- Question-1
- Explanation

If the reminder obtained by subtracting a number from its own square is 6 times the number, What is the number?

a) 4

b) 3

c) 6

d) 7

**Answer:**

This is a very simple question. Reason is as follows.

Remainder is obtained by subtracting the number from its own square is 6 times the number.

That means x^{2} – x = 6x

X^{2} = 7x

X = 7

- Question-2
- Explanation

25^{2.7 }* 5 ^{4.2} / 5 ^{6.4} = 25 ^{(?)}

a) 1.7

b) 3.2

c) 1.6

d) 3.6

**Answer:** c) 1.6

(5^{2})^{2.7} * 5 ^{4.2} / 5 ^{6.4} = (5^{2})^{?}

(5^{5.4} * 5 ^{4.2})/ 5 6^{.4} = (5^{2})?

5 ^{3.2} = (5^{2}) ^{?}

2? = 3.2

? = 3.2/2 = 1.6

- Question-3
- Explanation

When a number is divided by 138 the remainder is 26. What will be the remainder if the same number is divided by 23?

a) 1

b) 3

c) 2

d) 4

**Answer:** b) 3

138 is a multiple of 23. (23 * 6 = 138).

So When the number is divided by 23 the remainder will be 26 – 23 = 3.

- Question-4
- Explanation

Mr. Mukhambo has two numbers and say that their difference, their sum and their product are to one another as 1: 7: 24. Mukhambo wants to find out whether you can get him the product of those two numbers:

a) 24

b) 6

c) 48

d) 12

Answer: c) 48

Difference between the two numbers ratio wise is 1

Sum of the two numbers ratio wise is 7

Products of the two numbers ratio wise is 24.

i.e. 1: 7: 24

Choice b) and d) cannot be the answer because product has to be ratio wise 24.

It is case a) or c)

For Product to be 24 it has to be 4 and 6. But their sum is 10 and difference is 6.

So 2: 10: 24 simplifying also it comes 1: 5: 12. This cannot be the answer.

For Product to be 48 – numbers can be 6 and 8.

Sum – 14

Product – 48, So difference: Sum: Product = 2: 14: 48 = 1: 7: 24

- Question-5
- Explanation

Three – fourth of a number is equal to 60% of another number and the difference between the two numbers is 20. What is the sum of the two numbers?

a) 220

b) 180

c) 170

d) 320

Answer: b) 180

This is another simple question dealing with algebraic equations. Reason is as follows.

Let the numbers be X and Y.

3/4X = 60/100Y = 3/5Y

3/5Y = 3/4X

12Y = 15X

12Y – 15X = 0 —–(i)

But from the question, Y – X = 20. Multiplying LHS and RHS by 12 we get,

12Y – 12X = 240—–(ii)

Simplifying both the equations, 12Y – 15X – 12Y + 12X = 0 – 240

-3X = 240

X = 80 and Y = 80 + 20 = 100

Sum of the two numbers = 80 + 100 = 180.