# Grade 7 Olympiad – Tuyển chọn câu hỏi Olympiad lớp 7

Table Of Contents

Grade 7 Olympiad

## Week 1

### Choose correct answer(s) from the given choices

(1) If sides of a triangle are 42 cm, 40 cm and 56 cm, what is the type of triangle?

a. obtuse angled triangle

b. Right angled triangle

c. Acute angled triangle

d. Can not be determined

(2) ♣ ♦ ♠ ♥ ♣ ♦ ♠ ♥

What will be the shape at the 17th position?

a. ♠ b. ♣

c. ♦ d. ♥

(3) If \frac{x}{y} = \frac{{21}}{2}, then identify the incorrect expression from the following.

a. 2 x= 21 y

b. \frac{x + y}{x - y} = \frac{{23}}{19}

c. 2 y = 21 x

d. \frac{x - y}{x + y} = \frac{{19}}{23}

### Fill in the blanks

(4) 2^{p} + 2^{p + 1} = 12.

The value of p is ………. .

(5) ……….. unique rectangles can be formed by joining 77 identical squares? All 77 squares must be used and no square can overlap each other.

(6) If the number in the center is the sum of rest of the numbers, y = ………

### Answer the questions

(7) A train traveling at the speed of 40 kmph leaves the station at 1 pm. Another train leaves the station at 2 pm. If the second train travels at a speed of 50 kmph, then at what time will it catch up with the first train?

(8) Victoria’s parents planted a tree on her birth. If the tree grows 2 inches per year, what is Victoria’s age today?

(9) A dog is walking around the periphery of a right-angled triangle shown in the picture. Find the distance traveled by the dog in 6

rounds. (All units are in meters)

(10) Tap A can fill a tank in 4 hours, while tap B can empty the full tank in 5 hours. If both taps are open together, how long will it take to fill an empty tank?

## Week 2

### Choose correct answer(s) from the given choices

(1) If the number in the center is the sum of the rest of the numbers, find the value of z.

a. 4 b. 5

c. 3 d. 6

(2) There are 17 senators in a senate. The senate needs to be divided into n committees such that each senator is on exactly one committee. Each senator hates exactly 2 other senators and is hated by exactly 2 senators. If senator A hates senator B then senator B does not necessarily hate senator A) . Find the smallest value of n such that it is always possible to arrange the committees in a way that no senator hates another senator on his or her committee

a. 11 b.5 c. 14 d. 3

(3) Allison folds the pattern shown below to form a cube. After folding, which letter will be opposite to the letter ‘D’?

a. E b. B

c. C d. F

(4) Find value of missing angle.

a. 44° b. 49°

c. 34° d. 39°

(5) If \frac{x}{y} = \frac{13}{2}, then identify the incorrect expression from the following.

a. \frac{2}{13} x - y = 0

b. \frac{x - y}{x + y} = \frac{11}{15}

c. 2 y = 13 x

d. 2 x= 13 y

### Fill in the blanks

(6) Zoe is arranging the tiles as shown below, if she continues it the same way, there will be tiles in the next column of grey tiles.

(7) Michael changes a picture on his computer such that the width of the image is 60% of the original image and the height of the image is 50% of the original image. If the area of the new image is 43.2 cm2, the area of the original image = cm2.

### Check True/False

(8) Two right-angled triangles are congruent if the hypotenuse of one of the triangles is equal to the hypotenuse of the other triangle.

a. True b. False

### Answer the questions

(9) Find the missing term.

(10) An iron pipe is kept against the wall as shown in the picture. The length of the pipe is 116 feet. Find the distance of the bottom end of the pipe from the wall.

## Week 3

### Choose correct answer(s) from the given choices

(1) If AB and PQ are parallel, compute the measure of ∠X.

a. 102° b. 107°

c. 73° d. 253°

(2) A shopkeeper mixes two variants of rice in the ratio 5:3. The first variant costs 40 per kg, while the other costs 24 per kg. If the mixed rice is sold at the price of 37.4 per kg then find the profit/loss percent incurred by shopkeeper.

a. 5% profit b. 10% profit

c. 10% loss d. 5% loss

(3) Find the missing number

a. 9 b. 8

c. 6 d. 5

### Fill in the blanks

(4) Sofia’s father is 4 times as old as Sofia. After 12 years, her father will be 2 times as old as Sofia. Sofia is ………….. years old and her father is …………. years old now.

(5) A number is multiplied by 10 and 26 is added to their product. If their result is 176, the original number was …………..?

(6) A garden is 50 meters wide and 120 meters long. There is a pathway that runs along the perimeter inside the garden. If the area of the pathway is half of the area of the garden, then the width of the pathway is ………….. meters.

(7) Justin is walking in the south direction. After walking for 77 meters, he takes a left turn and walks for another 36 meters. He is at a distance of …………… meters from the starting point.

(8) If the average of numbers 23, 22, 21, 20 and x is 25, value of x = ……………

### Answer the questions

(9) A is to the West of B, and C is to the South of B. In what direction is A with respect to C?

(10) Find area of shaded region (All measurements are in cm).

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