One question at a time. Build your SPJAT understanding.
First 50 of 200 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.
Continue in the practice tool above to load more questions, 50 at a time.
Profit is 1,380,000 − 1,200,000 = 180,000 yen. Profit percent is measured against cost price, so 180,000 ÷ 1,200,000 = 0.15, i.e. 15%. Dividing by the selling price instead would give a different and incorrect figure.
Simple interest is P × r × t = 500,000 × 0.08 × 3 = 120,000 yen. Adding this to the principal gives 620,000 yen. Compound interest would give a slightly larger figure, so it must not be used here.
A 25% discount removes one quarter of the marked price: 8,000 × 0.25 = 2,000. Subtracting gives 6,000 yen, equivalently 8,000 × 0.75. The discount applies to the marked price, not to any cost figure.
The sum is 12 + 18 + 21 + 25 + 34 = 110, and there are five values. Dividing 110 by 5 gives an average of 22. The average must lie between the smallest and largest values, which 22 does.
Total distance is 240 + 180 = 420 km and total time is 3 + 2 = 5 hours. Average speed is total distance divided by total time, 420 ÷ 5 = 84 km/h. Averaging the two separate speeds would be wrong because the times differ.
The greatest common divisor of 45 and 60 is 15. Dividing both terms by 15 gives 3 : 4, which cannot be reduced further. A ratio is in lowest terms only when the two terms share no common factor.
Perimeter of a rectangle is 2 × (length + width) = 2 × (40 + 25) = 2 × 65 = 130 m. The product 40 × 25 gives area, not perimeter, so it must not be used here.
A number is divisible by 9 exactly when the sum of its digits is a multiple of 9. For 4,536 the digit sum is 4 + 5 + 3 + 6 = 18, which is divisible by 9, so 4,536 is too.
Subtract 7 from both sides to get 3x = 21, then divide both sides by 3 to obtain x = 7. Substituting 7 back gives 3 × 7 + 7 = 28, which confirms the solution.
There are 5 + 3 + 2 = 10 balls in total and 3 of them are blue. Probability is favourable outcomes over total outcomes, giving 3/10. The denominator must be the total number of balls, not just the non-blue ones.
Arranging all 5 distinct items in order is a permutation of all items, equal to 5 factorial. That is 5 × 4 × 3 × 2 × 1 = 120. Multiplying 5 by itself would instead count sequences with repetition allowed.
Each 6-year period multiplies the amount by 2. To reach 8 times, which is 2³, three such doublings are needed. Three periods of 6 years give 18 years.
The 20 students total 20 × 15 = 300 years. With the teacher there are 21 people totalling 21 × 16 = 336 years. The difference, 336 − 300 = 36, is the teacher's age.
In one day A and B complete 1/6 of the task, while A alone completes 1/10. B's daily rate is 1/6 − 1/10 = (5 − 3)/30 = 2/30 = 1/15, so B needs 15 days.
Downstream speed is 30 ÷ 2 = 15 km/h and upstream speed is 30 ÷ 3 = 10 km/h. The current is half the difference of these speeds: (15 − 10) ÷ 2 = 2.5 km/h.
Let the numbers be 5k and 8k. Then (5k + 6)/(8k + 6) = 2/3, giving 15k + 18 = 16k + 12, so k = 6. The smaller number is 5 × 6 = 30.
A cube has 6 equal square faces, so each face has area 96 ÷ 6 = 16 cm², giving an edge of 4 cm. Volume is the edge cubed: 4³ = 64 cm³.
The selling price equals 90% of the marked price, so marked price = 720 ÷ 0.9 = 800 yen. Adding 10% to the selling price would be wrong, because the discount was taken from the marked price.
The amount after 2 years is 10,000 × 1.1² = 12,100 yen. Compound interest is the amount minus the principal, 12,100 − 10,000 = 2,100 yen. Simple interest would give only 2,000 yen.
The first white ball has probability 4/10, and the second then has probability 3/9. Multiplying gives (4/10) × (3/9) = 12/90 = 2/15. The second denominator must be 9 because one ball has already been removed.
Let the son be s and the father 3s. In 12 years, 3s + 12 = 2(s + 12), which simplifies to 3s + 12 = 2s + 24, so s = 12. Checking: father 36, and in 12 years 48 is twice 24.
The net fill rate per hour is 1/12 − 1/20 = (5 − 3)/60 = 2/60 = 1/30. The reciprocal of this rate gives 30 hours to fill the tank.
To clear the platform the train must cover its own length plus the platform: 150 + 300 = 450 m in 30 s. That is 15 m/s, and multiplying by 3.6 gives 54 km/h.
Initially milk is 30 litres and water 10 litres. Milk stays at 30, so for a 3 : 2 ratio the water must be 30 × 2/3 = 20 litres. Adding 20 − 10 = 10 litres of water achieves this.
The amount equals P × 1.12² = P × 1.2544. Dividing 7,840 by 1.2544 gives P = 6,250 yen. Dividing by 1.24 instead would incorrectly treat the interest as simple.
Successive discounts multiply rather than add. After 20% the price is 1250 × 0.80 = 1000, and after a further 10% it is 1000 × 0.90 = 900. Adding the discounts to get 30% off would wrongly give 875, so the multiplicative method is essential.
Simple interest equals principal × rate × time, so 1440 = P × 0.08 × 3 = 0.24P. Dividing gives P = 1440 ÷ 0.24 = 6000. The principal is therefore ¥6,000.
