Test: Number bases - 3 - JAMB MCQ

Suppose the numbers are P and Q

So, according to the question -

P + Q = 12

P * Q = 35

Sum of reciprocals of P and Q is = 1/P + 1/Q

= Q + P/PQ

= 12/35

Suppose the number is a.

So, according to the question -

a + 1/a = 2

(a² + 1)/a = 2

a² + 1 = 2a

Or, a² + 1 -2a = 0

We can say that (a - 1)² = 0

So, a =1

Hence the required number is 1, whose sum and reciprocal are equal to 2.

Let the numbers be 'a' and 'b'. According to the question -

(a + b) = 3(a - b)

(a + b) = 3a - 3b

2a = 4b

a = 2b

So, a/b = 2 : 1

Let a be the smallest even number

So, according to the question -

(a) + (a + 2) + (a + 4) + (a + 6) = 748

4(a) + 12 = 748

4a = 736

Or, a = 184

So, the smallest number be 184

Alternative solution

We can use an alternative solution of it

Middle term = 748/4 = 187

So, the numbers will 184, 186, 188, and 190

And the smallest number between them is 184.

According to the identity,

a² - b² = (a + b) (a - b)

It is given that (a² - b²)/(a + b) = 25

So, it can be written as (a + b) (a - b)/(a + b) = 25

Hence, (a - b) = 25

Given 1397 x 1397

We can also write it as (1397)²

Or, (1400 - 3)²

On expanding we get,

= (1400)² + (3)² - (2 x 1400 x 3)

= 1960000 + 9 - 8400

= 1960009 - 8400

= 1951609

Here, we can apply the formula of a² - b² = (a + b) (a - b)

So, after applying the formula, we will get

(64 + 36) (64 - 36) = 20 * x

100 * 28 = 20 * x

x = 100 * 28/ 20 = 140

After evaluating all options, only option C is correct

Given ration 7 : 9

So, let the numbers be 7a and 9a. According to the question -

7a * 9a = 1575

63a² = 1575

a² = 1575/63

Or a² = 25

And a =5

So, the two numbers will be -

7a = 7 * 5 = 35

And 9a = 9 * 5 = 45

Hence, the greater number is 45 between the given numbers.

Given a = -4 and b = -2

On putting the values in the given equation, we will get -

(-4)³ - 3 x (-4)² + 3 x (-4) + 3 x (-2) + 3 x (-2)² + (-2)³

= -64 - 48 - 12 - 6 + 12 - 8

= -126