IMO - Mock Test

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IMO - Mock Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

If × is -, + is ×, ÷ is +, and - is ÷, then what will be the value of the expression 135 × 5 + 45 - 5 ÷ 15?

A
105

B
115

C
125

D
95

Solution

135 x 5 + 45 - 5 ÷ 15
= 135 - 5 x 45 ÷ 5 + 15
= 135 - 5 x 9 ÷ 5 + 15
= 135 - 45 + 15
= 150 - 45 = 105
Question 2
1 / -0

Directions For Questions

Study the following information to answer the question:

Rachel, Joshua, Ceasar, Klinton and Olivia are five friends.

1. Rachel is younger than Joshua
2. Ceasar is younger than Rachel.
3. Klinton is younger than both Ceasar and Olivia.
4. Olivia is younger than Ceasar.

...view full instructions

What is the correct decreasing order of their ages?

A
Joshua > Ceasar > Rachel > Olivia > Klinton

B
Joshua > Rachel > Ceasar > Klinton > Olivia

C
Joshua > Rachel > Ceasar > Olivia > Klinton

D
Joshua > Olivia > Rachel > Ceasar > Klinton

Solution

According to the 1^st statement, Joshua > Rachel
According to the 2^nd statement, Rachel > Ceasar
According to the 3^rdstatement, Ceasar/Olivia > Klinton
According to the 4^thstatement, Ceasar > Olivia
So, we can conclude that the decreasing order is as follows:
Joshua > Rachel > Ceasar > Olivia > Klinton
Question 3
1 / -0

There is some relationship between the two numbers on the left of the sign (: :). The same relationship exists between the two numbers on the right, out of which one is missing. Find the missing one from the given alternatives.

5 : 126 : : 7 : ____

A
50

B
344

C
349

D
400

Solution

The sequence is (n³ + 1).
Missing number = 7³ + 1 = 343 + 1 = 344
Question 4
1 / -0

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

54 ___ 54 ___ 54 ___ 54 ___ 54___54 = -1

A
-, ÷, ×, +, ÷

B
÷, +, ×, +, ×

C
÷, ×, -, -, ÷

D
+, ×, +, ÷, ×

Solution

54 ÷ 54 × 54 - 54 - 54 ÷ 54
= 1 × 54 - 54 - 1
= 54 - 54 - 1
= - 1
Question 5
1 / -0

Fill the missing term in the following series:

T15QR, T13QS, ________, T9QU

A
T11RT

B
T11QT

C
P11QT

D
Q13QT

Solution

The first and the fourth character T and Q respectively are static. The last characters (a letter) are in alphabetical order, beginning with R and form a series as R, S, T, U.
The number series is in descending order with a difference of two numbers beginning with 15 and decrease as 15, 13, 11, 9.
So, the series would be as T15QR, T13QS, T11QT, T9QU.
Question 6
1 / -0

There is some relationship between the two terms on the left of the sign (: :). The same relationship exists between the two terms on the right, out of which one is missing. Find the missing one from the given alternatives.

8/7 : 64/49 : : 3/7 : ____

A
9/40

B
9/49

C
9/48

D
9/47

Solution

The sequence is a/b : a²/b².

Missing fraction = 3²/7²= 9/49
Question 7
1 / -0

Ben thinks of a number. He multiplies it by 1000. He then divides the answer by 10. In the end, he gets 567 as the final answer. What is the number that Ben thought of?

A
0.5670

B
5.670

C
56.70

D
567

Solution

To find the required number, we need to use the inverse operations.
Let the number be Y.
567 × 10 = 5670
5670 ÷ 1000 = Y
Y = 5.670
Question 8
1 / -0

Complete the series:

20, 31, 44, 59, ?

A
64

B
74

C
76

D
86

Solution

The pattern which is being followed is as given below:
5² - 5 = 25 - 5 = 20
6² - 5 = 36 - 5 = 31
7² - 5 = 49 - 5 = 44
8² - 5 = 64 - 5 = 59
Hence, next term = 9² - 5 = 81 - 5 = 76
Question 9
1 / -0

If 'BEUTY' is written as ECXRB. How is 'STUDY' written in that code?

A
VRXBB

B
YDUTS

C
TUVEZ

D
WRXCB

Solution

B + 3 = E -- S + 3 = V
E - 2 = C -- T - 2 = R
U + 3 = X -- U + 3 = X
T - 2 = R -- D - 2 = B
Y + 3 = B -- Y + 3 = B
Question 10
1 / -0

If A is 5, B is A - 2 and C is B × 3, then what is the value of A + B + C?

A
10

B
16

C
17

D
35

Solution

A = 5
B = 5 - 2 = 3
C = 3 × 3 = 9
So, A + B + C = 5 + 3 + 9 = 17
Question 11
1 / -0

The length and breadth of a rectangle are 5x² + 3y² and x² + 3xy, respectively. Find the area of the rectangle.

