Prompt analysis

a<3 and b<11

Superset

The answer will be a positive single digit.

Translation

In order to find the digit, we need:

1# exact value of a and b.

2# the properties of a/b.

3# two equation to find a and b.

Statement Analysis

St1: Rounding to nearest hundredth, a/b = 0._1

Put a = 2 and plug values of b from 3 to 10 --> Rounding to the hundredths digit does not result in 1.

a = 1; b = 10 --> a/b = 0.1 --> Not possible

a = 1; b = 9 --> a/b = 0.11 --> Possible

a = 1; b = 8 --> a/b = 0.13 --> Not possible

As b decreases value of a/b increases and hundredths digit does not equal to 1 --> Only possible value of a/b = 0.11

Value of a/b rounded to nearest tenth = 0.1

Sufficient

St2: Rounding to nearest ten thousandth, a/b = 0._ _ _ 9

We need a recurring values to find this

Possible values = 2/3 = 1/6 = 0.6667 --> Not possible

2/6 = 1/3 = 0.3333 --> Not possible

2/7 = 0.28571 = 0.2857 --> Not possible

2/9 = 0.2222; 1/9 = 0.1111 --> Not possible

1/7 = 0.14285 = 0.1429 --> Possible

a/b rounded to the nearest tenth = 0.1

Sufficient

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