M4maths Previous Puzzles

15 Feb 2017 Log

If log4 + log(13x+1) = log(5x+9) + 1, then value of x is ?
Note: Assume all log represented above is to the base of 10.

OPtion

1) 15/8
2) 3
3) -43/4
4) 43/4
5) 86
6) -43
7) 43/2
8) 1
9) -43/2
10) None of these

Solution

Considering base is 10, so 1 could be represented as Log10
=> log4 + log(13x+1) = log(5x+9) + log10

Let’s revise the formula for Logs
Log(XY) = LogX+LogY
Applying the formula we get:
Log[4*(13x+1)] = Log[10*(5x+9)]
Solving
=> 52x + 4 = 50x + 90
=> 2x = 86
=> x = 43

Option 10)

Correct Option: 10 Best Solution (17)

14 Feb 2017 Profit

In a shop, the profit is 175% of the cost. If the cost increases by 25% but the selling price remains constant, find out approximately what percentage of the selling price is the profit?

OPtion

1) 54.5
2) 56.5
3) 57.5
4) 58.5
5) 59.5
6) 115
7) 120
8) 125
9) 130
10)135

Solution

Let the CP be Rs. 100
SP considering 175% of profit = 100+175 = Rs. 275
CP after 25 increase = Rs. 125

Profit = 275 – 125 = Rs. 150
Profit % on SP = (150/275)*100 = 54.5 (approximately)


Option 1)

Correct Option: 1 Best Solution (0)

13 Feb 2017 Age Problem

Sweety's father was 34 years of age when she was born while her mother was 35 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?

OPtion

1) 1 Year
2) 1.5 Years
3) 2 Years
4) 2.5 Years
5) 3 Years
6) 3.5 Years
7) 4.5 Years
8) 5 Years
9) 6 Years
10)None of these

Solution

Age of Sweety's father when Sweety was born = 34
Age of Sweety's mother when Sweety was born = 35−4 =31
Required difference of age =34−31= 3 Years

Option 5)

Correct Option: 5 Best Solution (29)

03 Feb 2017 Coding Decoding

If
CHINA = 7
KOREA = 10
BURMA = 11

Then NAURU = ?

OPtion

1) 5
2) 7
3) 9
4) 10
5) 11
6) 13
7) 14
8) 15
9) 16
10)17

Solution

Each word is code as = (Sum of values of each alphabet)/Total number of letters in word
CHINA = 35/5 = 7, similarly for KOREA and BURMA
So for NAURU = 75/5 = 15
Option 8)

Correct Option: 8 Best Solution (23)

02 Feb 2017 Area

The length, breadth and height of a room are in the ratio 7:3:1. If the breadth and height are doubled while the length is halved. Then the total area of the 4 walls of the room will:

OPtion

1) Increase by 30%
2) Increase by 40%
3) Increase by 50%
4) Increase by 60%
5) Increase by 70%
6) Increase by 80%
7) Increase by 90%
8) Increase by 18%
9) Increase by 10%
10)No Change in total area of 4 walls

Solution

l:b:h=7:3:1
let h=x, b=3x and l=7x
Area of 4 walls = 2*(l+b)*h
Initial Area
Area1= 2*(7x+3x)*x = 20x^2
New dimensions
l2=7x/2
b2=6x
h2=2x
New Area
Area2= 2*(7x/2+6x)* 2x = 38x^2
% Increase in area = (38-20)*100/20 = 90%
Option 7)

Correct Option: 7 Best Solution (16)

01 Feb 2017 Mean, Median and Mode

Find the sum of mean, median and mode (i.e. you need to find mean+median+mode)for the following list of values:
14, 11, 13, 11, 21, 16, 12

OPtion

1) 34
2) 35
3) 36
4) 37
5) 38
6) 39
7) 40
8) 41
9) 42
10)43

Solution

Mean = Sum of nos. / Count of numbers = (14+11+13+11+21+16+12)/7 = 98/7 = 14
Median = Middle term when number are arranged in ascending order (11, 11, 12, 13, 14, 16, 21) = 13
Mode = Number which is present maximum number of times (11, 11, 12, 13, 14, 16, 21) =11
Sum = 14+13+11 = 38

Option 5)

Correct Option: 5 Best Solution (21)

31 Jan 2017 Discount

During festival season a trader keeps the marked price of an item 44% above its cost price. The percentage of discount allowed to gain 26% is

OPtion

1) 13 %
2) 13.5 %
3) 14 %
4) 14.5 %
5) 14.5 %
6) 15 %
7) 16 %
8) 17%
9) 18%
10)None of these

Solution

Let CP be Rs. 100 then Marked Price = 144
Actual SP = 126
Discount on marked price = (Marked Price – Actual SP)*100/ Marked Price = (144-126)*100/144 = 12.5%

Option 10)

Correct Option: 10 Best Solution (19)

30 Jan 2017 Probability

One card is randomly drawn from a pack of 52 cards. What is the probability that the card drawn is a Queen card or a King card?

OPtion

1) 2/52
2) 2/26
3) 2/13
4) 4/13
5) 4/25
6) 2/25
7) 8/26
8) 2/44
9) 8/51
10)None of these

Solution

Total number of cards, n(S) = 52

Total number of King & Queen cards, n(E) = 8

P(E) = n(E)/n(S) = 8/52 = 4/26 = 2/13

Option 3)

Correct Option: 3 Best Solution (28)

27 Jan 2017 Probability

With Dhoni and Yuvraj at the creaseCricket Team of India needs to score 9 runs in last 2 balls to win the match. What is the probability that India wins the match? Assume that:
- There were no wide balls or no balls bowled in these 2 balls.
- No Wicket has fallen in these 2 balls
- No Overthrows or extra runs were scored in these 2 balls
- In case if run(s)are scored on any of these 2 balls it can only be one of these values: 1, 2, 3, 4 & 6
This also implies that it’s quite possible that zero runs are scored on a particular ball

OPtion

1) 1
2) 1/6
3) 1/9
4) 1/9
5) 1/4
6) 1/36
7) 3/36
8) 5/36
9) 7/36
10)8/36

Solution

On any of these 2 balls the possible runs which can be scored are: 0,1,2,3,4,6
So total possible number of runs which can be scored in 2 balls are = 6C1*6C1 = 36
Let’sassume that run scored on first ball is x and 2nd ball is y
To win the match x+y>= 9. Possible pair of values of x and y are:
(x, y)
(4, 6), (6, 4), (6, 3), (3, 6) and (6, 6)
Count of set of values for India to win the match = 5
Probability = Positive outcome/Total Possible Outcomes = 5/36
Option 8)

Correct Option: 8 Best Solution (12)

26 Jan 2017 Cost Price

Riya bought a cycle with 21% discount on the labeled price. She sold the cycle for Rs.3000 with 20% profit on the labeled price. At what price did she buy the cycle?

OPtion

1) Rs. 2500
2) Rs. 2450
3) Rs. 2375
4) Rs. 2250
5) Rs. 2175
6) Rs. 2025
7) Rs. 1975
8) Rs. 1850
9) Rs. 1725
10)Rs. 1650

Solution

Riya sold the cycle with 20% profit on the Labeled Price
⇒3000=120×Labeled Price/100
⇒Labeled Price=(3000×100)/120= 2500
Riya bought cycle with 21% discount on the labeled price
=> CP = Labeled Price×79/100=2500×79/100=1975

Option 7)

Correct Option: 7 Best Solution (21)