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<a(18)<76`

we can divide both sides by 18

`(71)/(18) <b<(76)/(18)`

now, we can simplify it

`3.944<a<4.222`

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<a(8)<76`

we can divide both sides by 8

`(71)/(8) <b<(76)/(8)`

now, we can simplify it

`8.875<a<9.5`

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<a(8)<76`

we can divide both sides by 12

`(71)/(12) <b<(76)/(12)`

now, we can simplify it

`5.9166<a<6.333`

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<a(5)<76`

we can divide both sides by 7

`(71)/(7) <b<(76)/(7)`

now, we can simplify it

`10.14285<a<10.857`

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<a(5)<76`

we can divide both sides by 5

`(71)/(5) <b<(76)/(5)`

now, we can simplify it

`14.2<a<15.2`

Since, 'a' is a integer

so, a=15

so, this interval is true

so, this is FALSE