Given,
Each brand was categorized based on whether its increased its whole sale price per pound this year compared to last year.
brand surveyed increased their price this year = ?
lets consider total brands survey = T
Brand surveyed - increased price = BI
Brand surveyed - not increased price = BNI
T = BI + BNI
we need to find (BI/ T) * 100
Statement 1 : of the brands that increased their price, 25% increased by at least 2 dollars per pound
Here, we can observe that, brands within group have increased their price, but doesn't give us any relation between T and BI
Therefore statement 1 is not sufficientStatement 2 : of all the brands surveyed, 15% increased their price by at least 2dollars per pound
here, we can observe that, it says about T (total), but doesn't give out about BI
Therefore statement 2 is not sufficientNow lets consider statement 1 and statement 2,
we form following equation 1 from statement 1=> increased by at least 2 dollars per pound = 0.25 * BI
we form following equation 2 from statement 2=> increased by at least 2 dollars per pound = 0.15 * T
equation 1 = equation 2 => 0.25 * BI = 0.15 * T => 5BI = 3T => BI/T = 3/5 => in percentage = 3/5 * 100 = 60
Therefor, Both statement 1 and statement 2 are sufficient