Quant - Rounding

Question 1

When the positive number a is rounded to the nearest tenth, the result is the number b. What is the tenths digit of a?

(1) When a is rounded to the nearest integer, the result is less than a.
(2) When b is rounded to the nearest integer, the result is greater than b.

Answer 1

Say a = n.xyz
Then b = n.x or n.(x+1) depending on what y is.
(Say 1.342 will round to 1.3 (x stays the same) but 1.382 will round to 1.4 (x becomes x+1))

We need to know the value of x.

(1) When a is rounded to the nearest integer, the result is less than a.

When rounded, n.xyz gives n.
Since it is rounded down, it means x is one of 0/1/2/3/4.

(2) When b is rounded to the nearest integer, the result is greater than b.

b = n.x or n.(x+1)
For b to be rounded up, the tenths digit (x or x+1) is one of 5/6/7/8/9.

Using both statements, there is only one value of x that works.
x must be 4 which means x+1 must be 5 and that is how the tenths digit of b will lead to rounding up.

Hence x = 4