First, convert all scores to percentages: \(0.76 = 76%\); \(7/10 = 0.7 = 70%\); \(85%\) is already a percentage. To have an average of 80% on four tests, the sum of the scores must be at least \(4 \times 80% = 320%\). The sum of her first three scores is \(76% + 70% + 85% = 231%\). Let the fourth score be x. Then \(231% + x \ge 320%\). Subtracting 231% from both sides gives \(x \ge 89%\). The lowest score she can get is 89%.

Evaluate Column A: Convert 0.2% to a decimal by dividing by 100, which gives 0.002. Then, \(0.002 \times 1,000 = 2\). Evaluate Column B: Convert 1,000% to a decimal by dividing by 100, which gives 10. Then, \(10 \times 0.2 = 2\). Since both columns evaluate to 2, the quantities are equal.

Let's express the increase in Column A as a percentage. The fraction \(1/5\) is equal to \(1 \div 5 = 0.20\), which is \(20%\). So, Column A represents P increased by 20%. Column B represents P increased by 25%. Since P is a positive number, an increase of 25% will result in a larger value than an increase of 20%. Therefore, the quantity in Column B is greater.

This question tests the ISEE middle level quantitative reasoning skill of converting between fractions, decimals, and percents. Understanding this concept involves knowing that fractions, decimals, and percents are different representations of the same value and can be converted through place value understanding. To convert 0.125 to a fraction, we recognize that 0.125 = 125/1000, which simplifies by dividing both numerator and denominator by 125, giving us 1/8. The correct answer choice B (1/8) is correct because 0.125 = 125/1000 = 1/8 when fully simplified. A common mistake would be selecting 125/10 (choice A) by misunderstanding decimal place value, or 8/1 (choice C) by inverting the correct answer. To help students master this skill, teaching strategies should emphasize understanding decimal place values (0.125 has three decimal places, so the denominator is 1000). Recognizing that 0.125 is half of 0.25, which is 1/4, can help students see that 0.125 must be 1/8.

This question tests the ISEE middle level quantitative reasoning skill of converting between fractions, decimals, and percents. Understanding this concept involves knowing that fractions, decimals, and percents are different representations of the same value and can be converted through multiplication or division by 100. To convert the decimal 0.20 to a percent, we multiply by 100, which gives us 0.20 × 100 = 20%. The correct answer choice B (20%) is correct because it accurately follows the conversion method of multiplying a decimal by 100 to get a percent. A common mistake would be selecting 2% (choice A) by incorrectly moving the decimal point only one place, or 200% (choice C) by confusing the conversion direction. To help students master this skill, teaching strategies should emphasize that moving the decimal point two places to the right when converting to percent is the same as multiplying by 100. Practice with real-world shopping scenarios helps students understand that 0.20 off means a 20% discount.

This question tests the ISEE middle level quantitative reasoning skill of converting between fractions, decimals, and percents. Understanding this concept involves knowing that fractions, decimals, and percents are different representations of the same value and can be converted through multiplication or division by 100. To convert 25% to a fraction, we write it as 25/100 and then simplify by dividing both numerator and denominator by their greatest common factor, which is 25, giving us 1/4. The correct answer choice A (1/4) is correct because 25% = 25/100 = 1/4 when simplified. A common mistake would be selecting 3/4 (choice B), which represents the amount still to be paid rather than the discount amount. To help students master this skill, teaching strategies should focus on understanding that percent means 'per hundred' and practicing simplification of fractions. Visual representations like pie charts showing 25% as one quarter of a circle can reinforce this concept.

This question tests the ISEE middle level quantitative reasoning skill of converting between fractions, decimals, and percents. Understanding this concept involves knowing that fractions, decimals, and percents are different representations of the same value and can be converted through multiplication or division by 100. To convert 1/8 to a percent, we first convert to a decimal by dividing: 1 ÷ 8 = 0.125, then multiply by 100 to get 12.5%. The correct answer choice B (12.5%) is correct because 1/8 = 0.125 = 12.5%. A common mistake would be selecting 8% (choice A) by confusing the denominator with the percent value, or 125% (choice D) by forgetting the decimal point. To help students master this skill, teaching strategies should include recognizing common fraction-percent equivalents like 1/8 = 12.5%. Using visual models of dividing a whole into 8 parts and calculating what percent one part represents reinforces this conversion.

Let the original price be P. A 20% increase means the new price is \(P + 0.20P = 1.20P\). We are given that this new price is $54.00. So, \(1.20P = 54\). To find the original price P, divide 54 by 1.2: \(P = 54 / 1.2 = 540 / 12 = 45\). The original price was $45.00.

Calculate the savings for Plan X: The discount is 25% of $200, which is \(0.25 \times 200 = $50\). Now, calculate the savings for Plan Y. The first discount is 15% of $200, which is \(0.15 \times 200 = $30\). The sale price is \($200 - $30 = $170\). The second discount is \(1/10\) of this sale price, which is \((1/10) \times 170 = $17\). The total savings for Plan Y is \($30 + $17 = $47\). Plan X offers a saving of $50, and Plan Y offers a saving of $47. Plan X is the better plan. The difference in savings is \($50 - $47 = $3.00\).

Let the original price be $100. The first discount is 25%, so the sale price is $100 - (0.25 * $100) = $75. The second discount is 1/5 off the sale price. 1/5 is equivalent to 20%. The additional discount is 20% of $75, which is 0.20 * $75 = $15. The total discount is the sum of the two discounts: $25 + $15 = $40. As a percentage of the original $100 price, the total discount is 40%.