IMO - Mock Test

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IMO - Mock Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

If
3, 2, 4 = 10,
4, 3, 5 = 17,
5, 4, 6 = 26,
6, 5, 7 = 37,
then what is the value of 7, 6, 8?

A
21

B
28

C
34

D
50

Solution

3, 2, 4 = 3 × 2 + 4 = 6 + 4 = 10,

4, 3, 5 = 4 × 3 + 5 = 12 + 5 = 17,

5, 4, 6 = 5 × 4 + 6 = 20 + 6 = 26,

6, 5, 7 = 6 × 5 + 7 = 30 + 7 = 37.

Hence, 7, 6, 8 = 7 × 6 + 8 = 50
Question 2
1 / -0

How can INSTAL be written if BEHAVE is coded as DHLFBL?

A
KPUVCN

B
KQWYGS

C
KQWVCN

D
KPUYGS

Solution

The code is as follows.
B + 2 = D
E + 3 = H
H + 4 = L
A + 5 = F
V + 6 = B
E + 7 = L
So, INSTAL is coded as
I + 2 = K
N + 3 = Q
S + 4 = W
T + 5 = Y
A + 6 = G
L + 7 = S
So, INSTAL is coded as KQWYGS.
Question 3
1 / -0

In a certain code language,
135 means "good and tasty"
578 means "see good pictures"
729 means "pictures are faint".

Which of the following digits stands for "good pictures"?

A
58

B
37

C
57

D
38

Solution

135 means "good and tasty" ...(i)
578 means "see good pictures" ...(ii)
729 means "pictures are faint" ...(iii)

From (i) and (ii), we can see that 'good' and '5' are common to both.
So, good = 5

From (ii) and (iii), we can see that 'pictures' and '7' are common to both.
So, pictures = 7

Hence, "good pictures" is 57.
Question 4
1 / -0

If A is ÷, B is ×, C is + and D is -, then what will be the value of 375B125C105D45A15?

A
46970

B
45687

C
46870

D
46977

Solution

After substituting the signs, 375 × 125 + 105 – 45 ÷ 15 = 46875 + 105 - 3
= 46875 + 102 = 46977
Question 5
1 / -0

Complete the following pattern.

-2, 1, 6, 13, 22, ?

A
35

B
33

C
32

D
30

Solution

Given series is -2, 1, 6, 13, 22, ?

-2 + 3 = 1
1 + 5 = 6
6 + 7 = 13
13 + 9 = 22
22 + 11 = 33

So, the missing number is 33.
Question 6
1 / -0

How many digits are there which are succeeded by a letter and preceded by a special character?

Q W % T 1 7 B 8 j C # 4 $ b % + 7 & K 4 # 5 L ! T ? P 4 2 W %

A
1

B
2

C
3

D
0

Solution

Q W % T 1 7 B 8 j C # 4 $ b % + 7 & K 4 # 5 L ! T ? P 4 2 W %

From the given set, there is only 1 digit which is succeeded by a letter and preceded by a special character.
Question 7
1 / -0

Read the following information carefully and answer the question.

Rooney is taller than Lily.
Caesar is shorter than Rooney.
Ted is taller than Rachel, but shorter than Lily.

Who is the tallest?

A
Rachel

B
Rooney

C
Caesar

D
Ted

Solution

Rooney > Lily, Rooney > Caesar, Lily > Ted > Rachel
Thus, Rooney > Lily > Ted > Rachel and Rooney > Caesar
Clearly, Rooney is the tallest.
Question 8
1 / -0

Which of the following will replace '?'

8 : 104 : : 12 : ?

A
150

B
151

C
156

D
160

Solution

The relation is n : 13n.
The missing number is (12 × 13) = 156.
Question 9
1 / -0

Which of the following sets of signs would be needed for the given equation to be true?

72 ___ 72 ___ 72 ___ 72 ___ 72____ 72___72____72 = 5256

A
÷, +, -, ÷, ×, +

B
+, +, ×, -, ×, -

C
÷, -, ÷, +, ×, +

D
+, +, -, ÷, ×, ÷

Solution

72 ÷ 72 - 72 ÷ 72 + 72 × 72 + 72
= 1 - 1 + 72 × 72 + 72
= 5184 + 72 = 5256
Question 10
1 / -0

The angles of a quadrilateral are in the ratio of 2 : 3 : 4 : 6. What is the measure of the greatest angle among them?

A
124°

B
138°

C
144°

D
154°

Solution

2x + 3x + 4x + 6x = 360° (Sum of all the angles of a quadrilateral is 360°)

15x = 360°

x = 24°

Greatest angle = 6x = 6 × 24^o = 144°
Question 11
1 / -0

If the perimeter of a rectangle is 70 feet and the ratio of its dimensions is 2 : 3, then what is its area?

