numerical-reasoning-s01-q01
Add the two shelf counts directly: 24 + 38 = 62.
This is untimed educational practice for one cognitive skill. It is not a clinical, diagnostic, employment, or professionally recognized assessment, and it does not produce an IQ score or credential.
Add the two shelf counts directly: 24 + 38 = 62.
Equal sharing is division: 96 ÷ 8 = 12 pencils each.
Repeated equal amounts call for multiplication: 7 × £9 = £63.
Subtract the drained amount from the full tank: 500 − 137 = 363 litres.
Division is carried out before subtraction: 12 ÷ 3 = 4, so 18 − 4 = 14. Working left to right first would wrongly give 2.
Multiply carriages by seats per carriage: 6 × 72 = 432.
Multiply the number of boxes by apples per box: 12 × 15 = 180.
9 × 8 = 72 is the largest multiple of 9 that fits within 75, leaving a remainder of 75 − 72 = 3.
Multiplication comes before subtraction: 7 × 8 = 56, then 56 − 6 = 50.
From 9:00 am to 5:00 pm is 8 hours, plus the extra 30 minutes makes 8.5 hours.
Convert to a common denominator first: 1/2 = 2/4, so 2/4 + 1/4 = 3/4. Adding tops and bottoms separately is the classic trap.
Find one fifth first: 40 ÷ 5 = 8, then multiply by three: 3 × 8 = 24.
0.25 is one quarter, so multiplying by it is dividing by 4: 80 ÷ 4 = 20.
Converting to decimals makes the comparison easy: 3/5 = 0.6, 7/12 ≈ 0.583, 2/3 ≈ 0.667, and 5/8 = 0.625, so 2/3 is largest.
Line up the decimal places by writing 7.2 as 7.20, then subtract: 7.20 − 3.85 = 3.35.
Divide the total length by the piece length: 3.6 ÷ 0.4 = 36 ÷ 4 = 9 pieces.
Divide top and bottom by their highest common factor, 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, giving 3/4. Equivalent fractions like 6/8 are not fully simplified.
One third of 27 is 9, so two thirds is 2 × 9 = 18 pupils.
Multiply as whole numbers (3 × 4 = 12), then place two decimal digits because the factors have one each: 0.12.
Multiply the fraction by three: 3 × 3/4 = 9/4, which is 2 1/4 cups.
25% of $80 is $20, so the sale price is $80 − $20 = $60.
10% of 60 is 6 and 5% is 3, so 15% is 6 + 3 = 9.
Divide the score by the total and multiply by 100: 45 ÷ 60 = 0.75, which is 75%.
Percentage change is the change divided by the original amount: 8 ÷ 50 = 0.16, so a 16% increase.
12.5% is one eighth, so the charge is £40 ÷ 8 = £5, giving £40 + £5 = £45.
40% of 30 is 12 boys, so the remaining 30 − 12 = 18 students are girls.
If 30% is 21, then 10% is 21 ÷ 3 = 7, so the whole number (100%) is 7 × 10 = 70.
Convert the percentage to a decimal and multiply: 0.68 × 25 = 17 marks.
The fall is 200 people; divide by the original population: 200 ÷ 2,500 = 0.08, an 8% decrease.
Work both out: 25% of 80 is 20, while 30% of 70 is 21, so 30% of 70 is slightly greater.
The ratio 2 : 1 has 3 equal parts, each worth £60 ÷ 3 = £20; the larger share is 2 × £20 = £40.
Divide both sides by their highest common factor, 6: 12 : 18 becomes 2 : 3. Keep the order as asked: cats first.
Multiply the map distance by the scale: 4 cm × 50,000 = 200,000 cm, and converting units gives 2,000 m = 2 km.
Every 1 part of concentrate needs 4 parts of water, so 250 ml needs 4 × 250 = 1,000 ml of water.
9 cups of sugar is 3× the ratio's 3 cups, so flour scales the same way: 2 × 3 = 6 cups.
