
3) 12.5%
4) 14%
5) 16%
6) 16.67%
7) 18%
8) 17.33%
9) 11.66%
10) None of these

Solution

Let principal = P, Then, S.I.= P and Time = 8 years



We know that S.I. = PTR/100



Rate = [(100 x P)/ (P x 6)]% = 12.5% per annum.

Correct Option: 6 Best Solution (3)

10 Aug 2020 Profit & Loss

Find the cost price of 1KG of Cashews which is sold for Rs. 690 at a loss of 8%.

OPtion

1) 800
2) 725
3) 750
4) 820
5) 850
6) 860
7) 720
8) 775
9) 700
10) None of these

Solution

If CP 100 SP 92
i.e. When SP 92, CP 100
when SP 690, CP = 100*690/92 = 750

Correct Option: 3 Best Solution (1)

07 Aug 2020 Permutation and Combination

In how many ways a team consisting of 5 boys and 3 girls, can be chosen from 9 boys and 12 girls.

OPtion

1) 27710
2) 27720
3) 27740
4) 27780
5) 27716
6) 27732
7) 27764
8) 27128
9) 27700
10) None of these

Solution

Choose 5 boys out of 9 boys = 9C5 ways = 126 ways

Choose 3 girls out of 12 girls = 12C3 ways = 220 ways

The committee can be chosen in = 126 * 220 = 27720 ways

Correct Option: 2 Best Solution (1)