IMO - Mock Test

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IMO - Mock Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

Find the next number in the following pattern. 22, 222, 2001, 16012, ?

A
30023

B
112079

C
112089

D
202021

Solution

The pattern is 22 x 10 + 2 = 222
222 x 9 + 3 = 2001
2001 x 8 + 4 = 16012
16012 x 7 + 5 = 112089
Question 2
1 / -0

Find out the incorrect term in the series.

45, 48, 43, 46, 49, 44

A
43

B
49

C
48

D
44

Solution

The series goes as +3, -5.
Therefore,
45 + 3 = 48,
48 - 5 = 43,
43 + 3 = 46,
46 - 5 = 41,
41 + 3 = 44
So, the incorrect number is 49.
Question 3
1 / -0

If SNAP can written as RLXL, then BOLD can be written as

A
ANIZ

B
AMIA

C
AMIZ

D
DLOB

Solution

S - 1 = R
N - 2 = L
A - 3 = X
P - 4 = L
Similarly,
B - 1 = A
O - 2 = M
L - 3 = I
D - 4 = Z
Question 4
1 / -0

Five girls participated in a dance competition. Raveena ranked lower than Savita. Veena was ranked higher that Dyna. Kimmy ranked exactly between Raveena and Veena.

Who was ranked the highest?

A
Savita

B
Veena

C
Dyna

D
Kimmy

Solution

According to the question,
Raveena < Savita
Veena > Dyna

The ranking of the competition is Savita > Raveena > Kimmy > Veena > Dyna or Savita > Veena > Kimmy > Raveena > Dyna.
Thus, it is evident that Savita is ranked the highest.
Question 5
1 / -0

If A denotes '×', B denotes '÷', C denotes '+' and D denotes '–', then which of the following statements is true?

A
15B5C7D2 = 8

B
8A6C9B1 = 10

C
19C9C4B6 = 14

D
18A6B5B10 = 7

Solution

According to the given statement, A = '×', B = '÷', C = '+', and D = '–'.
The expression in the first option becomes 15 ÷ 5 + 7 - 2 = 8.
Or, 3 + 7 - 2 = 8
Or, 10 - 2 = 8
Or, 8 = 8
Question 6
1 / -0

What will be the approximate diameter of a circle if the area of the circle is 1964.28 cm²?

A
25 cm

B
40 cm

C
50 cm

D
100 cm

Solution

Area of a circle = πr², where π^₌ 22/7and 'r' is the radius of circle.
1964.28 cm² = 22/7 x r²
1964.28 x 7/22 cm² = r²
√624.9 cm = r,
r = 25 cm
D = Diameter of the circle = 2r
D = 50 cm
Question 7
1 / -0

If a + b = - 4, what will be the value of a³ + b³ + 64?

A
- 12

B
12

C
- 12ab

D
12ab

Solution

Given, a + b = -4.
Cubing both sides, we get
(a + b)³ = (- 4)³
We know, (a + b)³= a³ + b³ + 3ab(a + b)
a³ + b³+ 3ab(a + b) = - 64
Or, a³ + b³ + 64 = - 3ab(a + b)
= -3ab(- 4)
a³ + b³ + 64 = 12ab
Question 8
1 / -0

A test consists of 40 questions in all (logical reasoning and non-reasoning) and the total marks for this test are 200. The logical reasoning questions are worth 4 marks each and the non-reasoning questions are worth 6 marks each. How many logical reasoning questions are there in the test?

A
10

B
20

C
30

D
40

Solution

Let the logical reasoning questions be x and non-reasoning questions be y.
Now, A.T.Q
x + y = 40 ......(i)
4x + 6y = 200 .....(ii)
Multiplying eq. (i) by 4 and subtracting it from equation (ii), we get
2y = 40
y = 20
x + y = 40
x + 20 = 40
x = 40 - 20 = 20
So, the number of logical reasoning questions = 20
Question 9
1 / -0

The sum of digits of a two-digit number is 10. If 18 is added to the number the digits are interchanged. Find the original number.

A
64

B
46

C
37

D
35

Solution

Let the digit at unit's place be y and the digit at tens place be x.
A.T.Q.
x + y = 10....(1)
10x + y + 18 = 10y + x
This implies that 9y - 9x = -18
Therefore, y - x = 2......(2)
Adding equation (1) and (2), we get
2y = 12
y = 6
Put the value of y in equation (1).
Hence, x = 4
Thus, the original number = 10x + y = 10(4) + 6 = 46.
Question 10
1 / -0

Find the value of y in the given equation, if x = 2.

41x² + 62/31 xy – 14.5x + 25 – 18xy = 0

A
3

B
4

C
5

D
8

Solution

41x² + 62/31 xy – 14.5x + 25 – 18xy = 0

If x = 2, equation becomes

164 + 2 × 2y – 29 + 25 - 36y = 0

160 = 36y – 4y

y = 160/32
y = 5
Question 11
1 / -0

Which of the following statements is true?

A
One and only one circle can pass through two given points.

B
A minimum of 3 points are required to uniquely define a line.

C
Four non-collinear points may or may not be concyclic.

D
Any 3 points can uniquely define a circle.

