IMO - Mock Test - 2

This is a simple alternating addition and subtraction series.
4 is added in the first pattern and 3 is subtracted in the second.
That is:
7 + 4 = 11
11 - 3 = 8
8 + 4 = 12
12 - 3 = 9
9 + 4 = 13
13 - 3 = 10

D = (+2) = F
G = (-4) = C
H = (+6) = N
Similarly, M = (+2) = O
H = (-4) = D
G = (+6) = M

1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125, 6³ = 216

P + 2 = R

R - 2 = P

E + 2 = G

P - 2 = N

Similarly, R + 2 = T

E - 2 = C

M + 2 = O

E - 2 = C

M + 2 = O

B - 2 = Z

E + 2 = G

R - 2 = P

By rearranging the letters, we get BANANA and Banana belongs to fruit category.

7 is subtracted from the previous number every time.
56 - 7 = 49
49 - 7 = 42
42 - 7 = 35
35 - 7 = 28
28 - 7 = 21
21 - 7 = 14

The first letter becomes the fourth, the second letter remains second, the third becomes the first and the last becomes the third.

The correct sequence of the words according to the dictionary is
5. Wedding
3. Weekend
2. Weigh
1. Welfare
4. Western

% = x
@ = ÷
$ = -
& = +

Therefore, 25 ÷ 5 x 10 + 20 - 15 = 55

The first term of the series is a = 20
The common difference = d = 25 - 20 = 5
So, the 8^th term of the series = a + (n - 1)d = a + 7d = 20 + 35 = 55
The sixth term of the series = a + (n - 1)d = 20 + 5 x 5 = 20 + 25 = 45
So, the difference = 55 - 45 = 10

The nth term of the series is a + (n - 1)d.
The seventh term of the series = a + 6d = 75
The tenth term of the series = a + 9d = 111
So, subtract the seventh term from the tenth term.
3d = 36
d = 12
Substituting this value, a + 72 = 75
a = 3

x² + 7x + 12

Splitting the middle term, x² + 4x + 3x + 12 = x(x + 4) + 3(x + 4)

(x + 4)(x + 3) = 0

x = -4, - 3

Similarly, 2x² + 7x + 3 = 0

2x² + 6x + 1x + 3 = 0

2x(x + 3) + 1(x + 3) = 0

(x + 3)(2x + 1) = 0

x = - 3 and - 1/2

So, the common factor is - 3.

Given expression is (cot⁴ x + cot² x) - (cosec⁴ x - cosec² x)

= cot² x(cot² x + 1) - cosec² x(cosec² x - 1)

= cot² x cosec² x - cosec² x cot² x = 0

Total number of marbles = 48

Probability of getting a red marble = 5/6

Number of red marbles = 5/6 × 48 = 40

So, number of yellow marbles = 48 - 40 = 8

We will assume common ratio between angles to be 'x' and then see the total of all internal angles in a quadrilateral is 360^o.

Using that, we can find the value of 'x' and then angles accordingly.

5x + 8x + 4x + 7x = 360^o

24x = 360

x = 360/24 = 15

5x = 5 × 15 = 75^o

8x = 8 × 15 = 120^o

4x = 4 × 15 = 60^o

7x = 7 × 15 = 105^o

Mode = 3 Median - 2 Mean
Substituting the values: 90 = 3(110) - 2 Mean
90 = 330 - 2 Mean
2 Mean = 330 - 90
2 Mean = 240
Mean = 120

Let s be the side of the square.
If the width of the rectangle is 30 cm, its length would be 36 cm.
Area of the rectangle = Area of the square
l x w = s²
36 x 30 = s²
1080 = s²
s = 32.86 cm

The experimental probability is the number of times an event occurs out of the total number of trials. Write the experimental probability as a fraction in its simplest form.
P(Cheese) = Cheese/Total = 1/2
So, the probability of the next customer wanting cheese burger is ½.

First find the discount price. Write 45% as the decimal 0.45 before using it in the equation.

Discounted price = Original price – Discount = 8000 – 0.45 x 8000 = 8000 – 3600 = 4400

The discounted price was Rs. 4400.

Now, find the commission. Write 7% as the decimal 0.07 before using it in the equation.

Commission = Commission percentage × Sales = 0.07 x 4400 = 308

The commission was Rs. 308.

HCF of 247 and 156.

All prime factors of 247 and 156 = 13

So, each one will be arranged in 13 rows.

The portion of the tank filled when the pipe as well as the leak were open = 1/10 + 1/25 = 1/30

If x is the time taken to fill the tank when pipe and leak were open, then portion of the tank filled in x minutes = x/30

Remaining portion to be filled when the leak was sealed = 1 - x/30 = (30 - x)/30

Time taken to fill the remaining portion of the tank = 6 minutes

(30 - x)/30 = 6/10

Solving the above equation, we get
x = 12 minutes

Total time taken to fill the tank = 6 minutes + 12 minutes = 18 minutes

Assume that Mike got x% chocolates and Peter got (x - 16)% chocolates.

As the number of chocolates brought by Chetan is 100%, we can equate the problem as

100 = x + (x - 16)

x = 58

If Mike got 58% of the chocolates, then Peter got (58 - 16) % of the total chocolates i.e. 42%.

Chocolates received by Mike = 0.58 × 150 = 87

Chocolates received by Peter = 0.42 × 150 = 63

Therefore, the ratio is 87 : 63 = 29 : 21

The present ratio of P to Q is 3 : 1 and after 5 years, the ratio will be 2 : 1.

(3x + 5)/(x + 5) = 2/1

3x + 5 = 2x + 10

x = 5

The present age of P is 15 years and that of R is 25 years.

Five years back, age of P was 10 years and that of R was 20 years.

P was 10 years younger than R 5 years ago.

Given that the tiles required for flooring are square. Hence, the length of the tile should be equal to the width of the tile.

As the number of tiles required needs to be an integer value, the side of the square tile has to be a factor of the dimensions of the room.

Therefore, side of each square = HCF of 600 cm and 440 cm = 40 cm

Number of tiles required = (Area of bed room)/(Area of each tile) = (600 × 440)/(40 x 40) = 165

If price of each tile is Rs. 70, then minimum cost incurred = 165 × 70 = Rs. 11550

Number of hours in a day = 24
Number of hours in between 11 am and 5 pm = 6
Number of times crow comes in an hour = 2 (i.e after every 30 minutes)
Therefore, in 6 hours, it will come 12 times.
Number of days in a week = 7
Hence, number of times in a week = 12 × 7 = 84 times

1. The centre of the circle lies in interior of the circle.
2. A point whose distance from the centre of the circle is greater that its radius lies in exterior of the circle.
3. The longest chord of the circle is a diameter of the circle.

Batsman played 40 balls.

Therefore, total number of trials (S) = 40 where, S is the sample space.

Let, E be the event of hitting the boundary = 8

The number of balls not hitting the boundary = E = 40 - 8 = 32

The probability of not hitting a boundary = E/S = 32/40