Quantitative Comparison: Stop SOLVING and Start COMPARING

Say you are a dozen questions into a GRE Quant section. The screen shows Quantity A: 37 × 43. Quantity B: 40 × 40. I'll bet your hand is already moving toward the on-screen calculator. Maybe you are already doing long multiplication on your scratch paper. And THAT is the mistake I watch people make every single week.

The question never asked you what 37 × 43 is. It asked which side is BIGGER. Those are two very different jobs, and only one of them earns you the point.

What Quantitative Comparison actually asks

Quantitative Comparison (people call it QC) is one of the question types in the GRE Quantitative Reasoning section. You get two quantities, Quantity A and Quantity B, and sometimes a bit of information above them. Then you pick one of four fixed answers:

1. Quantity A is greater.
2. Quantity B is greater.
3. The two quantities are equal.
4. The relationship cannot be determined from the information given.

That's it. Four answers, the same four, every time. You never have to name a number. You only have to name a RELATIONSHIP.

Stop reading for a second and think about what that means. If you can prove that one side is bigger without knowing the exact value of either side, you are done. Every second you spend finding the exact value after that is wasted time you could spend on the next question. And on a section with 20 questions in 35 minutes, wasted time is the thing that sinks people.

Think like a scale, not a calculator

A calculator gives you a number. A scale tells you which side is heavier. QC is a scale question. Your job is to make both sides simpler until the tilt is obvious.

Let's go back to that opening question and do it the comparing way.

Cancel what both sides share

Here's the move that makes QC feel almost unfair. Anything that sits on BOTH sides in the same way can't change which side is bigger. So you can cross it out. Add the same thing to both sides, subtract the same thing, or multiply both by the same positive number, and the tilt stays the same.

Careful with that last one. Multiplying or dividing both sides by a NEGATIVE number flips the tilt. If you don't know whether a number is positive or negative, don't divide by it.

Variables? Test values, and test them MORE than once

When a QC question has a variable in it, the exact value is often unknown on purpose. That's where the fourth answer, "cannot be determined," lives. Your weapon here is TESTing VALUES: plug in real numbers that fit the rules and see what happens.

The rule I want burned into your head: if two different allowed values give you two different results, the answer is "cannot be determined." You can stop right there.

So which numbers should you test? Run through the weird ones on purpose: 0, 1, a negative, a fraction between 0 and 1, and a big number. Only use the ones the question allows. In that last example, 0 and negatives were off the table because x had to be greater than 0.

The mistakes I see every week

1. Solving both sides all the way to the end. You find two exact numbers, then compare them. It works, but it's the slow road, and every extra step is a chance for a silly mistake. INSTEAD: simplify both sides just until the tilt is clear, then stop.
2. Testing one value and calling it. One value can only show you one result. It can never show you that the answer changes. INSTEAD: test at least two DIFFERENT kinds of numbers, and always try the weird ones the question allows.
3. Picking "cannot be determined" on plain numbers. If both quantities are fixed numbers with no variables and no unknowns, the relationship CAN be determined. It's a real number versus a real number. INSTEAD: when there's nothing unknown, cross off the fourth answer right away.
4. Dividing both sides by a variable you don't understand. If that variable might be negative, you just flipped the scale and didn't notice. INSTEAD: only divide by something you KNOW is positive. Otherwise, test values.
5. Comparing in your head. "It's just two quantities, I don't need notes." That's pride talking, not speed. INSTEAD: write an A column and a B column on your scratch paper for every QC question. Cross out what cancels. Write each test value as its own row. It takes seconds and it saves you from yourself.

Here's the forced choice. What do you want MORE: the satisfying feeling of finding the exact number, or the point? The GRE pays you for the relationship. It does not pay you for the arithmetic.

Your challenge for today

Grab 10 QC questions you have already done. Don't look at your old work. Redo each one with a timer running, and this time you are NOT allowed to find an exact value for either side unless there is truly no other way. Draw your A and B columns, cancel what you can, test at least two values on every question with a variable.

Then compare your new times and your old times. I'll bet several of those questions took you HALF as long the second time. Once you see that on your own paper, you'll never go back to solving both sides again.