Question

If a and b are integers and 71 < ab < 76, then all of the following could be the values of b except: (A) 18 (B) 8 (C) 12 (D) 7 (E) 5

Answer 1

We are given that

a and b are integers and 71 < ab < 76

We will check each options

option-A:

b=18

we can plug it

$71$

we can divide both sides by 18

$\frac{71}{18}$

now, we can simplify it

$3.944$

Since, 'a' is a integer

so, a=4 lies on interval

so, this interval is true

so, this is FALSE

option-B:

b=8

we can plug it

$71$

we can divide both sides by 8

$\frac{71}{8}$

now, we can simplify it

$8.875$

Since, 'a' is a integer

so, a=9 lies on interval

so, this interval is true

so, this is FALSE

option-C:

b=12

we can plug it

$71$

we can divide both sides by 12

$\frac{71}{12}$

now, we can simplify it

$5.9166$

Since, 'a' is a integer

so, a=6 lies on interval

so, this interval is true

so, this is FALSE

option-D:

b=7

we can plug it

$71$

we can divide both sides by 7

$\frac{71}{7}$

now, we can simplify it

$10.14285$

Since, 'a' is a integer

so, no integer lies on this interval

so, this interval is false

so, this is TRUE

option-E:

b=5

we can plug it

$71$

we can divide both sides by 5

$\frac{71}{5}$

now, we can simplify it

$14.2$

Since, 'a' is a integer

so, a=15

so, this interval is true

so, this is FALSE