M4maths Previous Puzzles

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)

01 Apr 2022 Probability

A fraction x/y is formed by randomly choosing integers for x and y such that
1 ≤ x ≤ 10
1 ≤ y ≤ 7
What is the chance that the fraction is less than 1/2 ?

OPtion

1) 1/14
2) 4/35
3) 1/7
4) 3/35
5) 9/70
6) 2/35
7) 1/5
8) 6/35
9) 11/70
10) None of these

Solution

Possible fractions x/y are 1/1, 1/2, ...., 10/7 => Total Outcomes=10*7=70
For x=1, Fraction x/y < 1/2 are 1/3, 1/4, 1/5, 1/6, 1/7, Total=5
For x=2, Fractions x/y < 1/2 are 2/5, 2/6, 2/7, Total=3
For x=3, Fractions x/y < 1/2 is 3/7, Total=1
Similarly no values of fractions possible for x > 3
Total favorable outcomes=5+3+1=9
Hence, chance or probability that fraction < 1/2 = 9/70

Correct Option: 5 Best Solution (6)

31 Mar 2022 Arithmetic

Sum of first 13 terms of an arithmetic progression is 312. Which of the following can be the sum of the first 14 terms, if the first term and the common difference are positive integers?

OPtion

1) 356
2) 362
3) 350
4) 346
5) 370
6) 368
7) 359
8) 341
9) 355
10) None of these

Solution

In A.P. when First term=a, Difference=d, then Sum of n terms, Sn = (n/2)[2a + (n-1)*d]
.'. 312 = (13/2)*(2a + 12d)
48 = 2a + 12d
Now, Sum of first 14 terms = (14/2)*(2a + 13d) = 7(2a + 12d + d) = 7(48+d) = 336 + 7d
So, from the given options, only 350 is in the form of 336+7d

Correct Option: 3 Best Solution (2)

30 Mar 2022 Percentage

The value of a certain article is 'k' percent more than its value one year earlier, If the value of an article was 'a' rupees on January 1, 2019, and 'b' rupees on January 1, 2021, then in terms of 'a' and 'b' what was the value of an article (in rupees) on January 1, 2022 ?

OPtion

1) a²b
2) √b/√a
3) b + [(b-a)/2]
4) b + (√b/√a)
5) b/√a
6) b*√b/√a
7) √a/√b
8) b²/(2a)
9) 2b/√a
10) None of these

Solution

Price in 2019 = a
Price in 2020 = a∗(1 + k/100)
Price in 2021 = a*(1 + k/100)^2 = b => (1+ k/100) = √(b/a)
Price in 2022 = b∗(1 + k/100) = b*√(b/a) = b*√b/√a
Correct option 6)

Correct Option: 6 Best Solution (3)

29 Mar 2022 Ratio & Proportion

If (x+y) : (y+z) : (x+z) = 10 : 23 : 19 and x+y+z=13, then the value of z = ?

OPtion

1) 6
2) 3
3) 7
4) 5
5) 4
6) 8
7) 3.5
8) 4.5
9) 1.5
10) None of these

Solution

Let x+y=10x, y+z=23x, x+z=19x
Then, 2(x+y+z) = 10x+23x+19x = 52x
2*13 = 52x
x = 1/2
.'. x+y=10*(1/2)=5 --- (i)
y+z=23*(1/2)=23/2 ---(ii)
x+z=19*(1/2)=19/2 ---(iii)
Solving (i), (ii) & (iii), we get x=1.5, y=3.5, z=8

Correct Option: 6 Best Solution (1)

28 Mar 2022 Arithmetic

Rohit prepared a project report of 225 pages, where content and page numbers are printed on one side of a paper. Due to printing mistake one page was missing and Rohit sum up all page numbers to 25268. Which among the following is a missing page ?

OPtion

1) 137
2) 175
3) 159
4) 197
5) 169
6) 119
7) 157
8) 183
9) 154
10) None of these

Solution

Page numbers are 1,2,3,......,225
Sum of first n numbers = n(n+1)/2
.'. Sum of 225 pages = 225x226/2 = 25425
Given, sum of page numbers excluding missing page = 25268
Therefore, missing page number = 25425 - 25268 = 157

Correct Option: 7 Best Solution (4)