A
5x³ + 15x²y + 3xy + 9xy²

B
6x⁴ + 18x³y + 3x²y² + 9xy³

C
5x⁴ + 15x³y + 3xy + 9xy³

D
5x⁴ + 15x³y + 3x²y² + 9xy³

Solution

Area = L x B = (5x² + 3y²) ×(x² + 3xy)

⇒5x⁴ + 15x³y + 3x²y² + 9xy³
Question 12
1 / -0

Three numbers are in the ratio 5 : 2 : 3. The sum of their cubes is 1280. The numbers are _______, respectively.

A
10, 6 and 4

B
10, 4 and 6

C
15, 6 and 9

D
20, 8 and 12

Solution

Let the numbers be 5x, 2x and 3x.
(5x)³ + (2x)³ + (3x)³ = 1280
125x³ + 8x³ + 27x³ = 1280
160x³ = 1280
x³ = 8
x = 2
So, the numbers are 10, 4 and 6.
Question 13
1 / -0

The cube of an odd natural number is ______.

A
even

B
odd

C
negative

D
0

Solution

Let the odd natural number be 2n + 1.

Cube of (2n + 1) = (2n + 1)³= 2m + 1 = odd; where m is an integer.
Question 14
1 / -0

If (x² + 3x + 5)(x² – 3x + 5) = m² – n², then m =

A
x² – 3x

B
3x

C
x² + 5

D
Both (1) and (2)

Solution

[(x² + 5) + 3x] [(x² + 5) - 3x] = m² - n²
According to formula (A + B)(A - B) = A²- B² = (x² + 5)² - (3x)²
∴ m = x² + 5 and n = 3x²
Question 15
1 / -0

x% of 932, when added to 30, gives 309.6. What is the value of x?

A
29

B
32

C
30

D
31

Solution

First, subtract the value 30 from the resultant value 309.6.
It comes out to be 309.6 - 30 = 279.6
So, according to the question, x% of 932 is 279.6.
Then, x = (279.6 × 100)/932 = 30%
Question 16
1 / -0

Calculate the sum: 12³ + 7³ - 5³

A
1952

B
1950

C
1948

D
1946

Solution

12³ + 7³ - 5³= 1728 + 343 – 125 = 1946
Or, we can use the formula A³+ B³ for 12³+ 7³, and then subtract 5³to get the answer.
Question 17
1 / -0

The difference between the digits of a two-digit number is 1, and their sum is 17. If the number is multiplied by 2, the result obtained will be

A
178

B
154

C
196

D
Cannot be determined

Solution

Let the two digits of the number be x and y, where x is at the tens place and y is at the units place.
According to the question, x - y = 1 or y - x = 1, and x + y = 17
Now, working with the following equations,
x - y = 1
x + y = 17
2x = 18
We get x = 9 ,and y = 8 (since x - y = 1)
Now, using the following equations,
y - x = 1
y + x = 17
2y = 18
We get y = 9, x = 8 (since y - x = 1)
So, the number could be either 89 or 98.
Question 18
1 / -0

Sonal bought a car for Rs. 1,50,000. The following year, its price decreased by 12.50%, and it further decreased by another 10%. What was the overall percentage decrease in the price of the car?

A
21.25%

B
20.50%

C
24.50%

D
21.50%

Solution

Cost of the car = Rs. 1,50,000

12.50% of 1,50,000 = Rs. 18,750

The price of the car after 12.50% decrease = 1,50,000 - 18,750 = 1,31,250

10% of 1,31,250 = Rs. 13,125

Total decrease = 18,750 + 13,125 = Rs. 31,875

Overall percentage change = (31,875/1,50,000) × 100 = 21.25%
Question 19
1 / -0

In a school prayer, the teacher asks the students to stand in such a way so that the number of lines is equal to the number of students in each line. If there are 676 students, then how many students will there be in each line?

A
26

B
75

C
150

D
250

Solution

Number of lines = Number of students in each line = √676 = 26
Question 20
1 / -0

Rahul purchased an old television for Rs. 12,000 and spent Rs. 2850 on its repair. Then, he sold it to Ankush for Rs. 13,860. What percentage did he gain or lose in the transaction?

A
5%

B
6%

C
6.67%

D
7%

Solution

Purchase price = Rs. 12,000, Overheads = Rs. 2,850

Total cost price = Rs. 14,850

Selling price = Rs. 13,860

Loss = Rs. 990
Question 21
1 / -0

To complete a particular task, 3 people take 4 days. If the same work is done by 4 persons, how long will they take to complete the task?

A
2 days

B
3 days

C
4 days

D
5 days

Solution

Total units of work = 3 × 4 = 12 units
So, 12 units of work will be completed by 4 people in y days.
y = 12/4 = 3 days
Question 22
1 / -0

For a charity, the members of the charity trust decided to collect exactly the same amount from each member. The amount thus collected turned out to be Rs. 7225, when each member gave 1 rupee. How many charity members were there?

