Data Sufficiency

swerve wrote: ↑

Thu Feb 20, 2020 9:43 am

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.

The OA is C

Source: Manhattan Prep

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 radios
Case b: There are 30 radios and 14 clocks. In this case, the answer to the target question is there are 30 radios
Case c: There are 31 radios and 13 clocks. In this case, the answer to the target question is there are 31 radios
Since 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 radios
Case b: There are 28 radios and 16 clocks. In this case, the answer to the target question is there are 28 radios
Case c: There are 27 radios and 17 clocks. In this case, the answer to the target question is there are 27 radios
Since 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 radios
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent