patanahi wrote:
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.
(2) In a particulare sample of 100 batteries selected from the shipment, 3 were defective.
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 batteriesCase 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 batteriesSince 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 batteriesCase 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 batteriesSince 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 batteriesCase 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 batteriesSince we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent