| Quantity A | Quantity B |
|
|
| 2 × 3 × 4 = 24 | 24 |
QC questions will sometimes ask you to compare the sum or product of sets of consecutive integers. The trick is to avoid finding the actual sums or products by eliminating overlap:
| Quantity A | Quantity B |
| The product of all the integers from 2 to 23, inclusive | The product of all the integers from 5 to 24, inclusive |
Both of these products are far too large to calculate in a reasonable amount of time, even with a calculator. Instead, you need to figure out which numbers appear in both products, and cancel those numbers.
In this problem, the numbers 5 through 23 appear in both sets. You can rewrite the products as:
| Quantity A | Quantity B |
| 2 × 3 × 4 × (5 × 6 × … 22 × 23) | (5 × 6 × … 22 × 23) × 24 |
The product of the numbers 5 through 23 is positive, and has the same value in each quantity. Therefore, because of the invisible inequality, you can divide out (5 × 6 × … 22 × 23), and focus on what is left:
| Quantity A | Quantity B |
|
|
|
| 2 × 3 × 4 = 24 | 24 |
The values in the two quantities are equal. The correct answer is (C).