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# CAT Number system Practice Problems Set 13

Question 1:
If a, a + 2 and a + 4 are prime numbers, then the number of possible solutions for a is
Topic: Basics

 One
 Two
 Three
 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

 $\left( {\frac{a}{{27}},\frac{b}{e}} \right)$
 $\left( {\frac{a}{{36}},\frac{c}{e}} \right)$
 $\left( {\frac{a}{{12}},\frac{{bd}}{{18}}} \right)$
 $\left( {\frac{a}{6},\frac{c}{d}} \right)$

Question 3:
Let x and y be positive integers such that x is prime and y is composite. Then,
Topic: Basics

 y – x cannot be an even integer
 xy cannot be an even integer
 $\frac{{\left( {x + y} \right)}}{x}$ cannot be an even integer
 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

 4
 5
 2
 3

Question 5:
The total number of integers pairs (x, y) satisfying the equation x + y = xy is
Topic: Factors

 0
 1
 2
 None of the above

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