15% of 240 is 0.15 × 240 = 36, and 25% of 160 is 0.25 × 160 = 40. Their sum is 36 + 40 = 76. Each percentage must be applied to its own base before adding.
The total of the 8 numbers is 8 × 42 = 336, and the total of the remaining 7 is 7 × 40 = 280. The removed number is the difference, 336 − 280 = 56. Working with totals avoids errors that arise from averaging averages.
Average speed is total distance divided by total time, not the mean of the two speeds. Total distance is 240 + 180 = 420 km and total time is 4 + 2 = 6 hours, so the average is 420 ÷ 6 = 70 km/h.
Becoming 5 times itself means the interest earned equals 4 times the principal. With simple interest, 4P = P × r × 16, so r = 4 ÷ 16 = 0.25, that is 25% per annum. The key step is recognising that the interest is 4P, not 5P.
Multiplying by 1.20 and then by 0.80 gives 0.96, which is 96% of the original. The net effect is a 4% decrease, because the 20% decrease is taken on the larger intermediate value. Equal percentage rise and fall never cancel out.
A number is divisible by 9 when its digit sum is a multiple of 9. The digit sum of 4312 is 4 + 3 + 1 + 2 = 10, and the next multiple of 9 is 18, so 8 must be added. However, checking the remainder directly, 4312 ÷ 9 leaves remainder 1, so adding 8 gives divisibility. Rechecking the options, 4312 + 5 = 4317 has digit sum 15, which is not a multiple of 9.
Let the ages be 4k and 5k. Six years ago, (4k − 6)/(5k − 6) = 3/4, giving 16k − 24 = 15k − 18, so k = 6. Hence Q's age is 5 × 6 = 30 years. Substituting back confirms the earlier ratio of 18 : 24 equals 3 : 4.
In one day A does 1/18 and B does 1/24, so together they do 7/72. In 6 days they finish 42/72 = 7/12, leaving 5/12 of the job. B alone completes 1/24 per day, so the time needed is (5/12) × 24 = 10 days.
For trains moving in opposite directions, relative speed is the sum: 54 + 36 = 90 km/h, which is 90 × 5/18 = 25 m/s. The distance to be covered is the combined length, 120 + 180 = 300 m. Time = 300 ÷ 25 = 12 seconds.
Downstream speed is 12 + 3 = 15 km/h, so 45 km takes 3 hours. Upstream speed is 12 − 3 = 9 km/h, so the return takes 5 hours. The total time is 3 + 5 = 8 hours; note the option set requires care, as 8 hours is listed first.
A does 1/12 and B does 1/15 of the work per day, so together they do 5/60 + 4/60 = 9/60 = 3/20 per day. The time required is the reciprocal, 20/3 days, about 6.67 days. Adding the individual times would be incorrect.
Milk is 7/10 of 60 = 42 litres and water is 18 litres. For the milk and water to be equal, water must also be 42 litres, so 42 − 18 = 24 litres of water must be added. Only water is added, so the milk quantity stays fixed at 42 litres.
For two years at 10%, the amount factor is 1.21, so the interest factor is 0.21. Setting 0.21P = 630 gives P = 630 ÷ 0.21 = 3000. The sum is therefore ¥3,000, which can be checked since 3000 grows to 3630, an interest of 630.
Because the order of selection does not matter, this is a combination: 8C3 = (8 × 7 × 6) ÷ (3 × 2 × 1) = 56. Using permutations would overcount each committee by the 6 orders in which its members could be listed.
There are 36 equally likely outcomes. Sums of 9 arise from (3,6), (4,5), (5,4) and (6,3), which is 4 outcomes, so the probability is 4/36 = 1/9. Counting ordered pairs is essential because each die is distinct.
There are 4 kings and 13 hearts, but the king of hearts is counted in both, so the favourable count is 4 + 13 − 1 = 16. The probability is 16/52 = 4/13. The subtraction avoids double-counting the overlapping card.
The rectangle's perimeter is 2 × (18 + 10) = 56 cm, so the square's side is 56 ÷ 4 = 14 cm. The area of the square is 14 × 14 = 196 cm². Equating perimeters first, then squaring the side, is the required order of operations.
The volume of a cylinder is πr²h. Here r² = 49, so the volume is (22/7) × 49 × 10 = 22 × 7 × 10 = 1540 m³. Cancelling 49 with 7 before multiplying keeps the arithmetic simple.
If the amount factor over two years is 1.44, the one-year factor is the square root of 1.44, which is 1.20. The rate is therefore 20% per annum. Taking the square root is necessary because the growth compounds each year.
A 20% gain on a selling price of ¥60 means the cost of the mixture is 60 ÷ 1.2 = ¥50 per kg. By the rule of alligation, the ratio of the ¥40 to the ¥60 variety is (60 − 50) : (50 − 40) = 10 : 10 = 1 : 1. The selling price must first be converted to cost price.
The total work is 12 × 15 × 8 = 1440 worker-hours. With 18 workers at 6 hours a day, the daily effort is 108 worker-hours, so the time is 1440 ÷ 108 = 13⅓ days. Combining both the worker count and the hours per day is essential.
Convert the speed to metres per second: 72 × 5/18 = 20 m/s. Crossing a pole means the train covers its own length, so the length is 20 × 9 = 180 m. The conversion factor 5/18 is the critical step.
For two years, the CI − SI difference equals P × (r/100)². Here that is P × 0.01 = 50, so P = 5000. The difference arises because compound interest charges interest on the first year's interest.