01
Proficient
PROFICIENT
Stable reasoning that traces the grounds from premises to conclusions.
Assessment
Numerical Reasoning Test Vol.2
1 sections16 questions
Quantify numerical reasoning across four sub-skills — ratios & percentages, sequences, equations, and rates & work — in 16 questions. Correctness is graded into an overall score and level, with a per-sub-skill breakdown, per-question results and explanations, strengths and growth areas, and study steps.
[Vol.2] A new 16-question set. A numerical-reasoning deep dive across four sub-skills — ratios & percentages, sequences, equations & word problems, and rates & work — in 16 questions. It grades your answers into an overall score and level, and shows a sub-skill radar, per-question results with explanations, strengths and growth areas, and a study plan. About 5–8 minutes.
What this assessment measures
Test result
Your level inferred from your score on 16 questions
02
Developing
DEVELOPING
The foundation is there; tightening how you link premises will lift you.
03
Emerging
EMERGING
Begin by getting used to the language of logic; diagramming will steady you.
Example result report
PROFICIENT
Proficient
You reason from premises to conclusions by tracing the grounds — stable and reliable.
PassOverall score
100/ 100
Correct
16/ 16
Top
95%ile
Accuracy
100%
Overall score and pass line
100
Ability profile
Your score across ability domains (out of 100)
Domain-by-domain analysis
Working with ratios, proportions, and percentages. Identify the base amount and compute increases or decreases against it to avoid errors.
Spotting the rule in a number sequence. Focus on the step structure — arithmetic, geometric, second-difference, or Fibonacci-like.
Turning a word problem into an equation and solving it. Let the unknown be a variable and write the relationship as an equation.
Handling per-unit quantities: speed/distance/time, work rate, and unit price. Reducing to a 'per-unit' rate makes these tractable.
Your strengths
You check the grounds and choose what can be stated with certainty.
You judge the link between premises and conclusion calmly.
You stay focused through to the end within the time.
Next challenges
A perfect score — well done. Try a harder problem set next.
Shorten the time limit and aim to keep both speed and accuracy.
Deepen negation, converse, and contrapositive until you can teach them.
Detailed analysis
This test measures logical reasoning across several ability domains. You reached the proficient level, with a steady grip on judging exactly what the premises guarantee. Your domain strengths and weak spots are shown directly in the radar and the per-question results above. For any item you missed, retrace 'why this option is correct' in its explanation, and a perfect score is within reach. Keep resisting reversal errors and over-generalization.
Question review
○
Q1
What is 30% of 300 people?
Correct: B) 90 people
300 × 0.30 = 90 people (B). 60 mistakes it for 20%, and 210 is the other 70%.
○
Q2
What number continues the series? 7, 11, 15, 19, ___
Correct: A) 23
An arithmetic series that rises by 4 each time. 19 + 4 = 23 (A). 22 adds 3, and 25 adds 6.
○
Q3
A number minus 9 equals 16. What is the number?
Correct: C) 25
x − 9 = 16, so x = 16 + 9 = 25 (C). 7 subtracts instead of adding.
○
Q4
You cover 150 km in 3 hours. What is your speed?
Correct: D) 50 km/h
Speed = distance ÷ time = 150 ÷ 3 = 50 km/h (D). 450 multiplies instead of dividing.
○
Q5
A 500-yen item goes up in price by 20%. What is the new price?
Correct: A) 600 yen
The increase is 500 × 0.20 = 100 yen, so the new price is 500 + 100 = 600 yen (A). 520 adds only 20 yen, and 400 subtracts 20% instead.
○
Q6
What number continues the series? 4, 8, 16, 32, ___
Correct: B) 64
A geometric series that doubles each time. 32 × 2 = 64 (B). 48 adds 16, and 96 triples instead.
○
Q7
Two numbers add up to 60, and the larger is 5 times the smaller. What is the larger number?
