**Question 1:**

If a, a + 2 and a + 4 are prime numbers, then the number of possible solutions for a is

Topic: Basics

[1] One

[2] Two

[3] Three

[4] more than three

**Question 2:**

Let a, b, c, d and e be integers such that a = 6b = 12c, and 2b = 9d = 12e. Then which of the following pairs contains a number that is not an integer?

Topic: Basics

[1] \(\left( {\frac{a}{{27}},\frac{b}{e}} \right)\)

[2] \(\left( {\frac{a}{{36}},\frac{c}{e}} \right)\)

[3] \(\left( {\frac{a}{{12}},\frac{{bd}}{{18}}} \right)\)

[4] \(\left( {\frac{a}{6},\frac{c}{d}} \right)\)

**Question 3:**

Let x and y be positive integers such that x is prime and y is composite. Then,

Topic: Basics

[1] y – x cannot be an even integer

[2] xy cannot be an even integer

[3] \(\frac{{\left( {x + y} \right)}}{x}\) cannot be an even integer

[4] None of these

**Question 4:**

Each family in a locality has at most two adults, and no family has fewer than 3 children. Considering all the families together, there are more adults than boys, more boys than girls, and more girls than families, Then the minimum possible number of families in the locality is

Topic: LR

[1] 4

[2] 5

[3] 2

[4] 3

**Question 5:**

The total number of integers pairs (x, y) satisfying the equation x + y = xy is

Topic: Factors

[1] 0

[2] 1

[3] 2

[4] None of the above

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