A
723

B
7145

C
7165

D
7225

Solution

Money collected = Rs. 7225
Amount given by each member = Re. 1
Therefore, total number of members = 7225/1 = 7225
Question 23
1 / -0

Junior's grandfather is 7 times as old as Junior is. After 6 years, Junior's grandfather will be 4 times as old as Junior will be then. How old are Junior and his grandfather at present?

A
6, 36

B
7, 49

C
6, 42

D
8, 48

Solution

Let Junior be x years old.
Age of Junior's grandfather will be 7x.
7x + 6 = 4(x + 6)
x = 6 and 7x = 42
Thus, present age of Junior is 6 years and that of Junior's grandfather is 42 years.
Question 24
1 / -0

Paras selects a cube-shaped gift of volume 729 cm³ for his friend. Find the length of each edge of the gift.

A
7 cm

B
9 cm

C
13 cm

D
15 cm

Solution

We know,
Area of a cube = Side³
729 cm³ = Side³
9³= Side³
So, length of the side/edge = 9 cm
Question 25
1 / -0

The total number of runs made by Sehwag in One-day Internationals is the greatest four-digit number which is divisible by both 15 and 25. Find the total number of runs scored by Sehwag.

A
8875

B
9975

C
9999

D
10023

Solution

Greatest 4-digit number is 9999, and LCM of 15 and 25 is 75.

To find the total number of runs scored by Sehwag, we need to divide 9999 by 75. It gives 24 as the remainder.

So, the final answer = 9999 - 24 = 9975
Question 26
1 / -0

There is a party at Manish's house and he buys 12 bottles of 2-litre drinks and 5 bottles of 1-litre drinks each. How many persons can he serve if every person consumes 250 ml of drinks?

A
114

B
116

C
168

D
170

Solution

Total drinks = (12 × 2) + 5 = 29 litres × 1000 = 29,000 ml

Number of persons that can be served = 29000/250 = 116
Question 27
1 / -0

Consider the following statements:

Ussen is older than Salman.
Sohail is older than Ussen.
Salman is older than Sohail.

If the first two statements are true, then pick the correct option from the following.

A
The third statement is definitely false.

B
The third statement is definitely true.

C
It cannot be determined whether the third statement is true or false.

D
The third statement is irrelevant to the first two statements.

Solution

Since the first two statements are true, therefore, Salman is the youngest of the three. So, the third statement must be false.
Question 28
1 / -0

Find the number, if in a two-digit number, the digit in the units place is four times the digit in the tens place and the sum of the digits is equal to 10.

A
25

B
26

C
27

D
28

Solution

Let the original number be 10a + b

Then, b = 4a and a + b = 10.

We put b = 4a in a + b = 10, so that a + 4a = 10,

i.e. 5a = 10

i.e. a = 2.

Therefore, a = 2

and b = 4a [where we know a = 2]

b = 4 × 2

b = 8

Hence, the number is 10a + b = 20 + 8 = 28.

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Re-Attempt Weekly Quiz Competition

IMO - Mock Test - 3

Result

IMO - Mock Test - 3

Score

-

Rank

-

SHARING IS CARING

Question 1

105

115

125

95

Solution

Question 2

Joshua > Ceasar > Rachel > Olivia > Klinton

Joshua > Rachel > Ceasar > Klinton > Olivia

Joshua > Rachel > Ceasar > Olivia > Klinton

Joshua > Olivia > Rachel > Ceasar > Klinton

Solution

Question 3

50

344

349

400

Solution

Question 4

-, ÷, ×, +, ÷

÷, +, ×, +, ×

÷, ×, -, -, ÷

+, ×, +, ÷, ×

Solution

Question 5

T11RT

T11QT

P11QT

Q13QT

Solution

Question 6

9/40

9/49

9/48

9/47

Solution

Question 7

0.5670

5.670

56.70

567

Solution

Question 8

64

74

76

86

Solution

Question 9

VRXBB

YDUTS

TUVEZ

WRXCB

Solution

Question 10

10

16

17

35

Solution

Question 11

5x3 + 15x2y + 3xy + 9xy2

6x4 + 18x3y + 3x2y2 + 9xy3

5x4 + 15x3y + 3xy + 9xy3

5x4 + 15x3y + 3x2y2 + 9xy3

Solution

Question 12

10, 6 and 4

10, 4 and 6

15, 6 and 9

20, 8 and 12

Solution

5x³ + 15x²y + 3xy + 9xy²

6x⁴ + 18x³y + 3x²y² + 9xy³

5x⁴ + 15x³y + 3xy + 9xy³

5x⁴ + 15x³y + 3x²y² + 9xy³

x² – 3x

x² + 5