Solved this one by plugging in values directly.
Need to check if area of circle R is less than that of S-C Q
(1) Radius of circle R < Radius of SC Q
Let Radii of R and Q equal 3 and 4 respectively
Area R=9Ï€ and Area Q=8Ï€
Area R > Area Q
Let Radii of R and Q equal 1 and 4 respectively
Area R=Ï€ and Area Q=8Ï€
Area R < Area Q
Two different values, hence insufficient.
(2) Circumference R < Perimeter Q
Perimeter of SC is Diameter+Ï€(Radius)
Let Radii of R and Q equal 1 and 4 respectively. When we make this assumption,
Circumference of R is 2Ï€ and Perimeter of Q 8+4Ï€ which meets the condition and,
Area R=Ï€ and Area Q=8Ï€
Area R < Area Q
Let Radii of R and Q equal 3 and 4 respectively. When we make this assumption,
Circumference of R is 6Ï€ and Perimeter of Q 8+4Ï€ which meets the condition and,
Area R=9Ï€ and Area Q=8Ï€
Area R > Area Q
Conflicting values, hence Insufficient.
Combining (1) and (2)
We'll use the example where we considered the Radii of R and Q as 1 and 4. Which meets the requirement in statement 1 as well as st.2 as Circumference R=2Ï€ which is less than Perimeter Q=8+4Ï€.
In this case Area R=Ï€ which is LESS THAN Area Q=8Ï€
Now, onto the next example where we use the Radii of R and Q as 3 and 4. Which meets the requirement in statement 1 as well as st.2 as Circumference R=6Ï€ which is less than Perimeter Q=8+4Ï€. However, Area of R=9Ï€ which is more than Area Q=8Ï€ . Both Statements combined are Insufficient.
Hence [spoiler]E
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geometry
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Source: Beat The GMAT — Data Sufficiency |
