Logical And Numeracy

Steve arranges 20 balls in the shape of a Triangular pyramid.

How many balls are at the bottom of this Triangular pyramid?

• 10

• 5

• 8

• 12

• 13

Answer explanation

he number of balls in the top row of the pyramid = 1

Number of balls in the second row from the top of the pyramid = 3

Number of balls in the third row from the top of the pyramid = 6

Hence, the number of balls in the bottom row of the pyramid = 10

16 kg of Brand M Cinnamon was made by combining 12 kg of Indonesian cinnamon which costs $19/kg with 4 kg of Thai cinnamon which costs $11/kg. 

Find the cost per kg of the mixture.

• $18

• $15

• $16.75

• $18.5

• $17

Answer explanation

Total cost of Indonesian cinnamon = 12 × 19 = $228.

Total cost of Thai cinnamon = 4 × 11 = $44.

Net cost of Band M cinnamon = 228 + 44 = $272.

Hence, per kg cost of the mixture = 272/16 = $17.

In Quarterly examinations, the following results were achieved by students taking English, Hindi and Moral Studies: 

Everyone who passed Hindi also passed English. 

Those who passed English, passed both Hindi and Moral Studies. 

No one passed both Hindi and Moral Studies. 

No one failed all three subjects.

No one passed all three subjects.

Which one of the following is not possible?

• Lucifer failed Hindi and Moral studies

• Lucifer passed Hindi but not English

• Lucifer passes Moral studies and English

• Lucifer didn’t pass both Hindi and moral studies

Answer explanation

Writing it out into a Venn diagram.

Hence, we can see Lucifer passed Hindi but not English.

The following two statements may be the effect of the same cause or independent causes. These statements may be independent causes without having any relationship.

Read both the statements and select the correct answer.

Statement A. Indonesia is prone to many annual earthquakes.

Statement B. Seismologists say that there is tremendous tectonic plate activity happening in the belt under the Indonesian islands.

• Both Statements A and B are the effects of independent causes

• Both Statements A and B are independent causes.

• Statement A is the cause, and Statement B is the effect.

• Statement B is the cause, and Statement A is its effect.

Answer explanation

The tectonic plate activity under the Indonesian islands is the cause of Indonesia’s annual earthquakes. Therefore, Statement B is the cause of Statement A.

Select the pair that has a different relationship between its words compared to the rest. 

• Drink:Drive

• Kind:Kid

• Green:Grass

• Fire:File

Answer explanation

Each pair starts with the same letter; however, in Kind:Kid, the words do not share the same number of letters in both words like the other pairs. 

If 𝑥 ≠ 0; and 3𝑥 = 2y and 7z = 18𝑥 then what is the ratio of z:y?

• 12:7

• 8:14

• 7:12

• 5:14

• 14:3

Answer explanation

Finding the same number of x in the ratios will give us

16:12 = x:y

7:16 = z:x

Since both are 16x the one to one ratio of z:y is 7:12

Find the speed of a motorbike in meters per second which covers a distance of 90km in 2 hours.

• 5.5m/s

• 15m/s

• 13m/s

• 12m/s

• 45m/s

Answer explanation

Hermies has set up a number pattern:

10, 8, 18, 26, 44 .,,

Which one of the following is the 7th term of this sequence?

• 114

• 70

• 82

• 59

• 96

Answer explanation

The pattern is that each number is the sum of the two preceding ones.

The pattern will look like this:

10, 8

(10 + 8) = 18, 

(8 +18) = 26, 

(18 + 26) = 44

(26 + 44) = 70

(44 + 70) =114

A tire covers 21 metres in 7 rotations. What is the circumference of the tire?

• 3m

• 2m

• 1m

• 1.5m

• 2.5m

Henry combines 4 smaller squares with a perimeter of 4 cm into a larger square, as seen below.

What is the perimeter of the larger square?

• 12cm

• 16cm

• 10cm

• 4cm

• 8cm

Answer explanation

Step 1:

As the perimeter of the smaller square is 4cm, it must have a side length of  = 1cm.

From the diagram, we can see that two of the smaller square sides make up one of the larger square sides.

 

Step 2:

Hence, the larger square has a side length of 2cm.

Therefore, the larger square has a perimeter of 2cm + 2cm + 2cm + 2cm = 8cm.

 

Thus, the answer is 8cm.