Checking With Estimation - SHSAT Math

1. A bakery produces 1,847 cupcakes per day. The owner calculates that in 23 days, they will produce 42,481 cupcakes total. To verify this calculation using estimation, what should the owner conclude?
   Answer: The calculation appears correct since $1,800 \times 25 = 45,000$ is reasonably close Round 1,847 to 1,800 and 23 to 25 (or keep 23). 1,800 × 25 = 45,000, which is close enough to 42,481 to confirm the calculation is reasonable. The actual calculation: 1,847 × 23 = 42,481 is correct. Choice B uses 1,900 (too high) but keeps 23. Choice C changes both numbers too drastically. Choice D uses 20 instead of 23, which creates too much error.
2. A water tank holds 2,400 liters. A pump removes water at 18.7 liters per minute. An engineer claims it will take about 2 hours to empty the tank. Which estimation best checks this?
   Answer: Round the rate to 20 L/min; 2 hours is 120 minutes, so 20 × 120 = 2,400 L, matching the tank volume. When you encounter rate problems asking you to check an engineer's estimate, you're being tested on your ability to use reasonable approximations to verify calculations quickly. To check if 2 hours is reasonable to empty a 2,400-liter tank at 18.7 liters per minute, you need to estimate how much water gets removed in 2 hours. The key insight is rounding 18.7 to a friendly number that makes mental math easier. Choice A demonstrates the correct approach: round 18.7 to 20 L/min, convert 2 hours to 120 minutes, then calculate $20 \times 120 = 2,400$ liters. This matches the tank capacity exactly, confirming the engineer's 2-hour estimate is reasonable. Choice B makes a poor rounding decision by using 10 L/min instead of 20. Since 18.7 is much closer to 20 than 10, this creates an unrealistic underestimate that removes only 1,200 liters in 2 hours. Choice C abandons the estimation approach entirely by calculating exactly, defeating the purpose of a quick check. While mathematically sound, it's unnecessarily complex for verification. Choice D shows a fundamental misunderstanding by adding the rate and volume, which has no mathematical meaning in this context. Strategy tip: When checking estimates in rate problems, round to numbers that make multiplication easy (like 20 instead of 18.7), and always convert time units to match your rate. The goal is quick verification, not precise calculation.
3. A recipe calls for 3.75 cups of flour per batch. Diego mistakenly thinks 5 batches need 28 cups of flour. Which quick estimation best checks if his total is reasonable?
   Answer: Round 3.75 up to 4 cups, multiply by 5 to get 20 cups—Diego's 28 cups is far too high. When you encounter estimation problems, you're being tested on your ability to use rounding and mental math to quickly check whether a calculation is reasonable. The goal isn't precision—it's catching major errors through smart approximation. Let's find what 5 batches actually need. Since each batch requires 3.75 cups, we need $3.75 \times 5$. For quick estimation, round 3.75 to the nearest whole number: 4 cups. Then $4 \times 5 = 20$ cups. Diego's answer of 28 cups is significantly higher than our estimate of 20 cups, suggesting his calculation contains a substantial error. Looking at the wrong answers: Choice B rounds 3.75 down to 3 cups, giving $3 \times 5 = 15$ cups, then incorrectly concludes that 28 is "close" to 15—but 28 is nearly double 15, which isn't close at all. Choice C uses an unnecessarily complicated approach, doubling 3.75 to get about 7.5 cups for 2 batches, then somehow concludes that adding 3 more cups reaches 5 batches (it doesn't—that would only be about 3 batches), arriving at an unreasonably low estimate. Choice D abandons the estimation concept entirely by using the exact value 3.75, then inexplicably multiplies by 8 instead of 5, which doesn't test Diego's work at all. Study tip: For estimation problems, round to the nearest convenient number (usually whole numbers), do the mental math quickly, then compare your estimate to the given answer. If they're far apart, the original calculation likely has an error.
4. A grocery ad lists 4 pounds of apples for $6.36. Howard plans to buy 10 pounds and budgets $15. Does estimation show his budget is enough?
   Answer: Approximate $6.36 as $6.40; 4 lb for $6.40 means 8 lb for $12.80, so 10 lb is about $16—over his budget. When you encounter estimation problems on the SHSAT, you need to make reasonable approximations that simplify calculations while staying close to the actual values. The goal is to get a ballpark figure that helps you make decisions. Let's work through this systematically. Howard needs to estimate whether $15 is enough for 10 pounds of apples when 4 pounds cost $6.36. Choice A uses sound estimation by rounding $6.36 to $6.40 (close to the original). If 4 pounds cost $6.40, then 8 pounds cost $12.80 (doubling both quantity and price). To get from 8 pounds to 10 pounds, you need 2 more pounds. Since 4 pounds cost $6.40, each pound costs $1.60, so 2 pounds cost $3.20. Adding: $12.80 + $3.20 = $16.00, which exceeds Howard's $15 budget. Choice B drastically underestimates by assuming $5 for 4 pounds instead of $6.36—that's off by over $1, making the estimation unreliable. Choice C makes a critical error by claiming that doubling the weight (4 to 8 pounds) doesn't change the cost, which violates basic proportional reasoning. Choice D assumes $1 per pound, but $\frac{6.36}{4} = 1.59$ per pound, so this significantly underestimates the true cost. For estimation problems, make approximations that are reasonably close to the original numbers and maintain proportional relationships. Avoid rounding that changes values too dramatically, as this defeats the purpose of getting a reliable estimate.
5. A student calculated that a car traveling at 68 mph will cover 952 miles in exactly 14 hours. Which estimation best checks whether this calculation is reasonable?
   Answer: $70 \times 14 = 980$ miles, so the answer seems reasonable Round 68 mph to 70 mph and keep 14 hours exact. 70 × 14 = 980 miles, which is very close to the calculated 952 miles, confirming the calculation is reasonable. Choice A incorrectly changes 14 hours to 15 hours. Choice C changes both values unnecessarily. Choice D rounds 68 mph too far down to 60 mph, making the estimation less accurate.
6. A rectangle measures 9.8 cm by 14.2 cm. A student states that its area is about 139 cm². Which mental calculation best evaluates this claim?
   Answer: Round 9.8 to 10 and 14.2 to 14, multiply to get 140 cm², nearly matching 139 cm². When you need to quickly check if a calculation is reasonable, mental math using rounding is your best tool. For area problems, you're looking for a quick way to estimate the product of two dimensions. The most effective approach is to round each dimension to nearby "friendly" numbers that are easy to multiply mentally. Here, 9.8 cm rounds to 10 cm, and 14.2 cm rounds to 14 cm. Multiplying $10 \times 14 = 140$ cm², which is extremely close to the student's claim of 139 cm². This suggests the calculation is reasonable. Let's see why the other approaches fail. Choice B makes a fundamental error by adding the dimensions (9.8 + 14.2 ≈ 24) instead of multiplying them. Adding gives you perimeter, not area, and comparing 24 to 139 makes no sense. Choice C suggests doubling one dimension to estimate area, but $2 \times 9.8 ≈ 20$ has no mathematical relationship to the actual area formula. Choice D rounds too aggressively—rounding 9.8 down to 9 and 14.2 down to 14 gives $9 \times 14 = 126$, which creates unnecessary error and leads to the wrong conclusion that 139 is "far off." Study tip: For estimation problems, round numbers to make mental math easier, but don't round so much that you introduce significant error. When both original numbers are close to their rounded values (like 9.8→10 and 14.2→14), your estimate will be very reliable.
7. A delivery route is 246 miles long. A truck averages 52 miles per hour. The driver claims the trip will take about 4 hours. Which estimation checks this quickly?
