Cambridge C2 Proficiency (CPE) — All Questions

The two departments have been ___ loggerheads for months over the budget.

• a.in
• b.at✓
• c.on
• d.under

The idiom 'at loggerheads (with)' means in strong disagreement. The fixed preposition is 'at'.

In terms of raw talent, the newcomer is very much ___ a par with the veterans.

• a.in
• b.at
• c.on✓
• d.to

'On a par with' means at an equal level with. The idiom fixes the preposition as 'on'.

We were ___ no illusion about how difficult the negotiations would be.

• a.in
• b.on
• c.at
• d.under✓

The fixed phrase is 'under no illusion', meaning fully aware of the reality. 'Under' is the required preposition.

When it comes to Renaissance art, she is ___ authority everyone consults.

• a.the✓
• b.an
• c.a
• d.-

The emphatic, stressed 'the' marks her as the single pre-eminent authority. 'An'/'a' would reduce her to merely one of several.