PRACTICE QUESTIONS WITH SOLUTIONS
BCG Cognitive Test:
Questions and worked solutions.
Numerical, verbal and logical reasoning are the three core areas of the BCG Cognitive Test. These examples show you how to approach questions, avoid common mistakes and reach the solution step by step.
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Numerical reasoning
Question 01
Percentages · working backwards
A company sells 20% more devices in April than in March. In May, it sells 25% fewer than in April. Sales in March and May total 760 devices. How many devices are sold in April?
Solution and brief explanation
ANSWER B
1. Use March as the starting point. We do not yet know how many devices were sold in March. Call this quantity M. April sales are 20% higher, or 120% of March sales: April = 1.20 × M.
2. Express May sales in terms of March. May sales are 25% lower than April sales, leaving 75% of April sales. Therefore: May = 0.75 × April = 0.75 × 1.20 × M = 0.90 × M. May sales are therefore 90% of March sales.
3. Use the known total. March and May sales total 760 devices. That is 100% + 90% = 190% of March sales. Therefore: M = 760 ÷ 1.90 = 400.
4. Calculate the required April sales. Add 20% to the 400 devices sold in March: 400 × 1.20 = 480 devices.
As a check: May sales are 480 × 0.75 = 360 devices. March and May do indeed total 400 + 360 = 760.
Key pointThe percentage changes apply to different starting values. They cannot simply be offset against each other.
Question 02
Work rates · changing conditions
Four identical machines working at the same constant rate need 15 minutes to complete a job. All four start together. After five minutes, one machine fails; the others continue without interruption at the same rate. How long does the entire job take?
Solution and brief explanation
ANSWER C
The whole job requires 4 × 15 = 60 machine-minutes. In the first five minutes, 4 × 5 = 20 of these are completed.
Three machines need 40 ÷ 3 = 13 minutes 20 seconds for the remaining 40 machine-minutes. Including the first five minutes, the total is 18 minutes 20 seconds.
Key pointThe question asks for the total time from the start, not just the time after the failure.
Verbal reasoning
Question 03
Word analogy
Map is to terrain as model is to …?
Solution and brief explanation
ANSWER A
A map is a simplified representation of terrain. It depicts selected features without being the terrain itself.
Similarly, a model represents part of Reality in simplified form. Answer A therefore fits.
A hypothesis is a testable assumption, a simulation reproduces a process and a forecast predicts a development. These are related concepts, but they do not refer to the reality represented by a model.
Key pointExpress the relationship in the first pair as a short sentence. Then apply the same relationship in the same direction to the second pair.
Question 04
Grouping concepts
Which word does not belong with the others?
Solution and brief explanation
ANSWER C
A hypothesis is a provisional assumption to be tested. It is not itself a research finding or evidence supporting that assumption.
A finding records a research result, an observation records something perceived and a clue provides an indication. These three can help test a hypothesis. This makes answer C: hypothesis the odd one out.
Key pointSharing a topic is not enough. Look for the words' common role: here, evidence is contrasted with an assumption to be tested.
Logical reasoning
Question 05
Age comparisons
- Ada is younger than Ben.
- Cem is older than Dana.
- Dana is older than Ben.
- Eli is younger than Ben.
Who is the third-oldest person?
Solution and brief explanation
ANSWER D
The statements about Cem, Dana and Ben imply: Cem is older than Dana, and Dana is older than Ben. This means that at least two people are older than Ben.
Ada and Eli are both younger than Ben. Of the five people, exactly two are ahead of Ben and two behind him. Ben is the third-oldest person: answer D.
Whether Ada or Eli is younger is not specified. This does not affect Ben's position.
Key pointYou do not always need a complete ordering. For a fixed position, it is enough to identify unambiguously who is older and who is younger.
Question 06
Figure sequence
Which domino continues the sequence according to the same rule?
Show graphic as text
From left to right, row by row on small screens: (1 | 3), (3 | 2), (2 | 4), (4 | 3), (3 | 5), (? | ?). The numbers indicate the pips on the left and right halves.
Solution and brief explanation
ANSWER B
The right half becomes the left half of the next domino. The previous left half moves to the right and gains one pip.
For example, (2 | 4) becomes (4 | 3). The last visible domino, (3 | 5), is therefore followed by (5 | 4): answer B. The rule fits every transition in the visible sequence.
Alternative approach: The total number of pips increases by one with each domino: 4, 5, 6, 7, 8. The next domino must therefore have 9 pips. At the same time, the 5 pips on the previous right half move to the left. That leaves 9 − 5 = 4 pips on the right, again giving (5 | 4).
Both approaches describe the same relationship and lead to the same answer. However, the increasing pip total alone is not enough: answer C, (4 | 5), would also have 9 pips.
Key pointConsider the relationship between the left and right halves as well. Looking at each side separately can make you miss the transfer.
THE NEXT STEP
What changes with a time limit?
Solving individual questions at your own pace is a start. In the free practice test, you practise switching between reasoning areas under time pressure.