Olympiad Test : High Order Thinking Skills - 3 - Class 6 MCQ

Original garden area: 20 * 15 = 300 m²
New dimensions after the path: (20 - 2) * (15 - 2) = 18 * 13 = 234 m²
Remaining area: 234 m²

Let the total capacity of the tank be x liters.

The tank is initially 2/3 full, so the amount of water initially in the tank is (2/3) × x.

After removing 120 liters, the tank becomes 1/4 full, so the remaining water is (1/4) × x.

Thus, the equation is:

(2/3)x - 120 = (1/4)x

Now, solve for x:

(2/3)x - (1/4)x = 120

(8/12)x - (3/12)x = 120

(5/12)x = 120

5x = 120 × 12

5x = 1440

x = 1440 / 5 = 288

1. Subtract (1/4)x from both sides:
2. Find the least common denominator (LCD) of 3 and 4, which is 12:
3. Simplify the equation:
4. Multiply both sides by 12:
5. Simplify:
6. Divide by 5:

Answer: The total capacity of the tank is 288 liters.

Thus, the correct answer is C: 288 liters.

To find the Least Common Multiple (LCM) of 12, 15, and 20, we first find the prime factorizations of each number

12 = 2² * 3

15 = 3* 5

20 = 2² * 5

LCM calculation: 2² * 3 * 5 = 60

Speed = 54,000 meters/hour
Distance in 30 seconds: 54000 * (30 / 3600) = 450 meters

We are given the two equations:

1. x - y = 3
2. x² - y² = 15

We can use the difference of squares identity for the second equation:

x² - y² = (x - y)(x + y)

Substitute the value from the first equation x - y = 3 into the difference of squares equation:

15 = 3(x + y)

Now, solve for x + y:

x + y = 15 / 3 = 5

Answer: The value of x + y is 5.

Thus, the correct answer is A: 5.

To find the number of students who prefer chocolate ice cream, we calculate 45% of 40:

Thus, 18 students prefer chocolate ice cream. The correct answer is B: 18.

The perimeter P of a rectangle is given by the formula:

P = 2 × (Length + Width)

We are given that the perimeter is 36 cm, and the length is twice the width. Let the width be w, so the length is 2w.

Substitute these values into the perimeter formula:

36 = 2 × (2w + w)

Simplify:

36 = 2 × 3w

36 = 6w

Solve for w:

w = 36 / 6 = 6 cm

Now, the length is 2w = 2 × 6 = 12 cm.

Answer: The dimensions of the rectangle are 6 cm (width) and 12 cm (length).

Thus, the correct answer is A: 6 cm and 12 cm.

Given:

Average of five numbers = 27

Average after exclusion of 1 number = 25

Formula used:

Average =(Sum of values)/(Total number of values)

Calculation:

Sum of five numbers = 27 × 5 = 135

Sum of four numbers = 25 × 4 = 100

Excluded number = 135 – 100 = 35

∴ The removed number is 35.