M4maths Previous Puzzles

15 Apr 2022 Permutation & Combination

Find the number of ways to arrange the letters of the word ' GOODFRIDAY ' if letters ' DAY ' are always together.

OPtion

1) 1814400
2) 151200
3) 907200
4) 241920
5) 120960
6) 15120
7) 60480
8) 30240
9) 45360
10) None of these

Solution

The word GOODFRIDAY has 10 different letters
When the letters DAY are kept together they can be supposed to form one letter.
Then we have to arrange letters GOODFRI (DAY)
Now 8 letters (7+1) can be arranged in 8!/2! (O being repeated twice)
The letters DAY can be arranged among themselves in 3! ways.
.'. Required number of ways = (8!/2!)*3! = 120960

Correct Option: 5 Best Solution (1)

14 Apr 2022 Ratio and Proportion

Two numbers are such that their difference, their sum and their product are in the ratio 1:5:24. The product of these two numbers is

OPtion

1) 60
2) 72
3) 48
4) 84
5) 96
6) 64
7) 144
8) 108
9) 120
10) None of these

Solution

Let the numbers be x and y, then (x-y) : (x+y) : xy = 1 : 5 : 24
(x-y)/(x+y)=1/5 ⇒ 2x=3y ---(i)
(x+y)/xy=5/24 ⇒ 24x + 24y = 5xy ----(ii)
On solving Eqn. (i) & (ii), we get x=12, y=8
.'. Required product x*y = 12*8 = 96

Correct Option: 5 Best Solution (2)

13 Apr 2022 Probability

A packet contains some blue, red and green pens such that the probability of picking a blue pen is 2/9 and probability of picking a green pen is 4/9. If number of red pens is 15 and if all the pens are numbered starting from 1, 2, 3, ... and so on, then what is the probability of getting one pen numbered as multiple of 7 or 11 ?

OPtion

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

Solution

Given, P(Blue)=2/9, P(Green)=4/9 and number of red pens=15
As we know, P(Blue) + P(Red) + P(Green) = 1
P(Red) = 1 - P(Blue) - P(Green) = 1 - (2/9) - 4/9 = 3/9 = 1/3
As number of red pens = 15 = 1/3 of total pens
.'. Total number of pens=15*3=45 ⇒ Pens are numbered from 1 to 45
Numbers that are multiple of 7 = 7, 14, 21, 28, 35, 42
And numbers that are multiple of 11 = 11, 22, 33, 44
So, favourable outcomes = 6+4 = 10
So, probability of getting pen of multiple 7 or 11 = 10/45 = 2/9

Correct Option: 5 Best Solution (2)

12 Apr 2022 Time Distance & Speed

Train A whose length is four-fifth of that of train B crosses it travelling in opposite direction in a time which is 4/7 th of the time taken by train A to cross it when travelling in same direction. Calculate the ratio of the speeds of train A and train B.

OPtion

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

Solution

Let lengths of trains B = x, then length of train A = (4/5)*x
Distance covered in each case =x + (4/5)*x = (9/5)*x
Let the speed of train A and train B be S1 and S2 respectively.
Relative speed in same direction = (S1-S2)
Relative speed in opposite direction = (S1+S2)
According to given condition, Time taken to cross train B in opposite direction = (4/7)*Time taken to cross train B in same direction
(9/5)*x / (S1 + S2) = (4/7)*[(9/5)*x / (S1 - S2)]
7(S1 - S2) = 4(S1 + S2)
3S1 = 11S2
S1/S2 = 11/3

Correct Option: 4 Best Solution (0)

11 Apr 2022 Number Series

Find next number in the series 24, 36, 38, 95, 98, ?

OPtion

1) 245
2) 298
3) 343
4) 380
5) 362
6) 284
7) 392
8) 352
9) 367
10) None of these

Solution

Alternate multiplication and addition series
24 x 1.5 = 36
36 + 2 = 38
38 x 2.5 = 95
95 + 3 = 98
98 x 3.5 = 343

Correct Option: 3 Best Solution (1)

08 Apr 2022 Averages

The average salary of executives in a company is Rs. 42,000 and that of non-executives is Rs. 30,000. The average salary of all the employees is Rs. 33,000. What is the percentage of non-executives in a company ?