Solution

Option 1: Minimum of 3 non-collinear points are required to uniquely define a circle. Hence, infinite number of circles can pass through 2 given points.
Option 2: Minimum of 2 points are sufficient to define a line. In fact, 3 points may or may not lie on the same line.
Option 3: 3 non-collinear points will definitely lie on a unique circle. The 4th may or may not lie on the same circle. Hence, 4 points may or may not be concyclic.
Option 4: Any 3 points do not uniquely define a circle. Any 3 non-collinear points define a circle uniquely.
Question 12
1 / -0

If the product of abscissa and ordinate of a point is negative, then the point lies in which of the following quadrants?

A
1^stquadrant or 3^rdquadrant

B
1^stquadrant or 4^rdquadrant

C
2^ndquadrant or 3^rdquadrant

D
2^ndquadrant or 4^thquadrant

Solution

A.T.Q.
xy = Negative, which means that either x is negative and y is positive or x is positive and y is negative.
So, the point lies in either 2^nd quadrant or in 4^th quadrant.
Question 13
1 / -0

Find the mean of the following.

x + 2, x + 4, x + 6, x + 8, x + 10, x + 12, x + 14

A
x + 4

B
x + 6

C
x + 8

D
x + 10

Solution

By visual inspection, it is sufficient to point out that the mean is going to be the median, which in this case is x + 8.
Question 14
1 / -0

If 4x + 5y = 9 and x and y are positive integers, then y could be

A
5

B
4

C
3

D
None of these

Solution

Here, x and y should be positive.
Now, 4x + 5y = 9
Going through options, if y = 5, then using value of y in the equation, we get
4x + 25 = 9
Or, 4x = -16
Or, x = -4, which is not possible.
Neither y = 4 nor y = 3 is possible. This is because both would give negative values of x.
The only possible value could be x = y = 1.
Question 15
1 / -0

The diameter of a circular floor design at Gagan's house is 4 m. Calculate the area of floor design.

A
4π m²

B
6π m²

C
8π m²

D
10π m²

Solution

The area of a circle is A = πr²
First, we have to find the radius.
d = 2r
d/2 = r
4/2 m = r
2 m = r
The radius is 2 m.
Now, we have to find the area.
A = πr²
= π x r²
= 4π m²
Question 16
1 / -0

Cassie already knew 3 starter recipes before starting culinary school and she will learn 1 new starter recipe during each week of the school. After 32 weeks of culinary school, how many total starter recipes will Cassie know?

A
35

B
36

C
37

D
38

Solution

After 32 weeks of culinary school, Cassie will know a total of 35 starter recipes.
Question 17
1 / -0

First angle of a quadrilateral is 120^o. If the measure of its other 3 angles is equal to each other, then find the value of any one of the other angles.

A
80^o

B
100^o

C
150^o

D
200^o

Solution

Sum of all the angles of a quadrilateral = 360^o

According to the question,

120^o + x + x + x = 360^o, where x is the measure of any 1 of the other angles because all other angles are equal.

120^o + 3x = 360^o

3x = (360^o- 120^o) = 240^o

Therefore, x = 240/3 = 80^o
Question 18
1 / -0

Richard and his family are at the pet store getting supplies for a their cat. The pet store has 2 kinds of type-1 dishes and 4 kinds of type-2 dishes. If they get one of each item, then how many different combinations of supplies can Richard's family get?

A
8

B
10

C
12

D
14

Solution

By applying fundamental principle of counting, total number of different combinations of supplies = 2 × 4 = 8.
Question 19
1 / -0

In a farmhouse, a swimming pool is constructed. The length of the pool is 12 m and the width is 9 m. As swimming pools are deeper from one side and shallow from the other, the deeper side is 4 m deep and the shallow side is 1 m deep. What will be the total volume of that swimming pool?

A
260 m³

B
270 m³

C
280 m³

D
287 m³

Solution

Volume will be length x breadth x height. In this case, two heights are given. So, we will take average.

Volume = [12 x 9 x ( 1+4/2)] m³= 12 x 9 x 2.5 m³= 270 m³

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Re-Attempt Weekly Quiz Competition

IMO - Mock Test - 5

Result

IMO - Mock Test - 5

Score

-

Rank

-

SHARING IS CARING

Question 1

30023

112079

112089

202021

Solution

Question 2

43

49

48

44

Solution

Question 3

ANIZ

AMIA

AMIZ

DLOB

Solution

Question 4

Savita

Veena

Dyna

Kimmy

Solution

Question 5

15B5C7D2 = 8

8A6C9B1 = 10

19C9C4B6 = 14

18A6B5B10 = 7

Solution

Question 6

25 cm

40 cm

50 cm

100 cm

Solution

Question 7

- 12

12

- 12ab

12ab

Solution

Question 8

10

20

30

40

Solution

Question 9

64

46

37

35

Solution

Question 10

3

4

5

8

Solution

Question 11

One and only one circle can pass through two given points.

A minimum of 3 points are required to uniquely define a line.

Four non-collinear points may or may not be concyclic.

Any 3 points can uniquely define a circle.

Solution

Question 12

1st quadrant or 3rd quadrant

1st quadrant or 4rd quadrant

2nd quadrant or 3rd quadrant

2nd quadrant or 4thquadrant

Solution

1^stquadrant or 3^rdquadrant

1^stquadrant or 4^rdquadrant

2^ndquadrant or 3^rdquadrant

2^ndquadrant or 4^thquadrant

4π m²

6π m²

8π m²

10π m²

80^o

100^o

150^o

200^o

260 m³

270 m³

280 m³

287 m³