LANTITE Numeracy practice questions

A "rise of 5 percentage points" adds 5 directly to the percentage. Term 1 rate = 65%. Term 2 rate = 65 + 5 = 70%. Option A (68.25%) is 65 × 1.05 = 68.25 and confuses percentage points (additive) with percent (multiplicative). 5% reports the rise itself. 95% takes the 5 away from 100. Tip: "percentage points" is additive (5 + 65 = 70); "5% rise" would be multiplicative (1.05 × 65 = 68.25). Watch this distinction in education statistics.

This is a two-step problem: (1) find 15% of the total, then (2) subtract that from the total to get what is left for the program. Step 1: 15% of $3,450. Convert percent to decimal: 15% = 0.15. Multiply: 0.15 × 3,450 = $517.50. Step 2: subtract from the original: 3,450 − 517.50 = $2,932.50. The trap distractor $517.50 is what you get if you stop after step 1 and forget step 2 (it is the admin amount, not what the program receives). Distractor $3,105.00 deducts 10% rather than 15%: 3,450 − 345 = 3,105. Distractor $3,967.50 adds the administration costs instead of subtracting them (3,450 + 517.50).

Step 1: Plan B costs $3 more to connect ($4 - $1). Step 2: each GB costs $1 less on Plan B than on Plan A ($2 - $1), so Plan B gains $1 per GB. Step 3: it takes 3 GB to gain back the $3. Check: at 3 GB, Plan A costs $1 + 3 × $2 = $7 and Plan B costs $4 + 3 × $1 = $7 ✓. Option A (2) gives $5 on Plan A and $6 on Plan B, which are not equal. Option B (5) added the two connection fees ($1 + $4). Option D (7) is the matching cost in dollars, not the amount of data. Tip: read what the question asks for, GB or dollars.

The total number of sheets needed comes from the number of students and the pages in each worksheet, which are 28 and 3. To turn that into packs you also need the number of sheets in one pack, 500. Option B (28 and 500) leaves out the pages in each worksheet. Option C (3 and 500) leaves out the number of students. Option D (28 and 3) gives the total sheets needed but not the size of a pack.

A rate of 14.5 students for each teacher describes the whole region on average, so on average there are 14.5 students for each teacher, even though no teacher has half a student. Option B (Each teacher has exactly 14.5 students) is wrong, because a rate is an average and the classes differ. Option C (There are 14.5 teachers in each school) is wrong, because the rate is about students. Option D (Each class has 14.5 teachers) is wrong for the same reason.

A rate of 6% means 6 out of every 100, so each $100 borrowed costs $6 in interest each year. Option A ($6 is charged on every loan) is wrong, because the interest depends on the amount borrowed. Option B ($60 interest is charged each year for every $100) would be 60%. Option C (The bank pays the borrower 6% each year) reverses who pays the interest.

Compare decimals place by place, not as whole numbers. Writing 0.6 as 0.60 gives 60 hundredths against 45 hundredths, so 0.6 is the larger number. Option A (Jake is right, because 6 is smaller than 45) treats the digits after the point as a whole number, which they are not. Option B (Jake is right, because 0.6 has fewer digits so it is a smaller number) mixes up the number of digits with the size of the number. Option D (The numbers are equal because they both start with 0) ignores the digits after the point.

Add the 2 hours to get 3:40 pm, then add 35 minutes: 3:40 + 20 minutes is 4:00, and 15 more minutes is 4:15 pm. Option A (4:15 pm) is correct. Option B (3:75 pm) adds the minutes without carrying into the hour. Option C (4:05 pm) adds only 25 minutes. Option D (3:15 pm) takes the 2 hours 35 minutes away from the time instead of adding.

Fencing goes round the outside edge, which is the perimeter. A rectangle has 2 lengths and 2 widths, so the fence is 2 × 40 + 2 × 25 = 130 m. Option B (40 × 25) gives the area inside the paddock, not the distance round it. Option C (40 + 25) adds one length and one width, which is only half of the way round. Option D (2 × 40 × 25) doubles the area, which has no meaning for a fence.

A ratio scale compares equal units, so 1 cm on the plan stands for 200 cm in real life. There are 100 cm in 1 m, so 200 cm is 2 m. Option D (1 cm on the plan stands for 2 m in real life) is correct. Option A (1 cm on the plan stands for 200 m in real life) forgets that both numbers are in centimetres. Option B (1 cm on the plan stands for 20 m in real life) changes 200 cm to metres by dividing by 10. Option C (1 cm on the plan stands for 0.2 m in real life) divides by 1,000 instead of 100.

A bath is deep enough to sit in and holds roughly a hundred or more litres of water, so 150 L is reasonable. Option A (150 mL) is only about half a cup. Option B (15 L) is about the size of a large bucket. Option C (15,000 L) is the size of a small backyard swimming pool.

The median is the middle value when data is sorted: it splits the dataset into two equal halves. So half the students scored at most 75 and half scored at least 75. Answer: Half scored at most 75; half scored at least 75. Distractor "most common is 75" describes the mode. "Most students scored above 75" - false (only half do, by definition). "Total ÷ count = 75" describes the mean. The three "averages" are different concepts and shouldn't be confused.

The interquartile range (IQR) spans from Q1 to Q3 and contains the middle 50% of the data. Q1 (58) is the 25th percentile (25% scored below); Q3 (82) is the 75th percentile. So half the students scored between 58 and 82. Answer: 58 and 82. Distractor 32-96 is the full range (100%). 32-82 = lower 75%. 70-96 = upper half but not the middle 50%.

Truncated y-axis (starting above zero) is a classic graph-deception trick. Without showing the full scale from 0, small differences appear visually larger because the visible range is compressed. A bar going from 80 to 90 looks dramatic on a 80-100 axis but tiny on a 0-100 axis. Answer: Larger (exaggerated). Distractor analysis: The same would only hold if the axis started at zero - truncation always changes the visual proportions. Smaller is the opposite of what truncation does - the trick amplifies differences, never minimises them. Inverted would require flipping the axis direction (e.g. high values at bottom), which truncation does not do. Always check the y-axis when interpreting bar charts - does it start at zero?

A chance of 90% is a probability of 0.9, close to 1, so rain is very likely though not certain. "Unlikely" would suit a small chance such as 10%. "An even chance" would suit 50%. "Certain" would need a chance of 100%, and 90% leaves a 10% chance that it will not rain.