M4maths Previous Puzzles

02 Jan 2019 Profit and Loss

A vendor bought 1300 toffees for 5850 rupees. How many toffees in 1053 rupees must he sell to gain 56%?

OPtion

1) 133.33
2) 134
3) 140
4) 150
5) 135
6) 155
7) 160
8) 250
9) 210
10)None of these

Solution

CP of 1 toffees = 5850/1300 = Rs. 4.5
SP of 1 toffees for 56% profit = 4.5*1.56 = Rs. 7.02
So in 1053 Rupees number of toffees to be sold = 1053/7.02 = 150

Option 4)

Correct Option: 4 Best Solution (10)

01 Jan 2019 Decode

If VERY= 7369, HAPPY= 54889 and NEW = 231 then code for YEAR would be

OPtion

1) 9345
2) 9846
3) 9316
4) 9376
5) 9046
6) 9348
7) 9346
8) 9340
9) 9356
10) None of these

Solution

AS VERY is coded as "7369", HAPPY is coded as "54889" and NEW as 231
So Y is coded as 9, E as 3, A as 4, R as 6

So code for YEAR would be = 9346

Correct Option: 7 Best Solution (11)

31 Dec 2018 Series

Find the next term of the series:
6, 11, 16, 21, 26, ?

OPtion

1) 27
2) 28
3) 29
4) 34
5) 35
6) 36
7) 31
8) 32
9) 30
10) None of these

Solution

Next term of series is derived
4*(n-1) + n+1 where n=1

So 4*1 + 2 = 6
4*2 + 3 = 11
4*3 + 4 = 16
4*4 + 5 = 21
4*5 + 6 = 26
4*6 + 7 = 31

Correct Option: 7 Best Solution (10)

28 Dec 2018 ODD Number

How many factors of 3622184564625 are odd numbers?

OPtion

1) 600
2) 188
3) 144
4) 180
5) 288
6) 576
7) 128
8) 256
9) 96
10) None of these

Solution

3622184564625 = 37^2 * 19^1 * 11^3 * 5^3 * 3^2 * 31^1

Any factor of this number should be of the form 37^a * 19^b * 11^c * 5^d * 3^e * 31^f

All the factors of this number would be an odd number as there is no even factor

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

Total number of odd factors = 3*2*4*4*4*2= 768

Option 10)

Correct Option: 10 Best Solution (0)

27 Dec 2018 Mixture

A mixture contains sugar solution and colored water in the ratio 3 : 5. If 16 liters of colored water is added to the mixture, the ratio becomes 4 : 7. Find the initial quantity of colored water in the given mixture (in liters).

OPtion

1) 192
2) 120
3) 240
4) 160
5) 180
6) 320
7) 360
8) 150
9) 200
10) None of these

Solution

The initial ratio is 3 : 5
Let ‘k’ be the common ratio.
=> Initial quantity of sugar solution = 3 k
=> Initial quantity of colored water = 5 k
=> Final quantity of sugar solution = 3 k
=> Final quantity of colored water = 5 k + 16

Final ratio = 3 k : 5 k + 16 = 4 : 7
=> 21 k = 20k + 64
=> k = 64
Therefore, initial quantity of colored water in the given mixture (in liters) = 5 * 64 = 320 liter

Correct Option: 6 Best Solution (6)

26 Dec 2018 Race

In a race of 500 m, A can beat B by 30 m and C by 20 m. In a race of 1200 m, C will beat B by:

OPtion

1) 75
2) 25
3) 100
4) 10
5) 15
6) 350
7) 150
8) 50
9) 175
10) None of these

Solution

When A covers 500m B Covers 470m
When A Covers 500m C covers 480

A : B = 500 : 470
A : C = 500 : 480

C/B = (C/A*A/B) = (480/470) = 480:470
When C covers 480 m, B covers 470 m.
When C covers 1200 m, B covers (470/480)*1200)m = 1175m
Therefore, C beats B by (1200 - 1175) m = 25 m.

Option 2)

Correct Option: 2 Best Solution (0)

25 Dec 2018 Solve

Given (73-a)(73-b)(73-c)(73-d)(73-e) = 910.

Find a+b+c+d+e= ?

OPtion

1) 210
2) 220
3) 410
4) 110
5) 840
6) 820
7) 910
8) 920
9) 420
10) None of these

Solution

Note: There is some issue with the points allotted to participant, we would be correcting it soon.

Lets try to simplify:
910 = 13*7*5*2*1 = (73-60)*(73-66)*(73-68)*(73-71)*(73-72)

So a+b+c+d+e = 60 + 66 + 68 + 71 + 72 = 337

Correct Option: 10 Best Solution (6)

24 Dec 2018 Probability

A letter is randomly picked from the following longest word in the dictionary: pneumonoultramicroscopicsilicovolcanoconiosis
what is the probability that it is a vowel?

OPtion

1) 1/3
2) 16/45
3) 17/45
4) 2/5
5) 19/45
6) 4/9
7) 7/15
8) 22/45
9) 1/4
10) None of these

Solution

Total number of letters in pneumonoultramicroscopicsilicovolcanoconiosis = 45
Number of vowels a, e, i, o, and u = 20

Probability = 20/45 = 4/9

Option 6)

Correct Option: 6 Best Solution (4)

21 Dec 2018 RANK

Find the rank of the word WORD in the dictionary of words formed by the letters of the word WORD

OPtion

1) 10
2) 11
3) 12
4) 13
5) 14
6) 20
7) 21
8) 22
9) 24
10) None of these

Solution

Lets arrange the letters alphabetically DORW

Words starting with D or O or R = 3*3! = 3*6 = 18
Words Starting with WD = 2! = 2
Words starting with WOD = 1 =1
Next word is WORD = 1 =1

Rank = 18+2+1+1 = 22

Correct Option: 8 Best Solution (3)

20 Dec 2018 Cost Price

Sweety went to buy eleven chocolates worth Rs. x. She gave Rs.100 rupee note to the shopkeeper to buy the chocolates then shopkeeper gave rest of the money in the denominations of 50 paise, 2 rupee, and 5 rupees. If the ratio of the number of coins is 7:6:7 respectively. Then what is the price of eight chocolates?

OPtion

1) 4.5
2) 49,5
3) 51.5
4) 5.5
5) 45
6) 38
7) 40.5
8) 36
9) 35
10) None of these

Solution

Possible coins = (7, 6, 7) & (14, 12, 14)
If (7, 6, 7) = 0.50*7+ 2*6 + 5*7 = 50.5

Chocolate cost = 100 - 50.5 = 49.5

Case 2: (14, 12, 14) = 0.50*14+ 2*12 + 5*14 = 101 which is more than 100 rupees so wrong

So cost of 11 chocolates = Rs 49.5

Cost of 8 Chocolates = (49.5/11)*8 = Rs 36

Option 8)

Correct Option: 8 Best Solution (8)