What percent of juice bottles are labeled correctly; that is, Guava Juice label on the bottles that have guava juice in them and Orange Juice label on the bottles that have orange juice in them.
(1) Of those which are labeled guava juice, 20 percent have orange juice in them.
(2) 80 percent of the bottles are labeled orange Juice.
We have 2 types of juice given - Guava and Orange, so we would have to account for both of them in order to arrive at the required answer.
Now, let's look at each statement individually and then at both of them together (if required):
Statement 1: Of those which are labeled guava juice, 20 percent have orange juice in them.
Through this statement, we know that of the bottles which are labeled guava juice, 80% have guava juice and 20% have orange juice. However, there is no information provided about the orange juice bottles. Hence, this statement is insufficient alone.
Now, let's take a look at Statement 2 closely:
Statement 2: 80 percent of the bottles are labeled orange Juice.
This statement only gives information about the labeling of the bottles, which is clearly insufficient to arrive at the answer. Hence, this statement too, is insufficient alone.
Now, let's look at the combination of both the statements:
From Statement 1, we know that that of the bottles which are labeled guava juice, 80% have guava juice and 20% have orange juice. From Statement 2, we know that 80 percent of the bottles are labeled orange Juice. Let's assume the total number of bottles to be X, the number of orange-labeled bottles as O and the number of guava-labeled juice as G.
X = O + G
Thus, O = 0.8X (as 80% of the bottles are labeled orange juice). Hence, 0.2X number of bottles are labeled as guava juice, i.e., G = 0.2X
Now, from Statement 1, we can also infer that 0.16X guava-labeled juice bottles actually have guava juice. However, we do not have any information on how many orange-labeled juice bottles actually have orange juice.
Hence, we are not able to arrive at the required answer using both the statements as well. Thus, the correct answer is
Option E - Neither statement alone nor together is sufficientHope this helps!