Correct: C) 50
Let the smaller be x: x + 5x = 60, so 6x = 60, x = 10. The larger is 5 × 10 = 50 (C). 10 is the smaller number.
○
Q8
A car travels 240 km on 15 L of fuel. At the same efficiency, how far can it go on 25 L?
Correct: D) 400 km
Efficiency is 240 ÷ 15 = 16 km/L. On 25 L: 16 × 25 = 400 km (D). 360 wrongly uses about 15 km/L.
○
Q9
350 candies are split between two people in the ratio 2:5. How many does the larger share have?
Correct: A) 250
The ratio totals 2 + 5 = 7, so one part is 350 ÷ 7 = 50. The larger share is 5 × 50 = 250 (A). 100 is the smaller share (2 × 50).
○
Q10
What number continues the series? 3, 7, 13, 21, 31, ___
Correct: C) 43
The gaps are 4, 6, 8, 10 — rising by 2 — so the next gap is 12: 31 + 12 = 43 (C). 41 keeps the gap at 10.
○
Q11
What value of x satisfies 7x − 5 = 4x + 16?
Correct: B) 7
Subtract 4x from both sides: 3x − 5 = 16, so 3x = 21, x = 7 (B). 21 forgets to divide by 3.
○
Q12
A finishes a job in 4 days and B in 12 days. Working together, how long does it take?
Correct: A) 3 days
Daily work: A = 1/4, B = 1/12. Together 1/4 + 1/12 = 1/3, so the whole job takes 3 days (A). 8 wrongly averages the days.
○
Q13
A 2000-yen item is marked up 10%, then marked down 10%. What is the final price?
Correct: C) 1980 yen
After the markup: 2000 × 1.1 = 2200 yen. Then 10% off: 2200 × 0.9 = 1980 yen (C). 2000 wrongly assumes the changes cancel; because the base changes, it ends 20 yen lower.
○
Q14
What number continues the series? 2, 5, 11, 20, 32, ___
Correct: D) 47
The gaps are 3, 6, 9, 12 — rising by 3 — so the next gap is 15: 32 + 15 = 47 (D). 44 keeps the gap at 12.
○
Q15
There are 24 coins in all, of 100-yen and 500-yen pieces, totaling 6000 yen. How many 500-yen coins are there?
Correct: B) 9
Let y be the 500-yen coins; then 100-yen coins are (24 − y). 100(24 − y) + 500y = 6000, so 2400 + 400y = 6000, 400y = 3600, y = 9 (B). There are 15 hundred-yen coins.
○
Q16
An empty tank fills in 4 hours through inflow pipe A, but drains in 12 hours through outflow pipe B. With both open, starting empty, how long until it is full?
Correct: A) 6 hours
Per hour: A = +1/4, B = −1/12. Net = 1/4 − 1/12 = 1/6. To fill (1 tank): 1 ÷ (1/6) = 6 hours (A). 3 ignores the drain and adds the rates.
What to do next
For each item you missed, retrace 'why this option is correct' in its explanation.
Drill distinguishing negation, converse, and contrapositive to stop form-switching slips.
Practice timed sets to raise speed while keeping accuracy.
This test is reference information about logical-reasoning tendencies, not a formal qualification or a guarantee of ability.
DEVELOPING
Developing
The foundation is there. Tighten how you link premises and the next score band comes into view.
Almost thereOverall score
56/ 100
Correct
9/ 16
Top
56%ile
Accuracy
56%
Overall score and pass line
56
Ability profile
Your score across ability domains (out of 100)
Domain-by-domain analysis
Working with ratios, proportions, and percentages. Identify the base amount and compute increases or decreases against it to avoid errors.
Spotting the rule in a number sequence. Focus on the step structure — arithmetic, geometric, second-difference, or Fibonacci-like.
Turning a word problem into an equation and solving it. Let the unknown be a variable and write the relationship as an equation.