OPtion

1) 60
2) 80
3) 65
4) 70
5) 50
6) 75
7) 33.33
8) 66.66
9) Insufficient Data
10) None of these

Solution

Let number of Executives and non-executives be x and y respectively.
Then, average salary of all the employees = (42000x + 30000y) / (x+y) = 33000
9000x = 3000y
x/y = 1/3
⇒ Non-executives are 3/4 of the total employees and their % = (3/4)*100 = 75%

Correct Option: 6 Best Solution (2)

07 Apr 2022 Percentage

After sale in a first week, there were x% items left out of the total stocked items in a store. In next week, when retailer stocked 30% more items and sold 40% more items, the remaining items increased by 20%. Find the value of x.

OPtion

1) 50
2) 30
3) 40
4) 35
5) 60
6) 55
7) 25
8) 22.5
9) 12.5
10) None of these

Solution

In the first week, let a retailer had total 100 items, Remaining items=x, so items sold=(100-x)
In next week, new stocked items (+30%) = 130, New Selling (+40%) = 1.4(100-x), Remaining items=130 - 1.4(100-x)
Given, new remaining items are 20% more than the initial ⇒ 130 - 1.4(100-x) = 1.2x
130 - 140 + 1.4x = 1.2x
0.2x = 10
x = 50

Correct Option: 1 Best Solution (1)

06 Apr 2022 Number System

What least number must be subtracted from 1739 so that the resulting number when divided by 6, 10 and 12 will leave in each case the same remainder 5 ?

OPtion

1) 61
2) 54
3) 39
4) 49
5) 36
6) 59
7) 64
8) 65
9) 44
10) None of these

Solution

LCM of 6, 10 and 12 = 60
⇒ The multiple of 60 are also divisible by 6, 10 or 12.
.'. Nearest number below 1739 divisible by them = 60 x 28 = 1680
Now, 1685 will be the number that will give remainder 5.
Hence, number to be subtracted = 1739 – 1685 = 54

Correct Option: 2 Best Solution (2)

05 Apr 2022 Geometry

A hexagon has interior angles in arithmetic progression where difference of angles is double the smallest angle. The measure of largest interior angle of this hexagon is

OPtion

1) 240
2) 220
3) 185
4) 360
5) 440
6) 275
7) 110
8) 270
9) 330
10) None of these

Solution

Sum of interior angles of a polygon with 'n' sides = 180*(n-2)
.'. Sum of interior of of a hexagon = 180*(6-2) = 720°
Given, Internal angles are in A.P. Let the six angles be x, x+d, x+2d, x+3d, x+4d, x+5d
Also, the difference 'd' between angles is double the smallest angle ⇒ d=2x
.'. The angles are x, (x+2x), (x+4x), (x+6x), (x+8x), (x+10x) or x, 3x, 5x, 7x, 9x, 11x
Sum of interior angles = 36x = 720
⇒ x=20
Hence, largest angle = 11x = 220°

Correct Option: 2 Best Solution (4)

04 Apr 2022 Algebra

If x² + 1/x² = 198, Find x² - 1/x² = ?

OPtion

1) 70
2) 140
3) 280
4) 70√2
5) 140√2
6) 70√5
7) 280√2
8) 140√5
9) 280√5
10) None of these

Solution

Given, x² + 1/x² = 198
(x + 1/x)² = x² + 1/x² + 2 = 198+2 = 200 ⇒ ( x + 1/x) = 10√2
(x - 1/x)² = x² + 1/x² - 2 = 198-2 = 196 ⇒ ( x - 1/x) = 14
Now, x² - 1/x² =(x + 1/x) (x - 1/x) = 10√2*14 = 140√2

Correct Option: 5 Best Solution (3)