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Quantitative Reasoning: The Four Question Formats

The four shapes a GRE quant question can take, plus the on-screen calculator - starting with quantitative comparison, where most points are quietly lost.

12 topics · 50 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

Quantitative Comparison: The Four Fixed Answer Choices

  1. How it worksHow do the four choices map onto Quantity A greater, Quantity B greater, the two equal, and cannot be determined?
  2. How it worksWalk me through reading a comparison item so you never flip Quantity A greater and Quantity B greater by accident.
  3. Worked exampleFind which is greater when Quantity A is 3 to the 4th power and Quantity B is 4 to the 3rd power.
  4. Common mistakeWhy isn't there ever a fifth choice, like both quantities are negative, on a GRE comparison item?
  5. Going furtherWhat happens to the four choices when both quantities turn out to be the same number written two ways?
Your turnhard1 of 3
Quantity A is 3 raised to the power 7. Quantity B is 7 cubed.

Quantitative Comparison: Cannot Be Determined

  1. How it worksHow does finding two cases that point opposite ways prove a relationship cannot be determined?
  2. Worked exampleFind the relationship between Quantity A equal to x squared and Quantity B equal to x cubed with no restriction on x.
  3. Common mistakeWhy isn't cannot be determined the right choice just because a comparison item contains a variable?
  4. Common mistakeWhy doesn't a messy-looking comparison mean the relationship is genuinely undetermined?
  5. Going furtherWhat happens to cannot be determined once an item pins the variable to one single value?
Your turnhard1 of 3
x is any nonzero number. Quantity A is x squared. Quantity B is 7 times x.

Quantitative Comparison: Compare, Don't Compute

  1. How it worksHow do you strip matching pieces off both quantities until only the real difference is left?
  2. Worked exampleCompare 17 times 23 against 16 times 24 without multiplying either pair out.
  3. Common mistakeWhy doesn't computing both quantities in full count as the safe way to answer a comparison item?
  4. Worked exampleFind which is greater, 7 over 9 or 8 over 11, without converting either fraction to a decimal.
Your turnhard1 of 3
Quantity A is 25 times the sum of 25 and 7. Quantity B is 25 minus 1, times the sum of 25, 7 and 1.

Quantitative Comparison: Simplifying Both Sides in Parallel

  1. How it worksHow do you add, subtract or divide the same thing on both sides of a comparison without breaking it?
  2. How it worksWalk me through why multiplying both quantities by a negative number reverses which one is bigger.
  3. Worked exampleCompare Quantity A equal to 3x plus 7 with Quantity B equal to 7 plus 2x when x is greater than 0.
  4. Common mistakeWhy isn't cross multiplying two fractions in a comparison safe when a denominator could be negative?
Your turnhard1 of 3
Quantity A is x divided by 5, plus 7. Quantity B is the quantity x plus 5 times 7, all divided by 5.

Quantitative Comparison: Testing Strategic Values

  1. How it worksHow does one value that makes A bigger and another that makes B bigger settle an item instantly?
  2. Worked exampleFind the relationship between Quantity A equal to x and Quantity B equal to x squared by testing 0, one half and 2.
  3. Worked exampleCompare Quantity A equal to 1 over n with Quantity B equal to n when n is any nonzero number.
  4. Common mistakeWhy doesn't testing three numbers that all agree prove the relationship holds for every number?
  5. Going furtherWhat extra test values do you need once an item says the variable has to be an integer?
Your turnmedium1 of 3
n is any nonzero number smaller than 154. Quantity A is 1 divided by n. Quantity B is n.

Quantitative Comparison: Restricted Domains and Given Conditions

  1. How it worksHow does a stated restriction shrink the set of test numbers you are allowed to try?
  2. Going furtherWhat happens to a comparison when the restriction rules out every value that made the sides disagree?
  3. Worked exampleCompare Quantity A equal to x squared with Quantity B equal to x when x is between 0 and 1.
  4. Common mistakeWhy isn't a condition like y is not zero the same as a condition saying y must be positive?
Your turnhard1 of 3
x is between 0 and 1. Quantity A is x raised to the power 4. Quantity B is x.

Quantitative Comparison: The Errors That Cost Points

  1. How it worksHow do you spend under two minutes on a comparison item and know the moment to guess and move on?
  2. Common mistakeWhy isn't the bigger-looking expression automatically the greater quantity on a comparison item?
  3. Worked exampleFind the relationship when Quantity A is the average of 10 and 20 and Quantity B is the average of 12 and 18.
  4. Going furtherWhat changes in your approach when a comparison item shows a figure that is not drawn to scale?
Your turnhard1 of 3
Quantity A is the average of 20 and 43. Quantity B is the average of 20 plus 8 and 43 minus 8.

Multiple-choice: Select One Answer Choice

  1. How it worksHow do the answer choices themselves tell you whether to estimate or to compute exactly?
  2. Worked exampleFind the approximate cost of gasoline for a 350 mile drive at 33 miles per gallon and 2.95 per gallon.
  3. Common mistakeWhy isn't the number sitting at the end of your scratch work always the number the question asked for?
  4. Going furtherWhat happens when you work backwards from the middle answer choice instead of solving forwards?
Your turnmedium1 of 3
A car travels 35 miles on one gallon and gasoline costs 3.41 dollars per gallon. Write, in terms of m, the cost in dollars of driving m miles.

Multiple-choice: Select One or More Answer Choices

  1. How it worksHow do you judge each choice on its own merits instead of comparing the choices against each other?
  2. Common mistakeWhy isn't the number of correct choices always stated somewhere in the question stem?
  3. Worked exampleFind every value among 8, 12, 15, 18, 21 and 36 that is a multiple of both 2 and 3.
  4. Going furtherWhat changes when a select-all question asks for values in a range rather than items on a list?
  5. Ties togetherHow does pinning down the least and greatest possible average turn a select-all item into a range check?
Your turnmedium1 of 3
A select-all item offers 7 answer choices, and at least one must be selected. Find how many different selections a test taker could submit.

Numeric Entry: The Single Answer Box

  1. How it worksHow do you check units, rounding and order of magnitude before typing a numeric entry answer?
  2. Common mistakeWhy isn't 46.7 an acceptable entry when a question asks for the answer rounded to the nearest integer?
  3. Worked exampleFind the total cost of 18 pens at 25 cents each and 100 markers at 35 cents each.
Your turneasy1 of 3
Find the total cost, in dollars, of 24 pens at 33 cents each together with 135 markers at 36 cents each.

Numeric Entry: Fractions in Two Boxes

  1. How it worksHow do you enter a fraction answer when the numerator and the denominator get their own boxes?
  2. Going furtherWhat happens if you type 20 over 80 when the fully reduced answer would be 1 over 4?
  3. Common mistakeWhy doesn't the calculator's Transfer Display button work on a two-box fraction answer?
Your turneasy1 of 3
A jar holds 15 red marbles and 21 blue marbles. Find the fraction of the marbles that are red, as a decimal.

The On-Screen Calculator and When to Skip It

  1. How it worksHow does the on-screen calculator follow order of operations differently from a cheap pocket calculator?
  2. Worked exampleWalk me through computing the square root of 21 squared plus 54 squared without the root swallowing one term.
  3. Going furtherWhat happens on the GRE calculator when a result runs past eight digits or you divide by zero?
  4. Ties togetherHow does estimating first protect you from a mis-keyed calculator answer on a percent problem?
Your turneasy1 of 3
Find the square root of the sum of 46 squared and 59 squared.

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