The ratio 4 : 5 has 9 parts, each worth 45 ÷ 9 = 5 sweets; the smaller share is 4 × 5 = 20.
21 red cars is 7 times the ratio's 3, so scale the silver side the same way: 7 × 7 = 49.
Each printer produces 360 ÷ 3 = 120 pages per hour, so five produce 5 × 120 = 600.
The ratio has 3 + 2 + 1 = 6 parts, each worth 480 ÷ 6 = 80 g; butter is 2 parts, so 160 g.
One pen costs £6 ÷ 8 = £0.75, so 12 pens cost 12 × £0.75 = £9.
180 km ÷ 3 h = 60 km/h. At 60 km/h for 5 hours: 60 × 5 = 300 km.
There are 1,000 metres in a kilometre, so divide by 1,000: 3,200 m = 3.2 km.
Average speed is distance divided by time: 45 ÷ 2.5 = 18 km/h.
Break the journey into easy steps: 09:40 plus 20 minutes reaches 10:00, and the remaining 1 hour 15 minutes reaches 11:15.
Divide the volume by the rate: 90 ÷ 4 = 22.5 minutes.
Time is distance divided by speed: 12 ÷ 5 = 2.4 hours, and 0.4 of an hour is 0.4 × 60 = 24 minutes.
Multiply the pounds by the rate per pound: 60 × 1.15 = €69.
Divide by the 60 minutes in an hour: 45 ÷ 60 = 0.75. Writing 45 minutes as 0.45 hours is the common slip.
An hour contains three 20-minute periods, so the hourly total is 3 × 240 = 720 bottles.
Convert the time to a decimal: 2 hours 15 minutes = 2.25 hours, then multiply: 64 × 2.25 = 144 km.
The total spend is £7.35 + £4.20 = £11.55, so the change is £20 − £11.55 = £8.45.
Compare a common unit: per 100 g, the small pack costs £2.40 ÷ 5 = £0.48 while the large pack costs £3.30 ÷ 7.5 = £0.44, so the larger pack is cheaper per gram.
Simple interest pays the same amount each year: 5% of £800 is £40, so three years earn 3 × £40 = £120.
10% of £2,400 is £240, so 35% is 3.5 × £240 = £840.
$500 × 1.10 = $550 after year one; $550 × 1.10 = $605 after year two.
Divide the bill by the number of diners: £86.40 ÷ 6 = £14.40.
The deposit is 15% of £640 = £96, leaving £640 − £96 = £544, or simply take 85% of the price directly.
Multiply hours by the hourly rate: 38 × £12.50 = £475. Doubling £12.50 to £25 per 2 hours makes the mental sum easier: 19 × £25 = £475.
Eight drinks form two groups of four, and in each group one is free, so you pay for 6 drinks: 6 × £2.50 = £15.
The profit per plant is £2 − £1.20 = £0.80, so 40 plants earn 40 × £0.80 = £32.
Add the values and divide by how many there are: (4 + 8 + 9 + 11) ÷ 4 = 32 ÷ 4 = 8.
With the five values already in order, the median is the middle (third) value: 8.
The mode is the most frequent value, and 4 appears three times, more than any other.
The range is the largest value minus the smallest: 23 − 5 = 18.
A mean of 14 across five scores means a total of 5 × 14 = 70; the four known scores sum to 55, so the fifth is 70 − 55 = 15.
Weight each mean by its class size: total marks are 20 × 60 + 10 × 75 = 1,950, spread over 30 pupils gives 65. Simply averaging 60 and 75 ignores the different class sizes.
Average speed is total distance over total time: (120 + 60) ÷ (2 + 1) = 180 ÷ 3 = 60 km/h.
Sum the three days and divide by three: (40 + 55 + 25) ÷ 3 = 120 ÷ 3 = 40.
The original total is 6 × 10 = 60; adding 24 gives 84 across seven numbers, and 84 ÷ 7 = 12.