Handling per-unit quantities: speed/distance/time, work rate, and unit price. Reducing to a 'per-unit' rate makes these tractable.
Your strengths
You read the prompts to the end and compare the options.
You find a way in by mapping problems to everyday examples.
On items you grasp, you trace the grounds to the right answer.
Growth areas
Words of quantity and negation — all, some, not — can trip you up.
You sometimes rush, choosing beyond what the premises guarantee.
As conditions stack up, organizing them lags and you drop points.
Detailed analysis
This test measures logical reasoning across several ability domains. You are at the developing level, with the foundation in place. The radar and the per-question results above show which domains have the most headroom. For the items you missed, draw the premises as nested diagrams, sort the options into must / might / cannot be true, then reread the explanation — the same type of error will fade.
Question review
○
Q1
What is 30% of 300 people?
Correct: B) 90 people
300 × 0.30 = 90 people (B). 60 mistakes it for 20%, and 210 is the other 70%.
○
Q2
What number continues the series? 7, 11, 15, 19, ___
Correct: A) 23
An arithmetic series that rises by 4 each time. 19 + 4 = 23 (A). 22 adds 3, and 25 adds 6.
○
Q3
A number minus 9 equals 16. What is the number?
Correct: C) 25
x − 9 = 16, so x = 16 + 9 = 25 (C). 7 subtracts instead of adding.
○
Q4
You cover 150 km in 3 hours. What is your speed?
Correct: D) 50 km/h
Speed = distance ÷ time = 150 ÷ 3 = 50 km/h (D). 450 multiplies instead of dividing.
○
Q5
A 500-yen item goes up in price by 20%. What is the new price?
Correct: A) 600 yen
The increase is 500 × 0.20 = 100 yen, so the new price is 500 + 100 = 600 yen (A). 520 adds only 20 yen, and 400 subtracts 20% instead.
○
Q6
What number continues the series? 4, 8, 16, 32, ___
Correct: B) 64
A geometric series that doubles each time. 32 × 2 = 64 (B). 48 adds 16, and 96 triples instead.
○
Q7
Two numbers add up to 60, and the larger is 5 times the smaller. What is the larger number?
Correct: C) 50
Let the smaller be x: x + 5x = 60, so 6x = 60, x = 10. The larger is 5 × 10 = 50 (C). 10 is the smaller number.
○
Q8
A car travels 240 km on 15 L of fuel. At the same efficiency, how far can it go on 25 L?
Correct: D) 400 km
Efficiency is 240 ÷ 15 = 16 km/L. On 25 L: 16 × 25 = 400 km (D). 360 wrongly uses about 15 km/L.
○
Q9
350 candies are split between two people in the ratio 2:5. How many does the larger share have?
Correct: A) 250
The ratio totals 2 + 5 = 7, so one part is 350 ÷ 7 = 50. The larger share is 5 × 50 = 250 (A). 100 is the smaller share (2 × 50).
×
Q10
What number continues the series? 3, 7, 13, 21, 31, ___
Correct: C) 43
The gaps are 4, 6, 8, 10 — rising by 2 — so the next gap is 12: 31 + 12 = 43 (C). 41 keeps the gap at 10.
×
Q11
What value of x satisfies 7x − 5 = 4x + 16?
Correct: B) 7
Subtract 4x from both sides: 3x − 5 = 16, so 3x = 21, x = 7 (B). 21 forgets to divide by 3.
×
Q12
A finishes a job in 4 days and B in 12 days. Working together, how long does it take?
Correct: A) 3 days
Daily work: A = 1/4, B = 1/12. Together 1/4 + 1/12 = 1/3, so the whole job takes 3 days (A). 8 wrongly averages the days.
×
Q13
A 2000-yen item is marked up 10%, then marked down 10%. What is the final price?
Correct: C) 1980 yen
After the markup: 2000 × 1.1 = 2200 yen. Then 10% off: 2200 × 0.9 = 1980 yen (C). 2000 wrongly assumes the changes cancel; because the base changes, it ends 20 yen lower.
