M4maths Previous Puzzles

29 Aug 2018 Even Number

How many factors of 45434373264 are even numbers?

OPtion

1) 288
2) 360
3) 420
4) 432
5) 384
6) 360
7) 192
8) 240
9) 396
10) None of these

Solution

45434373264 = 89^1* 31^3 * 17^1 * 7^1 * 3^2 * 2^4

Any factor of this number should be of the form 31^a * 17^b * 7^c * 3^d * 2^e * 89 ^f

For the factors of this number to be an even number e should be non 0

a can take values 0, 1, 2, 3
b can take values 0, 1
c can take values 0, 1
d can take values 0, 1, 2
e can take values 1, 2, 3, 4
f can take values 0, 1

Total number of even factors = 4*2*2*3*4*2= 384

Option 5)

Correct Option: 5 Best Solution (1)

28 Aug 2018 Boats and Streams

A man goes down stream with a boat to some destination and returns upstream to his original place in 15 hours. If the speed of the boat in still water and downstream are 10km/hr and 14km/hr respectively, the distance of the destination from the starting place in KMs is

OPtion

1) 48
2) 51
3) 45
4) 66
5) 67
6) 68
7) 69
8) 70
9) 63
10) None of these

Solution

Let the distance be D

Speed of boat in still water = 10
Speed of boat in down stream = 14
Speed of Stream = 14=10 = 4
Speed of boat in upstream = 10-4 = 6

Time Downstream + Time upstream = 15
=> D/14 + D/6 = 15
=> 10D = 630
=> D = 63
Option 9)

Correct Option: 9 Best Solution (7)

27 Aug 2018 Simple Interest

At what simple interest rate percent per annum will a sum of money double in 14 years.

OPtion

1) 14.28
2) 7.00
3) 7.33
4) 13.50
5) 7.25
6) 7.14
7) 7.75
8) 6.75
9) 6.66
10) None of these

Solution

SI = PRT/100

SI = P

So P = P*R*14/100
= R= 100/14 = 7.14
Option 6)

Correct Option: 6 Best Solution (5)

24 Aug 2018 Age

A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 55 years now, what would be the son's age 4.5 years later?

OPtion

1) 31
2) 32
3) 30
4) 29
5) 28
6) 23
7) 24
8) 25
9) 26
10) None of these

Solution

Let the sons current age be x
So fathers age x years back when son was born => 55-x = x
Solving we get x = 27.5
4.5 Years later son's age = 27.5 + 4.5 = 32 years

Option 2)

Correct Option: 2 Best Solution (9)

23 Aug 2018 Work & Time

If 17 men and 18 women can do a piece of work in 11 days and 14 men and 13 women can do it in 15 days,

how many days will 27 men and 18 women take to do it?

OPtion

1) 11.00
2) 11.33
3) 11.60
4) 10.33
5) 11.75
6) 10.00
7) 10.25
8) 10.40
9) 10.75
10) None of these

Solution

Let a man's daily work be x units and that of a woman is y units.
So total amount of work, W = 11(17x + 18y) = 15(14x + 13y)

Solving we get, 187x - 210x = 195y - 198y
=> 23x = 3y

Now, 17 x + 18 y can do work in 11 days.
So, 17x + 6*23 x can do work in 11 days.
So, 155 x can do work in 11 days.

Now, 27x + 18y = 27x + 18*23x/3 = 165x

Hence, if 155x can do work in 11 days, 165x can do work in ((155xy)*11)/165y = 10.33 days

Option 4)

Correct Option: 4 Best Solution (2)

22 Aug 2018 Rakshabandhan

A brother has three sisters. He went to their house for Rakshabandhan. The 1st sister added the same amount of money he was carrying in his pocket. The brother gave her Rs.2500. The same thing happened over second and third sister's house. In the end, he had Rs. 4500 left with him. How much money did he carry from home?

OPtion

1) 2250
2) 2150
3) 2075
4) 2275
5) 2475
6) 2575
7) 2675
8) 2350
9) 2325
10) None of these

Solution

Lets assume that he carried Rs. X

After first sister's place amount of money remaining with brother
2X - 2500

After second sister's place amount of money remaining with brother
4X - 7500


After third sister's place amount of money remaining with brother
8X - 17500

As per the question
8X - 17500 = 4500
=> X = 2750

Correct Option: 10 Best Solution (0)

21 Aug 2018 Mixture

A merchant has 1925 kg of sugar, part of which he sells at 3% loss and the rest at 4% profit. He gains 2% on the whole. What is the difference between the quantities of sugar sold at 4% profit and that sold at 3% loss?

OPtion

1) 800 kgs
2) 550 kgs
3) 875 kgs
4) 1375 kgs
5) 825 kgs
6) 1120 kgs
7) 1280 kgs
8) 975 kgs
9) 1025 kgs
10)None of these

Solution

(Quantity of Cheaper)/(Quantity of Dearer) = (Price of Dearer - Mean Price)/(Mean Price - Price of Cheaper)

(Quantity of Cheaper)/(Quantity of Dearer) = (104 - 102)/(102-97) = 2/5

Total Quantity = 1925 KG

The quantity sold at 3% loss is = (2/7) * 1925 = 550 Kgs
The quantity sold at 4% profit is = (5/7) * 1925 = 1375 Kgs
Difference between Quantity = 1375 - 550 = 825 Kgs


Option 5)

Correct Option: 5 Best Solution (3)

20 Aug 2018 Series

What is the seventh term of following series:
4, 7, 12, 19, 28,

OPtion

1) 50
2) 52
3) 30
4) 36
5) 35
6) 40
7) 45
8) 39
9) 34
10) None of these

Solution

nth term = n^2 + 3
n=1, 2, 3, 4, 5, 6, and so on

So 7th term = 7^2 + 3 = 52

Option 2)

Correct Option: 2 Best Solution (12)

17 Aug 2018 RANK of the word

Find Rank of the word INDIAN in the dictionary of words formed by the letters of the word INDIAN

OPtion

1) 108
2) 105
3) 103
4) 101
5) 104
6) 100
7) 107
8) 99
9) 98
10) None of these

Solution

wer: 105

INDIAN
Lets arrange the letters alphabetically = ADIINN

Words starting with A = 5!/(2!*2!) = 30
Words starting with D = 5!/(2!*2!) = 30
Words starting with IA = 4!/(2!) = 12
Words starting with ID = 4!/(2!) = 12
Words starting with II = 4!/(2!) = 12
Words starting with INA = 3! = 6
Words starting with INDA = 2! = 2
and the next word is INDIAN = 1

Sum of all = 105

Option 2)

Correct Option: 2 Best Solution (0)

16 Aug 2018 Calendar

It was Friday on 15th August 1947. What day it would be after 66 days from 15th August 1947 :

OPtion

1) Monday
2) Tuesday
3) Thursday
4) Wednesday
5) Friday
6) Saturday
7) Sunday
8) Sunday or Tuesday
9) Saturday or Wednesday
10) None of these

Solution

Each day of the week is repeated after 7 days. So, after 63 days, it will be Friday.

After 66 days it will be Monday

Correct Option: 1 Best Solution (1)