A mean only fixes the total (5 × 50 = 250 points), not how the points are spread. Every player could have scored exactly 50, or one could have scored far more.
Each term increases by 4, so the next term is 17 + 4 = 21.
Each term is multiplied by 3, so the next term is 54 × 3 = 162.
Each term is halved, so the next term is 8 ÷ 2 = 4.
These are the square numbers 1², 2², 3², 4², 5², so the next is 6² = 36.
Each term is the sum of the two before it: 11 + 18 = 29.
The amount subtracted grows by one each step (3, 4, 5, 6), so the next step subtracts 7: 22 − 7 = 15.
Two sequences alternate: the odd positions climb 1, 3, 5, 7 while the even positions fall 10, 8, 6, so the next even-position term is 4.
The gaps grow by one each time (1, 2, 3, 4, 5), so the next gap is 6: 20 + 6 = 26.
8, 27, 64, and 125 are cube numbers (2³, 3³, 4³, 5³); 100 is a square but not a cube.
Apply the rule to 17: 2 × 17 = 34, then 34 − 1 = 33.
First find the capacity: 18 × 22 = 396 seats; then subtract the tickets sold: 396 − 315 = 81.
Remove the fixed fee first: £145 − £40 = £105 of hourly work, then divide by the rate: 105 ÷ 15 = 7 hours.
The trip uses 4.5 × 6 = 27 litres, and 27 × £1.50 = £40.50.
The 20% reduction takes £45 down to £36, and the £5 voucher then brings it to £31. The order of the steps matters.
Their combined age is three equal 'Beth-sized' parts (Beth plus twice Beth), so Beth is 36 ÷ 3 = 12 and Amir is 24.
Work backwards, undoing each step in reverse: 46 − 6 = 40, then 40 ÷ 4 = 10.
Monday's shipment is 15% of 1,200 = 180 units, leaving 1,020; Tuesday's delivery brings it to 1,020 + 250 = 1,270.
The floor area is 4 × 3 = 12 m², needing 12 ÷ 0.25 = 48 tiles, which is 48 ÷ 10 = 4.8, so 5 full boxes must be bought.
The tickets cost 2 × £9 + 3 × £5 = £18 + £15 = £33, so the change is £50 − £33 = £17.
June is 120% of May, so divide rather than take 20% off: 660 ÷ 1.2 = 550. Subtracting 20% of June's figure would give the wrong base.
Apply the multiplier twice: £2,000 × 0.9 × 0.9 = £1,620. The second year's 10% is taken from the reduced value, not the original.
Chain the multipliers: £150 × 0.8 = £120, then £120 × 0.9 = £108. Two successive discounts of 20% and 10% are not the same as one 30% discount.
£96 represents 120% of the original price, so divide by 1.2: 96 ÷ 1.2 = £80. Taking 20% off £96 would use the wrong base.
Work in rates: together they do 1/2 of the job per hour and A alone does 1/3, so B's rate is 1/2 − 1/3 = 1/6 per hour. A full job takes B 6 hours.
More time is spent at the slower speed, so the answer is below the midpoint. For a 120 km leg each way: 2 hours out plus 3 hours back is 240 km in 5 hours = 48 km/h.
A percentage of a percentage multiplies: 40% of 30% is 0.4 × 0.3 = 0.12, which is 12% of all staff.
Round to friendly numbers: 42,000 ÷ 70 = 600, so the quotient is about 600. Estimation is mainly about keeping track of the size of the answer.
Combined rate = 1/4 + 1/6 = 5/12 of the tank per hour, so time = 12/5 = 2.4 hours.
Start from the actual counts: 3 : 2 across 30 counters means 18 red and 12 blue; adding 6 blue gives 18 : 18, which simplifies to 1 : 1.
Multiply the two changes: 1.25 × 0.8 = 1, so the value ends exactly where it started. Percentage rises and falls of different sizes can cancel because they act on different bases.