jlgdr wrote:
A retailer sells only radios and clocks. If she currently has 44 total items in inventory, how many of them are radios?
(1) The retailer has more than 28 radios in inventory
(2) The retailer has less than twice as many radios as clocks in inventory.
Given: A retailer sells only radios and clocks, and she currently has 44 total items in inventory. Target question: How many radios are there in the inventory Statement 1: The retailer has more than 28 radios in inventory There are several scenarios that satisfy statement 1. Here are three:
Case a: There are 29 radios and 15 clocks. In this case, the answer to the target question is
there are 29 radiosCase b: There are 30 radios and 14 clocks. In this case, the answer to the target question is
there are 30 radiosCase c: There are 31 radios and 13 clocks. In this case, the answer to the target question is
there are 31 radiosSince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The retailer has less than twice as many radios as clocks in inventory.There are several scenarios that satisfy statement 2. Here are three:
Case a: There are 29 radios and 15 clocks. In this case, the answer to the target question is
there are 29 radiosCase b: There are 28 radios and 16 clocks. In this case, the answer to the target question is
there are 28 radiosCase c: There are 27 radios and 17 clocks. In this case, the answer to the target question is
there are 27 radiosSince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that the number of radios can be 29, 30, 31, 32, . . . . 44
Statement 2 tells us that the number of radios can be 29, 28, 27, 26, . . . . 0
Since BOTH statements are true, the only scenario that satisfies BOTH statements is when there are 29 radios
So, the answer to the target question MUST be
there are 29 radiosSince we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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