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?
- The two quantities are equal (choice C)
- What should be your first step when trying to solve a quantitative comparison problem?
- 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?
- The relationship cannot be determined (choice D)
- What should you do before attempting detailed calculations in a quantitative comparison?
- 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?
- 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?
- 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?
- 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?
- 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?
- 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?
- 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?
- 40 miles per hour (distance divided by time)
- What is a common error when setting up equations from word problems?
- 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?
- 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'?
- 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?
- 3/8 (3 boys out of 3 + 5 = 8 total students)