×
Q14
What number continues the series? 2, 5, 11, 20, 32, ___
Correct: D) 47
The gaps are 3, 6, 9, 12 — rising by 3 — so the next gap is 15: 32 + 15 = 47 (D). 44 keeps the gap at 12.
×
Q15
There are 24 coins in all, of 100-yen and 500-yen pieces, totaling 6000 yen. How many 500-yen coins are there?
Correct: B) 9
Let y be the 500-yen coins; then 100-yen coins are (24 − y). 100(24 − y) + 500y = 6000, so 2400 + 400y = 6000, 400y = 3600, y = 9 (B). There are 15 hundred-yen coins.
×
Q16
An empty tank fills in 4 hours through inflow pipe A, but drains in 12 hours through outflow pipe B. With both open, starting empty, how long until it is full?
Correct: A) 6 hours
Per hour: A = +1/4, B = −1/12. Net = 1/4 − 1/12 = 1/6. To fill (1 tank): 1 ÷ (1/6) = 6 hours (A). 3 ignores the drain and adds the rates.
What to do next
Draw premises as nested circles and check containment by eye before choosing.
Practice sorting options into must / might / cannot be true.
Do five basic items a day, untimed, accuracy first.
This test is reference information about logical-reasoning tendencies, not a formal qualification or a guarantee of ability.
EMERGING
Emerging
Start from the basics. Turning each premise into a diagram will steady your reasoning fast.
Almost thereOverall score
31/ 100
Correct
5/ 16
Top
33%ile
Accuracy
31%
Overall score and pass line
31
Ability profile
Your score across ability domains (out of 100)
Domain-by-domain analysis
Working with ratios, proportions, and percentages. Identify the base amount and compute increases or decreases against it to avoid errors.
Spotting the rule in a number sequence. Focus on the step structure — arithmetic, geometric, second-difference, or Fibonacci-like.
Turning a word problem into an equation and solving it. Let the unknown be a variable and write the relationship as an equation.
Handling per-unit quantities: speed/distance/time, work rate, and unit price. Reducing to a 'per-unit' rate makes these tractable.
Your strengths
You stay with the task to the end — a base to build on.
On items with familiar wording, you grasp the meaning.
Rereading the explanations helps you regrasp the approach.
Growth areas
Words of quantity and negation — all, some, not — are still shaky.
You tend to stall before finding the rule or the quantity relation.
You can overshoot what the premises actually guarantee.
Detailed analysis
This test measures logical reasoning across several ability domains. You are at the emerging level — not a ceiling on ability, but a sign the language of logic is still new. The radar and the per-question results above show where to start. Read aloud the explanations of the items you missed, draw the premises as nested circles, and mark only what must be true — start there and your foundation will steady.
Question review
○
Q1
What is 30% of 300 people?
Correct: B) 90 people
300 × 0.30 = 90 people (B). 60 mistakes it for 20%, and 210 is the other 70%.
○
Q2
What number continues the series? 7, 11, 15, 19, ___
Correct: A) 23
An arithmetic series that rises by 4 each time. 19 + 4 = 23 (A). 22 adds 3, and 25 adds 6.
○
Q3
A number minus 9 equals 16. What is the number?
Correct: C) 25
x − 9 = 16, so x = 16 + 9 = 25 (C). 7 subtracts instead of adding.
○
Q4
You cover 150 km in 3 hours. What is your speed?
Correct: D) 50 km/h
Speed = distance ÷ time = 150 ÷ 3 = 50 km/h (D). 450 multiplies instead of dividing.
○
Q5
A 500-yen item goes up in price by 20%. What is the new price?
Correct: A) 600 yen
The increase is 500 × 0.20 = 100 yen, so the new price is 500 + 100 = 600 yen (A). 520 adds only 20 yen, and 400 subtracts 20% instead.