   Answer: Round 52 mph to 50 mph; 250 miles ÷ 50 mph ≈ 5 hours, longer than claimed. When you encounter a word problem asking you to check whether an estimate is reasonable, you need to use quick mental math to verify the calculation. This question tests your ability to use rounding and estimation to check if the driver's 4-hour claim makes sense. The correct approach is option A: Round 52 mph to 50 mph, then calculate 250 miles ÷ 50 mph = 5 hours. Since the actual trip should take about 5 hours, the driver's claim of 4 hours is too optimistic. This estimation method uses simple rounding (246 → 250, 52 → 50) to create numbers that are easy to divide mentally. Option B contains flawed logic. Doubling the speed to 100 mph and getting 2.5 hours doesn't confirm that 4 hours is correct at the actual speed of 52 mph. The calculation is mathematically sound but irrelevant to checking the driver's estimate. Option C makes no sense mathematically. Adding speed (52 mph) and distance (246 miles) gives you nothing meaningful since you can't add different units. This violates basic principles of unit analysis. Option D uses an arbitrary speed of 25 mph instead of the given 52 mph. While it correctly identifies that 10 hours would make 4 hours too short, it's not checking the driver's claim using the actual conditions of the problem. Study tip: For estimation problems, always round to numbers that make mental math easy (like 50 or 100), keep your units consistent, and remember that $\text{time} = \frac{\text{distance}}{\text{speed}}$.
8. A smartphone battery drains 3.8% per hour while streaming. If the phone starts at 92% charge, a student predicts it will be empty after 20 hours. Which estimation best tests that prediction?
   Answer: Round 3.8% to 4%; 4% × 20 = 80%, so charge drops from 92% to about 12%, not empty. When you encounter estimation problems, you're being asked to check whether a rough calculation supports or contradicts a given prediction. The key is finding a reasonable approximation that's easy to calculate while staying close to the original values. Let's test the student's prediction that the phone will be empty after 20 hours. Starting at 92% charge with a 3.8% drain per hour, we need to estimate how much battery will remain. Choice A provides the best estimation approach: rounding 3.8% to 4% makes the math simple while staying very close to the actual rate. After 20 hours: $4\% \times 20 = 80\%$ total drain. Starting at 92%, the phone would drop to approximately $92\% - 80\% = 12\%$, meaning it wouldn't be empty. This directly contradicts the student's prediction. Choice B uses 5% per hour, which is too far from 3.8% to be a good estimation—it inflates the drain rate by over 30%. Choice C uses 2% per hour, which severely underestimates the actual drain rate. Choice D unnecessarily complicates the estimation by doubling the rate and halving the time, creating a "safety margin" that isn't asked for and makes the estimation less accurate. The best estimations for testing predictions stay close to the original values while simplifying calculations. Here, rounding 3.8% to 4% achieves both goals and clearly shows the student's prediction is wrong. Strategy tip: When estimating, round to the nearest "friendly" number that keeps calculations simple but doesn't stray too far from the original—typically within 10-15% of the actual value.
9. Patricia read 18 pages on Friday, 37 pages on Saturday, and 46 pages on Sunday. She says she read about 120 pages over the weekend. Which estimation is the quickest check?
   Answer: Round 18 to 20, 37 to 40, 46 to 50; add 20 + 40 + 50 ≈ 110, slightly less than 120. When you encounter estimation problems, you're looking for the method that gives you the most reasonable approximation with the least work. The key is balancing accuracy with efficiency. Let's check Patricia's claim by examining each approach. The actual total is $18 + 37 + 46 = 101$ pages, so her estimate of 120 pages is indeed too high. Choice A uses systematic rounding: 18 becomes 20, 37 becomes 40, and 46 becomes 50. Adding these gives $20 + 40 + 50 = 110$. This is close to Patricia's claim of 120 but noticeably lower, suggesting her estimate might be high. This method is both quick and accurate for checking reasonableness. Choice B only considers the two larger numbers: $37 + 46 = 83$. While this shows that even without the smallest number you're already at 83, it ignores a significant portion (18 pages) and doesn't give you a complete picture for comparison. Choice C multiplies the smallest number by 3: $18 \times 3 = 54$. This severely underestimates since it assumes all three days had the minimum reading amount, which clearly isn't the case given the much larger numbers for Saturday and Sunday. Choice D doubles the largest number: $46 \times 2 = 92$. This also underestimates and doesn't account for the third day of reading at all. For estimation problems on the SHSAT, look for methods that account for all given values while using simple rounding. Systematic rounding to nearby tens or hundreds typically provides the best balance of speed and accuracy.
10. Jason calculated that if he walks at 3.2 mph for 2 hours and 45 minutes, he will cover approximately 8.8 miles. Using estimation, how should he check this result?
