Bocconi admission test sample questions and answers

The rise multiplies the price by 1.15: €240 + €36 = €276.

The cut is 15% of the new price: 15% of €276 is €41.40, so the final price is €276 − €41.40 = €234.60.

In one step: $1.15 \times 0.85 = 0.9775$, so the final price is 97.75% of the original, 2.25% lower.

$|2x - 3| < 5$ means $-5 < 2x - 3 < 5$.

Add 3 to every part: $-2 < 2x < 8$. Divide by 2: $-1 < x < 4$.

The integers strictly between −1 and 4 are 0, 1, 2 and 3: four of them.

The applicant is chosen from those who passed, so they are the denominator: 90 + 40 = 130 passed.

Of those 130, 90 took the course. The probability is $\dfrac{90}{130} = \dfrac{9}{13}$, about 0.69.

Both logarithms need positive arguments: $x > 0$ and $x - 6 > 0$, so $x > 6$.

Combine the logarithms: $\log_3 [x(x - 6)] = 3$, so $x(x - 6) = 3^3 = 27$.

Then $x^2 - 6x - 27 = 0$, which factors as $(x - 9)(x + 3) = 0$, giving $x = 9$ or $x = -3$. Only 9 satisfies $x > 6$.

Check: $\log_3 9 + \log_3 3 = 2 + 1 = 3$.

The passage says that the purchasing power of the average wage fell by about 2%, which is what B says in other words. The figures agree: pay rose 4% while prices rose 6%, and $1.04 \div 1.06 \approx 0.98$.

These commentators accept the figures but say they describe an average, then contrast two groups of workers whose experience differed. Their point is that the average does not show what happened to any particular household: answer C.

Workshop A: 36 ÷ 120 = 0.30, or 30%. Workshop B: 50 ÷ 200 = 0.25, or 25%. The difference is 5 percentage points.

The “Places offered” column is not needed: the question defines the rate using applications.

Multiply each share by its own number of visitors:

• March: 15% of 8,000 = 1,200
• April: 12% of 10,000 = 1,200
• May: 10% of 12,500 = 1,250

May sold the most: 1,250 tickets.

The passage gives two changes that happened at the same time, the new lighting and more night patrols, and one result, fewer burglaries. Either change, both or neither could explain the fall, and the passage gives nothing that separates them. It neither confirms nor contradicts the statement, so the statement cannot be deduced.

60 − 8 = 52 students attend at least one workshop.

Adding the two workshops, 38 + 30 = 68, counts everyone who attends both twice. So 68 − 52 = 16 attend both.

From there: only statistics 38 − 16 = 22, only writing 30 − 16 = 14.

The argument says removing travel will raise attendance. That only works if travel is currently keeping away some members who would otherwise come.

Negate B: if travel stops nobody from attending, removing it cannot raise attendance, and the argument collapses. So B is necessary.

B does not guarantee the conclusion; other obstacles could remain. A necessary assumption is a link the argument needs, not proof that its conclusion is true.