What was the number of defective batteries in a shipment of

1. Not sufficient.

sample of 10 items has 1 defective item. that doesnt tell us anything about the rest of the 4990 items.we may or may not have defective items in the rest.

2. Not sufficient.

sample of 100 items has 3 defective items. that doesnt tell us anything about the rest of 3900 items. we may or may not have defective items in the rest.

together , still not sufficient as we only about the defective items in a 100 item sample . we still dont know aything about the rest of the items.

Answer is E.

Is this interpretation correct

No, it's not. We can not extrapolate the data on some particular sample to all shipment.

What was the number of defective batteries in a shipment of 4000 batteries ?

(1) In a particular sample of 10 batteries selected from the shipment 1 was defective --> just tells us that there is at least 1 defective battery in the shipment of 4000 batteries. Not sufficient.

(2) In a particulare sample of 100 batteries selected from the shipment, 3 were defective --> just tells us that there are at least 3 defective batteries in the shipment of 4000 batteries. Not sufficient.

(1)+(2) All we know is that there are at least 3 defective batteries in the shipment of 4000 batteries. Not sufficient.

Answer; E.

Option E

Because the question does not mention that the sample is an actual representaion of the whole lot.

Target question: What was the number of defective batteries in a shipment of 4000 batteries?

Statement 1: In a particular sample of 10 batteries selected from the shipment, 1 was defective.
Don't make the mistake of assuming that this means 1/10 of ALL batteries are defective. There's no reason to assume this.
There are several scenarios that satisfy statement 1. Here are two:
Case a: There's 1 defective battery in the 10-battery sample, and 0 defective batteries in the remaining 3990 batteries. In this case, the answer to the target question is there's ONE defective battery in the shipment of 4000 batteries
Case b: There's 1 defective battery in the 10-battery sample, and 2 defective batteries in the remaining 3990 batteries. In this case, the answer to the target question is there are THREE defective batteries in the shipment of 4000 batteries
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: In a particular sample of 100 batteries selected from the shipment, 3 were defective.
There are several scenarios that satisfy statement 2. Here are two:
Case a: There are 3 defective batteries in the 100-battery sample, and 0 defective batteries in the remaining 3900 batteries. In this case, the answer to the target question is there are THREE defective batteries in the shipment of 4000 batteries
Case b: There are 3 defective batteries in the 100-battery sample, and 2 defective batteries in the remaining 3900 batteries. In this case, the answer to the target question is there are FIVE defective batteries in the shipment of 4000 batteries
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several scenarios that satisfy BOTH statements. Here are two:
Case a: 1 defective battery in 1st sample, 3 defective batteries in 2nd sample, and 0 defective batteries in the remaining 3890 batteries. In this case, the answer to the target question is there are FOUR defective batteries in the shipment of 4000 batteries
Case b: 1 defective battery in 1st sample, 3 defective batteries in 2nd sample, and 4 defective batteries in the remaining 3890 batteries. In this case, the answer to the target question is there are EIGHT defective batteries in the shipment of 4000 batteries
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

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