Questions about Arithmetic

A 1:

If the sum of 3 consecutive integers is less than 75, what is the greatest possible value of the smallest of the three integers?

A 2:

If 2<x<4 and 3<y<7, what is the largest integer value of x+y?

A 3:

What is the smallest number that is divisible by both 34 and 35?

Answer  1:

Let the numbers be: n, n+1 , n+2. Then

n+ (n+1)+(n+2)+(n+3)=3n+3

Now by the given condition:

3n+3<75⇒3n<72⇒n<24

The most n can be is 23.

Now try three consecutive numbers whose sum is less than 75.

So, the numbers must be 23,24,25

Answer is 23.

Answer 2:

If x and y are integers, the largest value is 3+6=9. However, although x+y is to be an integer, neither x nor y must be. If x=3.8 and y=6.2, then x+y=10

So answer=10

Answer 3:

You are being asked for the LCM (least common multiple) of 34 and 35.

So the LCM of the numbers is 34×35=1190