    Answer: Convert to $3 \text{ mph} \times 3 \text{ hours} = 9 \text{ miles}$, which confirms the calculation When checking calculations through estimation, you want to round numbers to simple values that make mental math easy while staying reasonably close to the original numbers. Let's examine what Jason should do. He needs to estimate $3.2 \text{ mph} \times 2\text{ hours } 45\text{ minutes}$. First, convert the time: 2 hours 45 minutes = 2.75 hours. For estimation, the smartest approach is rounding 3.2 mph down to 3 mph and 2.75 hours up to 3 hours. This gives us $3 \times 3 = 9 \text{ miles}$, which is very close to Jason's calculated 8.8 miles, confirming his work is reasonable. Choice A rounds 3.2 up to 3.5 and keeps 2.75 as 2.75 - this isn't practical estimation since 2.75 requires more complex mental math. Choice B rounds time down to 2.5 hours, which is too far from the actual 2.75 hours (45 minutes is much closer to an hour than to 30 minutes). Choice C compounds the problem from choice A by also rounding time up to 3 hours, making the estimate too far from the original values. Choice D uses the most reasonable rounding strategy and produces an estimate closest to Jason's answer. The key insight is that good estimation involves rounding to numbers that make calculation simple while keeping your estimate reasonably close to the original problem. When your estimate confirms the calculated answer (as 9 miles confirms 8.8 miles), you can be confident in your work.
11. Sasha walked 2.4 miles on Monday, 3.1 miles on Tuesday, and 4.7 miles on Wednesday. She claims she walked about 13 miles in total. Which estimation gives the quickest check of her claim?
    Answer: Round each distance to the nearest mile: 2 + 3 + 5 ≈ 10 miles, so her claim is too high. When you encounter estimation problems, you're looking for the method that gives you a quick, reasonable approximation to check whether a claim makes sense. The goal isn't perfect accuracy—it's efficient verification. Let's examine what happens when you round each distance to the nearest whole mile: 2.4 becomes 2, 3.1 becomes 3, and 4.7 becomes 5. Adding these gives you $2 + 3 + 5 = 10$ miles. Since Sasha claims she walked about 13 miles, but your quick estimate shows only 10 miles, her claim appears too high. This is exactly what choice A demonstrates. Choice B rounds everything up (ceiling function), giving 3 + 4 + 5 = 12 miles. While this seems to support Sasha's claim, rounding up artificially inflates the total, making it less accurate than standard rounding. Choice C defeats the purpose entirely—adding decimals precisely (2.4 + 3.1 + 4.7 = 10.2) isn't estimation at all, and it actually proves her claim is wrong, not exact. Choice D uses an illogical strategy of doubling just Tuesday's distance, which has no mathematical basis for estimating a three-day total. The key insight is that standard rounding to the nearest whole number typically provides the most balanced estimate. Since even this generous approach (rounding 4.7 up to 5) only yields 10 miles, Sasha's claim of 13 miles is clearly too high. Study tip: When checking estimates, use standard rounding first—it's usually the most reliable quick method and avoids the bias of always rounding up or down.
12. A landscaper must spread 48 cubic yards of mulch. Each wheelbarrow holds 5.2 cubic feet. He estimates he will need about 250 wheelbarrow loads. Which of the following mental approximations best checks his estimate?
    Answer: Convert 48 cubic yards to about 1,300 cubic feet and divide by 5, giving roughly 260 loads—close to the estimate. When you encounter word problems involving different units of measurement, the key is converting to compatible units before doing any calculations. This problem tests your ability to mentally check whether an estimate makes sense by using reasonable approximations. To verify the landscaper's estimate of 250 wheelbarrow loads, you need to convert 48 cubic yards to cubic feet, then divide by the wheelbarrow capacity. Since there are 27 cubic feet in a cubic yard, 48 cubic yards equals $48 \times 27 = 1,296$ cubic feet. For mental math, this rounds to about 1,300 cubic feet. Dividing by the wheelbarrow capacity of 5.2 cubic feet (approximately 5) gives $1,300 \div 5 = 260$ loads. This confirms the estimate of 250 is reasonable. Choice A correctly follows this logic and arrives at roughly 260 loads, validating the estimate. Choice B uses a reasonable conversion to 1,000 cubic feet but then incorrectly divides by 10 instead of 5, yielding only 100 loads. Choice C makes a major conversion error, calculating 48 cubic yards as only 162 cubic feet—this completely ignores that cubic yards are much larger than cubic feet. Choice D skips the essential unit conversion entirely, comparing cubic yards directly to cubic feet, which is meaningless. Remember: when checking estimates in multi-step problems, each step must use compatible units. Always convert first, then calculate. The SHSAT often includes answer choices that reflect common mistakes like skipping conversions or using wrong conversion factors.
