| Column A | Column B |
|---|
| The sum of all integers from 19 to 50, including 19 and 50 | The sum of all integers
from 21 to 51, including 21 and 51 |
Explaination
The correct answer is (B). The two number strings have in common integers
21 through 50. So you can subtract (or cancel) all of these integers from both
sides of the comparison. That leaves you to compare (19 1 20) to 51. You can
now see clearly that Quantity B is greater.
Avoid Multiplying or Dividing Across Columns
To help simplify the two expressions, you can also multiply or divide across columns,
but only if you know for sure that the quantity you’re using is positive. Multiplying or
dividing two unequal terms by a negative value changes the inequality; the quantity
that was the greater one becomes the smaller one. So think twice before performing
either operation on both expressions.
Example
| Column A |
| Column B |
|---|
| x > y |
|
| x2y |
| xy2 |
Explaination
The correct answer is (D). To simplify this comparison, you may be tempted
to divide both columns by x and by y—but that would be wrong. Although you
know that x is greater than y, you don’t know whether x and y are positive or
negative. You can’t multiply or divide by a quantity unless you’re certain that
the quantity is positive. If you do this, here is what could happen: Dividing
both sides by xy would leave the comparison between x and y. Given x > y,
you’d probably select (A). But if you let x = 1 and y = 0, on this assumption,
both quantities = 0 (they’re equal). Or let x = 1 and y = - 1. On this
assumption, Quantity A = -1 and Quantity B = 1. Since these results conflict
with the previous ones, you’ve proven that the correct answer is choice (D).
Solve Centered Equations for Values
If the centered information includes one or more algebraic equations and you need to
know the value of the variable(s) in those equations to make the comparison, then
there’s probably no shortcut to avoid doing the algebra.
Example
| Column A |
| Column B |
|---|
| x + y = 6
x - 2y = 3 |
|
| x |
| y |
Explaination
The correct answer is (A). The centered information presents a system of
simultaneous linear equations with two variables, x and y. The quickest way to
solve for x is probably by subtracting the second equation from the first:
x + y = 6
-( x - 2y = 3)
3y = 3
y = 1
Substitute this value for y in either equation. Using the first one:
x + 1 = 6
x = 5
Since both equations are linear, you know that each variable has one and only
one value. Since x = 5 and y = 1, Quantity A is greater than Quantity B.
Don’t Rely on Geometry Figure Proportions
For Quantitative Comparison questions involving geometry figures, never try to make
a comparison by visual estimation or by measuring a figure. Even if you see a note
stating that a figure is drawn to scale, you should always make your comparison
based on your knowledge of mathematics and whatever nongraphical data the
question provides, instead of “eyeballing” it.
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