M4maths Previous Puzzles

21 Aug 2019 Fraction

If a/b = 9/14 , c/d = 49/51, b/c = 17/18, e/f = 34/35 and d/e = 27/28 then what is the value of (abc/def) ?

OPtion

1) 14/31
2) 15/32
3) 147/160
4) 49/106
5) 247/280
6) 147/320
7) 101/270
8) 145/280
9) 104/288
10) None of these

Solution

a/d = (a/b)*(b/c)*(c/d) = 7/12
b/e = (b/c)*(c/d)*(d/e) = 7/8
c/f = (c/d)*(d/e)*(e/f) = 9/10

So abc/def = (a/d)*(b/e)*(c/f) = (7/12)*(7/8)*(9/10) = 147/320
Option 6)

Correct Option: 6 Best Solution (0)

20 Aug 2019 Mixture

A mixture contains sugar solution and colored water in the ratio 7 : 9. If 13 liters of colored water is added to the mixture, the ratio becomes 4 : 7. Find the initial quantity of sugar solution in the given mixture (in liters).

OPtion

1) 22
2) 32
3) 24
4) 28
5) 36
6) 40
7) 48
8) 16
9) 14
10) None of these

Solution

The initial ratio is 7 : 9.
Let ‘k’ be the common ratio.
=> Initial quantity of sugar solution = 7 k
=> Initial quantity of colored water = 9 k
=> Final quantity of sugar solution = 7 k
=> Final quantity of colored water = 9 k + 13
Final ratio = 7 k : 9 k + 13 = 4 : 7
=> k = 4
Therefore, initial quantity of sugar solution in the given mixture (in liters) = 7 k = 28 liter

Correct Option: 4 Best Solution (5)

19 Aug 2019 Age

A is 7 years older than B who is two times as old as C. The total of the ages of A, B and C is 222 years. What is the value when the age of B is multiplied to the difference between ages of A and C ?

OPtion

1) 6400
2) 6600
3) 4400
4) 4200
5) 5400
6) 5600
7) 7600
8) 4300
9) 5800
10)None of these

Solution

Let’s assume Age of B be B years
Age of A = B+7
Age of C = B/2

Total age = B + 7 + B + B/2 = 222
Solving 5B/2 = 215
B = 430/5 = 86
A = B+7 = 93
C = 8/2 = 43

Final Value = Age of B * (Age of A - Age of C) = 86*(50) = 4300

Option 8)

Correct Option: 8 Best Solution (0)

16 Aug 2019 Even Number

How many factors of 8199625500 are even numbers?

OPtion

1) 600
2) 188
3) 144
4) 180
5) 216
6) 288
7) 128
8) 256
9) 96
10) None of these

Solution

8199625500 = 37^2 * 11^3 * 5^3 * 3^2 * 2^2

Any factor of this number should be of the form 37^a * 11^b * 5^c * 3^d * 2^e

For the factor to be an even number e should be non zero.

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

Total number of even factors = 3*4*4*3*2= 288

Option 6)

Correct Option: 6 Best Solution (0)

15 Aug 2019 Probability

One alphabet letter is randomly picked from the word INDEPENDENT.
What is the probability that it would be a vowel?

OPtion

1) 4/20
2) 2/10
3) 4/5
4) 2/5
5) 4/11
6) 1/5
7) 2/7
8) 3/10
9) 3/11
10) None of these

Solution

Total number of letters in the word INDEPENDENT = 11
Total number of vowels IEEE = 4

Probability = 4/11

Correct Option: 5 Best Solution (0)

14 Aug 2019 Profit & Loss

150 oranges are bought for Rs. 400 and sold at the rate of Rs. 72 per dozen. The percentage of profit or loss is:

OPtion

1) 125%
2) 12.5%
3) 130%
4) 120%
5) 13.0%
6) 12.0%
7) 122.5%
8) 112.5%
9) 115%
10) None of these

Solution

CP of 1 orange = Rs 400/150 = 2.67
SP of 1 orange = Rs 72/12 = Rs. 6
Profit = 3.33
% profit = 100* 3.33/2.67 = 125%

Correct Option: 1 Best Solution (0)

13 Aug 2019 RANK of the word

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

OPtion

1) 462660
2) 462668
3) 462652
4) 462664
5) 462644
6) 462636
7) 462628
8) 462608
9) 462168
10) None of these

Solution

RANK is:462668

Correct Option: 2 Best Solution (1)

12 Aug 2019 Interest

At what rate of compound interest per annum will a sum of Rs. 1000 become Rs. 1144.9 in 2 years?

OPtion

1) 6.5%
2) 7.5%
3) 7.75%
4) 8.5%
5) 7.25%
6) 7.0%
7) 8.0%
8) 6.75%
9) 8.25%
10) None of these

Solution

We know, A = P (1 + r/n)^t 
Solving for R, we get R= 7%

Correct Option: 6 Best Solution (0)

09 Aug 2019 Area

If the diagonal of a rectangle is 31cm long and its perimeter is 78 cm. Find the area of the rectangle in sq. cm.

OPtion

1) 140
2) 240
3) 248
4) 560
5) 260
6) 270
7) 280
8) 300
9) 180
10) None of these

Solution

Let length = x and breadth = y then

2(x+y) = 78 => x+y = 39
x²+y² = 31² = 961
now (x+y)² = 39² = 1521
=> x²+y²+2xy= 1521
=> 961 + 2xy = 1521
=> xy = 280
area = xy = 280 sq.cm

Option 7)

Correct Option: 7 Best Solution (1)

08 Aug 2019 Age

The present age of a brother is 6 years more than four times the age of his sister. Six years hence, brother’s age will be four years more than thrice the age of the sister. Find the present age of the brother.

OPtion

1) 38
2) 42
3) 30
4) 41
5) 48
6) 20
7) 21
8) 46
9) 18
10) None of these

Solution

Let the sister’s present age be ‘n’ years.
=> brother’s present age = (4n + 6) years
So, according to the question
(4n + 6 + 6) = 3 (n + 6) + 4
=> 4n + 12 = 3n + 22
=> n = 10
Hence, brother’s present age = (4n + 6) = 46 years

Correct Option: 8 Best Solution (0)