13. Each week a bookstore's profit grew by 12% over the previous week. After 5 weeks a clerk estimates the total growth to be about 60%. Which estimation best checks the clerk's figure?
    Answer: Raise 1.12 to the 5th power, noting it is about 1.76, or 76% growth, so 60% is too low. Growth of 12% per week compounds: each week's profit is 1.12 times the previous week's, so after 5 weeks the profit is multiplied by $1.12^5$. Compute in steps: $1.12^2 = 1.2544$, $1.12^4 \approx 1.2544^2 \approx 1.574$, and $1.12^5 \approx 1.574 \times 1.12 \approx 1.76$. That is about 76% total growth, so the clerk's 60% is too low. Multiplying 12% by 5 to get 60% treats the growth as simple, ignoring that each week's 12% is taken on a larger amount, so it understates the total. Squaring 12% to get 144% has no connection to five weeks of growth. Adding 12 and 5 to get 17% mixes a percent with a number of weeks.
14. A stairway has 14 steps, each 18 cm high. An architect converts the total rise to about 8 feet. Which estimation checks this conversion?
    Answer: 14 × 18 cm ≈ 252 cm; 1 ft ≈ 30 cm, so 252 ÷ 30 ≈ 8.4 ft, close to 8 ft. This question tests your ability to check unit conversions using estimation techniques—a crucial skill for avoiding calculation errors on the SHSAT. To verify the architect's conversion, you need to find the total height in centimeters, then convert to feet. The total rise is $14 \times 18 = 252$ cm. Since 1 foot equals about 30.48 cm, you can estimate 1 ft ≈ 30 cm for quick checking. Dividing: $252 \div 30 = 8.4$ feet, which is very close to the architect's estimate of 8 feet. This confirms the conversion is reasonable. Choice A correctly follows this logical approach with appropriate estimations. Choice B makes an error by doubling 18 cm first (getting 36 cm per step), which artificially inflates the total to 504 cm and 16 feet—this method has no mathematical basis. Choice C incorrectly adds the number of steps (14) to the height per step (18 cm) instead of multiplying, then falsely claims 32 cm equals 1 foot. Choice D assumes each step is 1 foot high, ignoring the given 18 cm measurement entirely, leading to a wildly inaccurate 14-foot total. When checking unit conversions, always follow the logical sequence: calculate the quantity in the original units first, then convert using reasonable approximations. Watch for answer choices that use operations incorrectly (adding instead of multiplying) or make unjustified assumptions about measurements. Quick estimation with rounded conversion factors (like 30 cm ≈ 1 ft) helps you verify answers efficiently.
15. To tile a floor, 1 box covers 18.2 square feet. A room is 11.5 ft by 14 ft. A contractor orders 8 boxes. Which estimation best checks if 8 boxes will likely be enough?
    Answer: Estimate the room as 12 ft by 14 ft for about 168 ft²; 8 boxes cover roughly 8 × 18 ≈ 144 ft², probably not enough. When you encounter estimation problems involving area and coverage, you need to make reasonable approximations that simplify calculations while staying close to the actual values. Let's find the room's area first: $11.5 \times 14 = 161$ square feet. With 8 boxes covering $8 \times 18.2 = 145.6$ square feet, there's clearly not enough material since 145.6 < 161. Now let's examine how well each estimation approach works. Choice A rounds 11.5 ft to 12 ft, giving $12 \times 14 = 168$ ft². It estimates box coverage as $8 \times 18 \approx 144$ ft². Since 144 < 168, this correctly predicts insufficient coverage and closely matches the actual calculation. Choice B rounds to $10 \times 15 = 150$ ft² and estimates 8 boxes cover "about 200 ft²." This box coverage estimate is wildly inaccurate—$8 \times 18.2 = 145.6$, not 200. This leads to the wrong conclusion that coverage is sufficient. Choice C suggests doubling the longer side to 28 ft, which creates an entirely different room ($11.5 \times 28 = 322$ ft²) that bears no resemblance to the original problem. Choice D assumes each box covers only 10 ft² instead of 18.2 ft², drastically underestimating box coverage and ignoring the room size entirely. Study tip: Good estimation maintains the essential relationships in the original problem. Round numbers to make calculations easier, but keep your estimates reasonably close to actual values. Dramatic changes to given numbers usually lead to meaningless results.
