Important for :

1

2

3

4

A

Let 4 consecutive even numbers = x, x + 2, x + 4, x + 6

3 consecutive odd numbers = y, y + 2, y + 4

According to the question,

(x + x + 2 + x + 4 + x + 6) – (y + y + 2 + y + 4) = 81

4x + 12 – 3y – 6 = 81

4x – 3y = 75 .... 1

sum of least odd and even numbers = 59

x + y = 59 ....2

Equation 1 + (Equation 2 × 3)

7x = 252

x = 36

Least odd number = 59 – 36 = 23, least even number = 36

Largest even number = 36 + 6 = 42, Lagest odd number = 23 + 4 = 27

Largest even number = 36 + 6 = 42, Lagest odd number = 23 + 4 = 27

Sum = 42 + 27 = 69

Let 4 consecutive even numbers = x, x + 2, x + 4, x + 6

3 consecutive odd numbers = y, y + 2, y + 4

sum of least odd and even numbers = 59

x + y = 59

Sum of the largest odd and even numbers = x + 6 + y + 4

= x + y + 10

= 59 + 10 = 69

Hence, option A is correct.

5

B

Let the larger number be x

Then, smaller number = x – 2

Now, x(x – 2) = 5328

Or, x^{2} – 2x – 5328 = 0

Or, x^{2} – 74x + 72x – 5328 = 0

Or, x(x – 74) + 72(x – 74) = 0

**∴ ** x = 74, –72

Therefore, the higher number = 74

Hence, option B is correct.

**Intuitive Approach:**

Option A: 64

Therefore, the smaller number must be 62, but we can infer that we won't be getting a number as big as 5328 even if we multiply 74 64 by 62. Option A thus gets eliminated.

Option B: 74

Therefore, the smaller number must be 72. Further, the product of the unit digits of both the smaller and the greater number is also 8 which matches that of the given product.

We can multiply and confirm whether it gives us the resultant number or not.

72 x 74 = 5328

It confirms that option B is the correct answer.

Option C: 72

If the larger number is 72, the smaller one must be 70. But if we multiply these two we'll get the unit digit as zero. Option C gets eliminated here.

Option D: 76

If the larger number is 76, the smaller one must be 74. But if we multiply these two, we'll get the unit digit as 4. Option D also gets eliminated.

Then, smaller number = x – 2

Now, x(x – 2) = 5328

Or, x

Or, x

Or, x(x – 74) + 72(x – 74) = 0

Therefore, the higher number = 74

Hence, option B is correct.

Option A: 64

Therefore, the smaller number must be 62, but we can infer that we won't be getting a number as big as 5328 even if we multiply 74 64 by 62. Option A thus gets eliminated.

Option B: 74

Therefore, the smaller number must be 72. Further, the product of the unit digits of both the smaller and the greater number is also 8 which matches that of the given product.

We can multiply and confirm whether it gives us the resultant number or not.

72 x 74 = 5328

It confirms that option B is the correct answer.

Option C: 72

If the larger number is 72, the smaller one must be 70. But if we multiply these two we'll get the unit digit as zero. Option C gets eliminated here.

Option D: 76

If the larger number is 76, the smaller one must be 74. But if we multiply these two, we'll get the unit digit as 4. Option D also gets eliminated.