Quantitative comparison and word problem strategies tested on the ISEE and SSAT quantitative reasoning sections.
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- In a quantitative comparison problem, if both quantities simplify to the same expression, which answer choice is correct?
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The two quantities are equal (choice C)- What should be your first step when trying to solve a quantitative comparison problem?
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Try to eliminate answer choices by testing simple values (like 0, 1, or -1) or by simplifying the expressions- In a quantitative comparison, if quantity A depends on a variable x and you can prove the answer changes based on x's value, which answer choice applies?
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The relationship cannot be determined (choice D)- What should you do before attempting detailed calculations in a quantitative comparison?
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Look for ways to simplify, factor, or estimate to see if you can eliminate choices without exact computation- In a quantitative comparison, if both quantities are equal when x is positive but unequal when x is negative, what can you conclude?
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The relationship cannot be determined, because it depends on the sign of x- When comparing quantity A = 2x + 3 and quantity B = 2x + 5, what is true regardless of x's value?
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Quantity B is always 2 units larger than quantity A, so B is greater- What is the first step when solving a word problem on the ISEE or SSAT?
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Read carefully and identify what the problem is asking you to find- After identifying what a word problem is asking, what should you do next?
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Define your variable or variables to represent the unknown quantities- How do you translate the phrase 'three times a number decreased by seven' into an algebraic expression?
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3n - 7 (where n represents the number)- If a word problem asks 'what is the average of 10, 15, and 20', what calculation do you perform?
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Add the numbers (10 + 15 + 20 = 45) and divide by how many numbers there are (45 / 3 = 15)- In a rate problem where distance = 120 miles and time = 3 hours, what is the rate?
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40 miles per hour (distance divided by time)- What is a common error when setting up equations from word problems?
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Misinterpreting what the variable represents or setting up the equation backwards (putting x on the wrong side)- If 25 percent of a number is 10, how do you find the whole number?
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Divide 10 by 0.25 to get 40, or set up 0.25x = 10 and solve- What equation represents the statement 'A is what percent of B'?
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A = (P/100) x B, where P is the percent you are solving for- If a ratio of boys to girls in a class is 3 to 5, what fraction of the class are boys?
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3/8 (3 boys out of 3 + 5 = 8 total students)
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