16. A factory produces 468 bolts per hour. During an 8-hour shift the manager predicts 3,600 bolts will be produced. Which mental calculation best evaluates whether this prediction is reasonable?
    Answer: Approximate 468 as 450; 450 × 8 = 3,600, matching the prediction closely. When you encounter estimation problems, you're being tested on your ability to choose approximations that make mental math easier while staying reasonably close to the original numbers. The key is finding the best approximation for 468 that makes multiplying by 8 simple. Let's evaluate each approach: Choice C approximates 468 as 450, giving us $450 \times 8 = 3,600$. This matches the manager's prediction exactly and uses a reasonable approximation since 450 is only 18 away from 468. Choice A rounds 468 to 500, yielding $500 \times 8 = 4,000$. While this makes the multiplication easy, 500 is 32 away from 468 – a larger approximation error that leads to concluding 3,600 is "a bit low" when it's actually quite accurate. Choice B approximates 468 as 400, giving $400 \times 8 = 3,200$. This 68-unit difference from the original creates a significant underestimate, making 3,600 appear "too high by a wide margin" when the prediction is actually reasonable. Choice D uses 300, which is 168 away from 468 – far too low an approximation. This gives $300 \times 8 = 2,400$, making the prediction seem "greatly overstated" when it's not. Strategy tip: For estimation problems, choose approximations that balance computational ease with accuracy. Numbers ending in 50 or 00 are usually easiest to work with, but pick the one closest to your original value. Don't automatically round to the nearest hundred – sometimes rounding to a "nice" number like 450 gives you both accuracy and simple arithmetic.
17. A plumber charges a $65 service fee plus $42.50 per hour. For a 3.5-hour job, a homeowner was billed $215 in total. Which estimation best judges if the bill is reasonable?
    Answer: Use $40 per hour: 3.5 × 40 = $140; add $65 to get about $205, so $215 is close. When you encounter word problems involving service charges plus hourly rates, you need to estimate both components and check if your result is close to the given total. Let's work through the correct estimation. The actual rate is $42.50 per hour, which rounds nicely to $40 per hour for estimation purposes. For 3.5 hours: $3.5 × 40 = 140$. Adding the $65 service fee gives us $205, which is very close to the actual bill of $215. This confirms the bill is reasonable. Now let's examine why each choice works or fails: Choice A correctly uses $40 per hour (close to the actual $42.50), properly includes the service fee, and reaches $205 — close enough to $215 to verify the bill is reasonable. Choice B uses $50 per hour, which overestimates the hourly rate significantly. This leads to $240 total, making the actual $215 seem low when it's actually correct. Choice C ignores the service fee entirely, a major error since the $65 fee is substantial. Without including this fixed cost, the estimation is meaningless for checking the total bill. Choice D compounds two errors: it rounds 3.5 hours up to 5 hours (a significant overestimate) and uses the rounded hourly rate, leading to $265 total. This makes the correct bill seem unreasonably low. Strategy tip: In estimation problems with multiple components, round each piece reasonably but don't skip any major parts. Service fees, hourly rates, and time worked all matter. Your estimate should be close enough to judge reasonableness, not necessarily exact.
18. A store sells items with a 15% discount. A customer calculated that an item originally priced at $78.40 will cost $66.64 after the discount. To verify this calculation using estimation, what approach should be used?
