Cognitive Ability Complete Review Guide 2026–2027

4. Profit and loss (percentages): selling price = cost × (1 + profit rate) or × (1 − loss rate), and cost = selling price ÷ that same factor.
5. Successive changes (percentages): multiply the change factors in order; a 20% then 10% discount = 0.8 × 0.9 = 0.72, i.e. a total discount of 28%.
6. Dividing in a ratio (ratio and proportion): add the parts of the ratio, divide the total by that sum to get the value of one part, then multiply by each share's parts.
7. Inverse proportion (ratio and proportion): workers × days = a fixed amount of work; when three quantities change together, multiply by the direct factor and divide by the inverse one.
8. Joint work (word problems): add the work rates; if one finishes in a hours and the other in b hours, together they take (a × b) ÷ (a + b); when one fills and the other drains, subtract the rates.
9. Motion of two bodies (word problems): in the same direction subtract the speeds, in opposite directions add them, then apply distance = speed × time.
10. Ages (word problems): the age difference between two people never changes, and each person ages by the same number of years; write both current ages, then add or subtract the years from both.
11. Days of the week (word problems): divide the number of days by 7; the remainder is how many days to count forward from the given day, and with no remainder it is the same weekday.
12. Unit conversion (arithmetic): 1 km = 1000 m, 1 m = 100 cm, 1 kg = 1000 g, 1 litre = 1000 ml, 1 hour = 60 minutes = 3600 seconds, 1 riyal = 100 halalas; multiply when going from larger to smaller units and divide when going from smaller to larger.
13. Measures of central tendency (arithmetic): mean = sum of values ÷ their count; median = the middle value after sorting (or the mean of the two middle values when the count is even); mode = the most frequent value.
14. Periodic events (arithmetic): if two events repeat every 4 days and every 6 days, they coincide every 12 days, the least common multiple of the two numbers.
15. Common series patterns (number series): a constant difference, a constant ratio, differences that grow regularly (constant or doubling second differences), two alternating rules, squares and cubes, each term being the sum of the previous two, or multiplying by 1, then 2, then 3.
16. Reading direction (number series): in Arabic text the series reads from right to left, so the first term is on the right, and the blank may be at the start, in the middle or at the end.
17. Two-way check (number series): confirm the rule with a second independent method, such as differences and then a general-term formula; the series 3, 6, 11, 18 has differences 3, 5, 7 and is also position squared + 2, and both give the next term 27.
18. Share in a table (charts and tables): a category's share = its value ÷ the row or column total × 100, and growth between two years = (new − old) ÷ old × 100.

Common mistakes in this chapter

• ✕ Increasing and then decreasing by the same percentage does not return to the original: 100 increased by 10% is 110, and 110 decreased by 10% is 99, not 100.
• ✕ A 20% discount followed by 10% is not a 30% discount but 28%, because the second discount applies to the reduced price; the 30% option is a common trap.
• ✕ Profit, loss and percentage change are calculated on the original value (cost price or old value), not on the new value.
• ✕ The number of posts or trees along an open line = distance ÷ gap + 1, doubled for both sides of the road; forgetting the +1 gives a ready-made wrong option.
• ✕ 'Between' is not 'from … to': the number of people between positions 5 and 12 is 12 − 5 − 1 = 6, while the number of pages from 40 to 60 is 60 − 40 + 1 = 21.
• ✕ The average speed for a round trip is not the mean of the two speeds: going at 60 km/h and returning at 40 km/h gives 2 × 60 × 40 ÷ 100 = 48 km/h, not 50.
• ✕ Mixing units: 45 minutes is 0.75 hours, not 0.45 hours, and a chart axis labelled 'in thousands' means 12 stands for 12,000.
• ✕ In series, a rule may fit only the first two or three terms; the correct rule fits every term, and an option that repeats a term already in the series is usually not the answer.