Tag: softskills

The verb 'disagree' is followed by the preposition 'with' when referring to a person. 'Disagree to' means rejecting a proposal or idea. 'Disagree for' is not standard English usage.

British English uses 'at the weekend' while American English prefers 'on the weekend'. Since 'at' is marked correct, this follows British conventions. 'In the weekend' is incorrect in both dialects.

'Lie to someone' is the correct phrase meaning to deliberately say something untrue to them. 'Lie with' is incorrect (that would mean 'sleep with'). 'Lie on' has a different meaning entirely.

'At midnight' refers to a precise time point (12:00 AM). 'In midnight' and 'on midnight' are incorrect - 'in' is for months/years/seasons and 'on' is for specific days. Note the typo 'proposition' instead of 'preposition' in option A.

To invite at least one person from 10, subtract the case of inviting nobody: 2^10 - 1 = 1024 - 1 = 1023. Each person has 2 choices (invited or not), giving 2^10 total subsets. Excluding the empty set leaves 1023 valid options.

Using weighted average: (2*50 + 3*40) / (2+3) = (100 + 120) / 5 = 220/5 = 44. With 2 boys and 3 girls, the boys contribute 100 and girls contribute 120 to total weight, divided by 5 students gives 44.

A square inscribed in a circle has a diagonal equal to the circle's diameter. With radius 5, the diameter is 10. The area of a square is (diagonal^2)/2, so (10^2)/2 = 100/2 = 50 square units.

Using allegation method: difference from 47% gives (50-47):(47-40) = 3:7. So Solution I (40%) and Solution II (50%) mix in ratio 3:7. Alternatively: (40x + 50y)/(x+y) = 47 gives x/y = 3/7.