    Answer: Estimate: $15\%$ of $\$80 = \$12$, so final price $\approx \$68$, which is close to $66.64 When you encounter a question asking you to verify a calculation using estimation, you're being tested on your ability to use mental math and rounding to quickly check if an answer is reasonable. The correct approach is option C because it uses smart rounding and applies the discount properly. By rounding $78.40 up to $80, you get a nice round number that's easy to work with. Then, $15\%$ of $\$80 = 0.15 \times 80 = \$12$. Subtracting this discount: $\$80 - \$12 = \$68$. This estimate of $68 is very close to the calculated $66.64, confirming the calculation is reasonable. Option A fails because it uses $10\%$ instead of the actual $15\%$ discount, leading to an underestimated discount and an inflated final price of $72. Option B makes two errors: it uses $20\%$ (too high) and doesn't round $78.40 to make the calculation easier, yet still gets a final price that's too low. Option D misses the point entirely—it's doing exact calculation, not estimation, which defeats the purpose of quickly verifying an answer. For estimation problems on the SHSAT, always round to numbers that make mental math easy (like multiples of 10), but keep your rounding reasonable—don't round $78.40 to $100. Use the correct percentages given in the problem, and remember that estimation should get you close to the exact answer, not exactly match it.
19. A rectangular garden is to be fenced on all four sides. Its length is 23.4 meters and width is 17.8 meters. A brochure quotes 85 meters of fencing. Which estimation tests this quote?
    Answer: Round to 24 m and 18 m; perimeter ≈ 2(24 + 18) = 84 m, matching the quote. When you encounter a fencing or perimeter problem, you need to calculate how much material goes around the entire border. For a rectangle, the perimeter formula is $P = 2(length + width)$ or $P = 2l + 2w$. The correct approach is shown in choice A. You round 23.4 meters to 24 meters and 17.8 meters to 18 meters, then calculate: $P = 2(24 + 18) = 2(42) = 84$ meters. This estimation of 84 meters closely matches the quoted 85 meters, confirming the quote is reasonable. Choice B makes a fundamental error by multiplying length times width (24 × 18 = 432), which gives you area in square meters, not perimeter in linear meters. You can't fence an area measurement. Choice C only adds the length and width once (23.4 + 17.8 = 41.2), giving you half the perimeter. This represents only two sides of the rectangle, not the complete fence needed for all four sides. Choice D doubles only the length (2 × 23.4 ≈ 47), which accounts for two long sides but completely ignores the two short sides that also need fencing. Remember: perimeter problems always require going around the entire shape. For rectangles, you need two lengths plus two widths. When estimating, round to convenient numbers first, then apply the correct formula. Watch out for the common trap of calculating area instead of perimeter—area uses multiplication, perimeter uses addition of all sides.
20. A baker needs 5.6 kilograms of sugar for a recipe scaled up by a factor of 6. The original recipe calls for 0.92 kilograms. The baker's figure is questioned. Which estimation best checks it?
    Answer: Round 0.92 to 1 kg; 1 × 6 = 6 kg, so 5.6 kg is close. When you encounter a problem asking you to check whether a calculation is reasonable, you need to use estimation to quickly verify if the answer makes sense. The baker claims that scaling up a recipe by a factor of 6 means multiplying the original amount by 6. Let's check: if the original recipe needs 0.92 kg of sugar, then scaling up by 6 should give us $0.92 \times 6 = 5.52$ kg. The baker's figure of 5.6 kg is indeed very close to this exact calculation. Choice A correctly demonstrates good estimation technique. By rounding 0.92 to 1 kg (a reasonable approximation), then multiplying by 6 to get 6 kg, we can see that 5.6 kg is reasonably close to our estimate. This confirms the baker's calculation is likely correct. Choice B makes a fundamental error by adding instead of multiplying. When scaling a recipe, you multiply each ingredient by the scale factor, not add the scale factor to the original amount. Choice C arbitrarily multiplies by 10 instead of 6, which has nothing to do with the scaling factor mentioned in the problem. Choice D uses 0.5 kg instead of 0.92 kg, making the estimation too far from the original amount to be useful for checking the calculation. Strategy tip: For estimation problems on the SHSAT, round to numbers that make mental math easy (like 1 instead of 0.92), but make sure you're using the correct operation. Always ask yourself: "Does my estimated answer land in the same ballpark as the given answer?"

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