Question: 36 -

If V = 12R / (r + R) , then R =

Vr / (12 - V)

V

V / (r - 12 )

Vr + (V /12 )

Answer:

Vr / (12 - V)

Solution:

We have to rearrange the equation to make R the subject.
Start by cross multiplying by (r + R); V (r + R) = 12R
Multiply out the bracket Vr + VR = 12R

Question: 37 -

A piece of ribbon 4 yards long is used to make bows requiring 15 inches of ribbon for each. What is the maximum number of bows that can be made?

10

8

9

11

Answer:

9

Solution:

The maximum number of bows will be 4 yards 
=> ( 4 x 36 inches) divided by 15 inches.
This gives 9.6. But as a fraction of a bow is no use, 
we can only make 9 bows.

Question: 38 -

n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2*n is divided by 4 ?

1

2

0

3

Answer:

2

Solution:

Let n=4*q + 3. Then, 2*n = 8*q + 6 = 4(2*q + 1) + 2.
Thus when 2*n is divided by 4, the reminder is 2.

Question: 39 -

Which of the following can be used to illustrate that not all prime numbers are odd? 

1

3

2

4

Answer:

2

Solution:

The only even numbers in the list are 2 and 4,
 but 4 is not a prime. So 2 can be used to illustrate 
the statement that all primes are not odd.

Question: 40 -

A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?

pq+27

(-p)

8p

pq

Answer:

pq+27

Solution:

pq is a cube and so is 27, but their sum 
need not be a cube. Consider the case 
where p =1 and q = 8, the sum of pq and 27 
will be 35 which has factors 5 x 7 and is not a cube.