Final answer:
The correct choice is 'came up with', which is the idiom for suggesting or thinking of a new idea. This phrase fits best in the provided sentence to indicate the recruit has thought of a brilliant idea to improve sales.
Step-by-step explanation:
The correct phrase to use in this sentence is 'came up with'. This idiom means to suggest or think of an idea or plan. The sentence should read, 'The new recruit came up with a brilliant idea to bolster the sales of the new product.'
The confusion may arise from the similar but incorrect phrases 'coming on with', 'come on with', and 'came on with'. However, 'came on with' does not convey the same meaning as 'came up with', which is specifically used to indicate the creation or conception of an idea. In this context, 'came up with' means to suggest or propose something, especially an idea or solution. It implies that the recruit thought of the idea themselves.
For example, if the new recruit 'came up with' a marketing campaign to increase sales, it means they created or developed the campaign idea.