A
484 ft²

B
294 ft²

C
284 ft²

D
244 ft²

Solution

Let length (l) be 2x ft and breadth (w) be 3x ft.

Then, P = 2(l + w)

Or, 70 = 2[2x + 3x]

⇒ 70 = 10x

⇒ x = 70/10

x = 7

So, dimensions = 2x = 2 × 7 = 14 ft

3x = 3 × 7 = 21 ft

Hence, area = l × w = 14 × 21 = 294 ft²
Question 12
1 / -0

If sum of two numbers is 24 and sum of their squares is 306, then the difference between the numbers is

A
3

B
5

C
6

D
7

Solution

Let the two numbers be x and y.

x + y = 24

x = 24 – y

(24 – y)² + y² = 306

576 + y² – 48y + y² = 306

2y² – 48y + 270 = 0

⇒ y = 9 or 15

So, the numbers are 9 and 15.

Required difference = 15 – 9 = 6
Question 13
1 / -0

Which of the following rational numbers does not lie between 3/8 and 3/4?

A
3/5

B
4/7

C
5/8

D
9/11

Solution

0.375 – 0.75

9/11 = 0.8181

3/8 = 0.375 and 3/4= 0.75

∴ 9/11 = 0.8181 does not lie between 3/8 and 3/4.
Question 14
1 / -0

A bag contains 50 p, 25 p and 10 p coins in the ratio 5 : 9 : 4, amounting to Rs. 206. Find the total number of coins.

A
700

B
720

C
668

D
672

Solution

A. T. Q.

0.50 × 5x + 0.25 × 9x + 0.10 × 4x = 206

2.5x + 2.25x + 0.4x = 206

5.15x = 206

x = 20600/515

x = 40

Total coins = 200 + 360 + 160 = 720
Question 15
1 / -0

In a survey of 200 ladies, it was found that 82 like coffee, while 118 do not like it. From these ladies, one is chosen at random. The probability that the chosen lady dislikes coffee is

A
59/100

B
41/100

C
100/59

D
100/51

Solution

Total number of ladies = 200

Number of ladies who do not like coffee = 118

Required probability = 118/200 = 59/100
Question 16
1 / -0

A sum of money is distributed among P, Q, R, S and T in the ratio 7 : 8 : 5 : 9 : 2 respectively and P gets Rs. 400 more than R. What is the total sum of money?

A
Rs. 6200

B
Rs. 6800

C
Rs. 6280

D
Rs. 7600

Solution

Let P's share = 7x
Similarly, Q's share = 8x
R's share = 5x
S's share = 9x
T's share = 2x
According to the given condition,
7x - 5x = 400
x = 200
Total sum = 7x + 8x + 5x + 9x + 2x = 31x = 31 × 200 = Rs. 6200
Question 17
1 / -0

A, B and C are three friends working in the same company but at different positions. The average monthly income of A and B is Rs. 12500, that of B and C is Rs. 14000 and that of A and C is Rs. 8500. Find out the monthly income of C.

A
Rs. 10000

B
Rs. 8200

C
Rs. 7500

D
Rs. 7000

Solution

Average income of A and B = A+B/2

A+B/2= 12500

A + B = 12500 × 2

A + B = Rs. 25000

B+C/2 = 14000

B + C = 14000 × 2

B + C = Rs. 28000

A+C/2 = 8500

A + C = 8500 × 2

A + C = Rs. 17000

A + B + B + C + A + C = 25000 + 28000 + 17000

A + B + B + C + A + C = 70000

2(A + B + C) = 70000

A + B + C = 70000/2 = 35000

25000 + C = 35000

C = 35000 – 25000

C = Rs. 10000

Monthly income of C is Rs. 10000.

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Re-Attempt Weekly Quiz Competition

IMO - Mock Test - 4

Result

IMO - Mock Test - 4

Score

-

Rank

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SHARING IS CARING

Question 1

21

28

34

50

Solution

Question 2

KPUVCN

KQWYGS

KQWVCN

KPUYGS

Solution

Question 3

58

37

57

38

Solution

Question 4

46970

45687

46870

46977

Solution

Question 5

35

33

32

30

Solution

Question 6

1

2

3

0

Solution

Question 7

Rachel

Rooney

Caesar

Ted

Solution

Question 8

150

151

156

160

Solution

Question 9

÷, +, -, ÷, ×, +

+, +, ×, -, ×, -

÷, -, ÷, +, ×, +

+, +, -, ÷, ×, ÷

Solution

Question 10

124°

138°

144°

154°

Solution

Question 11

484 ft2

294 ft2

284 ft2

244 ft2

Solution

Question 12

3

5

6

7

Solution

484 ft²

294 ft²

284 ft²

244 ft²