×
Q6
What number continues the series? 4, 8, 16, 32, ___
Correct: B) 64
A geometric series that doubles each time. 32 × 2 = 64 (B). 48 adds 16, and 96 triples instead.
×
Q7
Two numbers add up to 60, and the larger is 5 times the smaller. What is the larger number?
Correct: C) 50
Let the smaller be x: x + 5x = 60, so 6x = 60, x = 10. The larger is 5 × 10 = 50 (C). 10 is the smaller number.
×
Q8
A car travels 240 km on 15 L of fuel. At the same efficiency, how far can it go on 25 L?
Correct: D) 400 km
Efficiency is 240 ÷ 15 = 16 km/L. On 25 L: 16 × 25 = 400 km (D). 360 wrongly uses about 15 km/L.
×
Q9
350 candies are split between two people in the ratio 2:5. How many does the larger share have?
Correct: A) 250
The ratio totals 2 + 5 = 7, so one part is 350 ÷ 7 = 50. The larger share is 5 × 50 = 250 (A). 100 is the smaller share (2 × 50).
×
Q10
What number continues the series? 3, 7, 13, 21, 31, ___
Correct: C) 43
The gaps are 4, 6, 8, 10 — rising by 2 — so the next gap is 12: 31 + 12 = 43 (C). 41 keeps the gap at 10.
×
Q11
What value of x satisfies 7x − 5 = 4x + 16?
Correct: B) 7
Subtract 4x from both sides: 3x − 5 = 16, so 3x = 21, x = 7 (B). 21 forgets to divide by 3.
×
Q12
A finishes a job in 4 days and B in 12 days. Working together, how long does it take?
Correct: A) 3 days
Daily work: A = 1/4, B = 1/12. Together 1/4 + 1/12 = 1/3, so the whole job takes 3 days (A). 8 wrongly averages the days.
×
Q13
A 2000-yen item is marked up 10%, then marked down 10%. What is the final price?
Correct: C) 1980 yen
After the markup: 2000 × 1.1 = 2200 yen. Then 10% off: 2200 × 0.9 = 1980 yen (C). 2000 wrongly assumes the changes cancel; because the base changes, it ends 20 yen lower.
×
Q14
What number continues the series? 2, 5, 11, 20, 32, ___
Correct: D) 47
The gaps are 3, 6, 9, 12 — rising by 3 — so the next gap is 15: 32 + 15 = 47 (D). 44 keeps the gap at 12.
×
Q15
There are 24 coins in all, of 100-yen and 500-yen pieces, totaling 6000 yen. How many 500-yen coins are there?
Correct: B) 9
Let y be the 500-yen coins; then 100-yen coins are (24 − y). 100(24 − y) + 500y = 6000, so 2400 + 400y = 6000, 400y = 3600, y = 9 (B). There are 15 hundred-yen coins.
×
Q16
An empty tank fills in 4 hours through inflow pipe A, but drains in 12 hours through outflow pipe B. With both open, starting empty, how long until it is full?
Correct: A) 6 hours
Per hour: A = +1/4, B = −1/12. Net = 1/4 − 1/12 = 1/6. To fill (1 tank): 1 ÷ (1/6) = 6 hours (A). 3 ignores the drain and adds the rates.
What to do next
Start with basics: check 'all / some / not' using pictures and diagrams.
Draw premises as nested circles and mark only what is certain.
Do three easy items a day, pairing each with reading the explanation aloud.
This test is reference information about logical-reasoning tendencies, not a formal qualification or a guarantee of ability.
Who it's for
Anyone who wants to sharpen numerical reasoning, or to prep for the quantitative sections of aptitude tests in hiring and admissions.
What the result looks like
Shows an overall score and level, a four sub-skill profile, per-question results with explanations, strengths and growth areas, and next study steps.
This assessment has 1 sections and 16 questions.
Once you start, you cannot change the language. Switch beforehand if needed.