M4maths Previous Puzzles

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)

25 Mar 2022 Time and Work

A and B together can finish a work at their usual efficiencies in 36 days. If A had worked at 2/3 of his usual efficiently and B had worked at twice his usual efficiently, then the work would have been completed in 30 days. How many days would A take to finish the task if he works alone at twice the usual efficiency?

OPtion

1) 90
2) 45
3) 24
4) 20
5) 72
6) 30
7) 15
8) 60
9) 36
10) None of these

Solution

Let A and B can do A unit and B unit of work per day respectively, then 36A + 36B = 1 ----(i)
Now, with A working with 2/3 efficiently and B with twice efficiency, it takes 30 days to finish => 30*(2/3)*A + 30*2B = 1
20A + 60B = 1 ----(ii)
Solving (i) & (ii), we get, A=1/60, B=1/90
When A works alone with twice effeciency, his 1 day work = 2*A = 2*1/60 = 1/30
.'. A would finish the work in 30 days.

Correct Option: 6 Best Solution (2)

24 Mar 2022 Alligation and Mixture

Liquids A and B are mixed in the ratio 5:3 and the mixture is sold at Rs. 42 with a profit of 20%. If the liquid A costs Rs 4 more than the liquid B, then the cost price of liquid A (in Rs) is

OPtion

1) 35
2) 36
3) 40
4) 33.5
5) 37.5
6) 35.5
7) 32.5
8) 36.5
9) 34.5
10) None of these

Solution

The mixture is sold at 20% profit for Rs. 42 /Liter, .'. CP of mixture = (100/120)*42 = Rs. 35 /Liter
Let CP per liter of liquid A = Rs. x and liquid B =Rs. (x-4)
Given, ratio of liquid A & B = 5:3
In 8 liter mixture, liquid A= 5 liters and Liquid B=3 Liters
Then, CP of 8 liter mixture = [5x + 3(x-4)] / 8 = 35
8x - 12 = 280
x = 36.5 Rs.
Correct Option 8)

Correct Option: 8 Best Solution (3)

23 Mar 2022 Area and Volume

A cuboid with sides in the ratio 8:5:6 is cut perpendicular to its length to form three smaller cuboids of equal size. If sum of the surface areas of all three cuboids is 1080 cm² more than the surface area of original cuboid, then the volume of original cuboid (in cm³) is

OPtion

1) 4320
2) 5280
3) 6480
4) 6720
5) 6240
6) 7200
7) 6960
8) 5760
9) 7440
10) None of these

Solution

Let length, breadth & height of original cuboid be L, B, H respectively.
Then, its Curved Surface Area = 2(LB + BH + LH) -----(i)
Dimension of each new cuboid are L/3, B, H (Breadth and height being same)
Curved Surface Area of 3 new cuboids = 3*2[(L/3)B + BH + (L/3)H] = 2LB + 6BH + 2LH ---(ii)
Difference of Curved Surface Area (ii) - (i) = 4BH = 1080
BH = 270
Let Length, Breadth & Height of original cuboid be 8x, 5x, 6x respectively, then 5x*6x = 270
30x² = 270 or x = 3
So, sides of original cuboid are L=24 cm, B=15 cm, H=18 cm
.'. Volume of original cuboid = L*B*H = 24*15*18 = 6480 cm³.
Correct option 3)

Correct Option: 3 Best Solution (2)

22 Mar 2022 Profit & Loss

Ramesh purchased a mobile phone for Rs. 15,000. He sold it to Suresh at a gain of 20% of the selling price. Suresh further sold it to Mahesh for Rs. 20,000. What was the profit percentage of Suresh ?

OPtion

1) 16.66
2) 11.11
3) 66.66
4) 8.88
5) 6.66
6) 5.55
7) 33.33
8) 9.99
9) 22.22
10) None of these

Solution

Here, Ramesh sold mobile phone to Suresh at a gain of 20% on SP
SP = CP + Profit
SP = CP + 0.2*SP
0.8*SP = 15000
SP = 18750 = CP of Suresh
.'. Profit of Suresh = 20000 - 18750 = 1250 Rs.
% Profit = (1250/18750)*100 = 6.66 %

Correct Option: 5 Best Solution (2)

21 Mar 2022 Alligation and Mixture

A food contains 550 grams of a mixture of two foods varieties, X and Y. Food X contains 20% carbohydrate and food Y contains 35% carbohydrate. If this diet provides exactly 140 grams of carbohydrate, then how many grams of food X are in the mixture ?

OPtion

1) 385
2) 335
3) 380
4) 400
5) 345
6) 285
7) 330
8) 350
9) 325
10) None of these

Solution

Let x be the number of grams of Food X in the mixture, then number of grams of food Y=(550-x)
Total carbohydrate = Carbohydrate from Food X + Carbohydrate from Food Y
140 = 0.2x + 0.35(550-x)
52.5 = 0.15x
x = 350

Correct Option: 8 Best Solution (1)