Quantitative Reasoning: Lantern Steps Quantitative Reasoning Solutions Book 5

Using Example 2

To Get 27300

650 × 420 = 273000

To Get 650

27300 ÷ 420 = 650

To Get 420

273000 ÷ 650 = 420

Lantern Steps Quantitative Reasoning Exercise 2 ; Page 2

Using Example 3

The knowledge of Roman Numerals will guide students through this.

To Get XIII which means 13

IX means 9

IV means 4

Hence, 9+4= 13

In Roman figure or numerals, it’s XIII

To Get IX which means 9

XIII – IV

13 – 4 = 9

To Get IV which means 4

XIII – IX

13. –  9 = 4 is IV

Lantern Steps Quantitative Reasoning Exercise 3 ; Page 4

Using Example 1

To Get 10

6 × 5 = 30

30 ÷ 3 = 10

To Get 6

10 × 3 =30

30 ÷ 5 = 6

To Get 5

10 × 3 =30

30 ÷ 6 = 5

To Get 3

6× 5= 30

30 ÷ 10 = 3

Lantern Steps Quantitative Reasoning Exercise 4 ; Page 5

Think of equivalent numbers.

Subtract the numbers on the left column.

Add the numbers on the right column.

Using Example 3

89- 64 = 25

17 + 8 = 25

To Get 17

89- 64 = 25

25 – 8 =17

To Get 8 

89- 64 = 25

25 – 17= 8 

To Get 89

17 + 8 = 25

64 + 25= 89

To Get 64

17 + 8 = 25

89 – 25 = 64

Lantern Steps Quantitative Reasoning Exercise 5 (C Example); Page 6

For first Example

To Get 22

7 + 4 = 11

11 × 2 = 22

To Get 2

4 + 7 = 11

22 ÷ 11 = 2

To Get 7

22 ÷ 2 =11

11 – 4 = 7

To Get 4

22 ÷ 2 = 11

11 – 7 = 4

For The Second Example

To Get 7

25 – 4 =21

21 ÷ 3 =7

To Get 3

25-4 = 21

21 ÷ 3 = 7

To Get 25

7 × 3=21

21 + 4 = 25

To Get 4

7 × 3 = 21

25 – 21 = 4

Note: The first Example is the direct opposite of the second example

Lantern Steps Quantitative Reasoning Exercise 6 (A.example); Page 9

Mathematical operations to apply are;

• Multiplication
• Division

To Get 30000

600 × 50= 30000

To Get 600

30000÷50= 600

To Get 50

30000÷600=50

To Get 15000

30000÷2=15000

Lantern Steps Quantitative Reasoning Exercise 6 (B.example); Page 10

Using Example 1

To Get 24

2+2+1+3=8

8×S3=24

To Get 2(Up)

2+1+3=6

24÷3=8

8-6=2

To Get 2(Down)

2+1+3=6

24÷3=8

8-6=2

To Get 3

2+2+1=5

24÷3=8

8-5=3

To Get 1

2+2+3=7

24÷3=8

8-7=1

Using Example 2

To Get 39

0+4+3+6=13

13×3(The 3 with S)= 39

To Get 0

4+3+6=13

39÷3(the one attached to S)=13

13-13= 0

To Get 4

0+3+6=9

39÷3(the one attached to S)=13

13-9=4

To Get 3

0+4+6=10

39÷3(the one attached to S)=13

13-10=3

To Get 6

0+4+3=7

39÷3(the one attached to S)=13

13-7= 6

Lantern Steps Quantitative Reasoning Exercise 6 (C.example); Page 10

In this exercise, consider equivalent numbers.

Using Example 1

12+4=16

2×8=16

To get 12

2×8=16

16-4=12

To get 4

2×8=16

16-12=4

To Get 8

12+4=16

16÷2=8

To Get 2

12+4=16

16÷8=2

Lantern Steps Quantitative Reasoning Exercise 7 (B.example); Page 13

Consider squares and its root in this exercise.

From first Example

To get 9

Multiply 3 into 2 places

3×3=9

To Get 2

3(the power of an unknown)=9

3*=9

Hence, 3*= 3²

Divide both sides by 3

*=2

To get 3

Let X be unknown

X²=9

Divide both side by X²

X²=9

X²=3²

Cancel the Power of 2 on both sides

X=3

From the Second Example

To get 64

Multiply 4 into places

4×4×4=64

To Get 3

4(the power of an unknown)=64

4*=64

Hence, 4*= 4³

Divide both sides by 4

*=3

To Get 4

Let X be unknown

X³=64

Divide both side by X³

X³=64

X³=4³

Cancel the Power of 3 on both sides

X=4

Lantern Steps Quantitative Reasoning Exercise 9 (A.example); Page 19

From Example 1

• (9v8v4)=21

            9+8+4=21

• 10^6^4=0

            (10-6-4)=0

• 6v3^4= 5

            6+3-4 = 5

B. Example Page 19

• (20 d 4)= 5

            20÷4= 5

• (16b3)= 13

16-3= 13

• 12b 3d 9= 11²/³

12- 3÷ 9= 11²/³

3÷9= ⅓

12- ⅓= 11²/³

Lantern Steps Quantitative Reasoning Exercise 10 (A.example); Page 21

Using Example 1

To get 24

17+7=24

Or. 8×3= 24

To get 17

24-7=17

To get 7

24-17=7

Or 42÷6= 7

To get 8

24÷3=8

To Get 3

24÷8=3

To get 42

6×7=42

To Get 6

42÷7=6

Lantern Steps book 4: Quantitative Reasoning Examples for Primary School

Exercise 10: B.Example Page 22

Using Example 2

To Get 64

8²= 8×8=64

To Get 8

√64=8.  

Or 16×0.5= 8

To Get 0.5

8÷16= ½ or 0.5

To Get 16

8÷0.5= 16

Lantern Steps; Exercise 11 page 23

• 9+2=11

On the clock locate 9 and count two steps forward starting with 10.

• 7-6=1

On the clock, locate 7, count six backwards starting with 6.

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