Numerical Reasoning Practice: Questions with Answers
By Atlas Labs · Original teaching examples
Numerical reasoning is about interpreting relationships between quantities. Sometimes the arithmetic is simple and the real challenge is choosing the right operation, base value or unit. These examples focus on that decision rather than speed.
Work out each answer on paper if that helps, then expand the solution to compare your method. All three examples are original and free to read. They are not a timed aptitude exam, and completing them does not create an Atlas score.
3 numerical reasoning questions with answers
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0 of 3 answeredUntimed · Free practice
There’s no timer. Focus on understanding the method.
QUESTION 01 · Warm-up
Find the changing difference
In this sequence, the gap between neighboring terms increases by 2 each time: 6, 10, 16, 24, ?. What is the next term?
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Answer: C — 34.
The differences are 10 − 6 = 4, 16 − 10 = 6, and 24 − 16 = 8. The next difference is 10, giving 24 + 10 = 34.
Adding 8 again would produce 32, but it would stop the stated growth in the gaps. Check the differences as a sequence of their own.
Takeaway: When the terms do not have a constant gap, examine how the gaps change.
An item costs $80. Its price rises by 25%, then the new price is reduced by 20%. What is the final price?
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Answer: A — $80.
The increase is 25% of $80, which is $20. The new price is $100. The reduction is then 20% of $100, also $20, so the final price is $80.
Subtracting 20 from 25 to get a net 5% increase uses the wrong base. The two percentages apply to different amounts. Equivalently, 80 × 1.25 × 0.80 = 80.
Takeaway: Successive percentage changes multiply; their percentages do not simply add or subtract.
A machine packs 15 boxes in 5 minutes at a constant rate, with no setup time or interruptions. How many boxes does it pack in 14 minutes?
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Answer: B — 42.
The rate is 15 ÷ 5 = 3 boxes per minute. Over 14 minutes, the output is 3 × 14 = 42 boxes.
The constant-rate condition matters. Without it, the first five minutes would not be enough to determine the later output. Here, it is explicitly part of the problem.
Takeaway: Find the amount per one unit of time before scaling to a new duration.
Distinguish a total from a rate. Boxes per minute, dollars per item and percentage change all describe different relationships. Carrying the unit through a calculation can expose a reversed fraction.
Identify the base value
A percentage is always a percentage of something. With successive changes, the second percentage usually uses the updated value, not the starting amount. Write the intermediate amount before continuing.
Check the result in context
Estimate whether the answer should be larger or smaller, then substitute it back into the relationship. For a sequence, inspect differences or ratios and make sure the proposed rule fits every displayed step.
About these practice questions
Atlas Labs publishes these original learning exercises separately from the scored assessment bank. Each explanation checks the intended rule and describes why other choices fail. They help you practice a method; they do not estimate IQ, population rank or performance on an employer’s test.
Applying a percentage to the original value after the value has already changed.
Mixing minutes and hours, or dividing in the wrong direction when finding a rate.
Choosing a sequence rule from only one gap instead of checking all of them.
Questions about numerical reasoning practice
Do these questions require advanced mathematics?
No. These examples use subtraction, division, multiplication and percentages. The focus is on setting up the relationship correctly.
Can I use a calculator for this practice?
Yes. This page is for learning, so use one if it helps you check arithmetic. First write the calculation you intend to perform. Any separate exam may have different calculator rules.
How does this connect to the Atlas assessment?
Numerical reasoning is one of four Atlas domains. The full assessment combines it with abstract, logical and spatial questions, then provides a free overall result and personalized summary. Detailed domain scores are part of the optional paid report.
Explore all four sides of your reasoning
Try the 28-question Atlas assessment at your own pace. Your overall result and personalized summary are free; the full report with exact domain scores and deeper interpretation is an optional paid purchase.