Gre verbal Reasoning and Quantitative Reasoning With Explanations

The correct
answer is Choice A, Quantity A is greater
. 
9. 
Quantity A 
Quantity B 
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Explanation
Set up the initial comparison: 
Then simplify: 
Step 1: Subtract 2
w
from both sides and add 4 to both sides to get 
Step 2: Divide both sides by 5 to get 
20

---

The comparison cannot be simplified any further. Although you are given that 
you still 
don't know how 
w
compares to or 1.8. For example, if 
then 
but 
if 
then 
In other words, the relationship between 
w
and cannot be 
determined. Note that each of these simplification steps is reversible, so in reverse order, 
each simplification step implies that the 
relationship cannot be determined
in the preceding 
comparison. Thus, the relationship between Quantities A and B cannot be determined. 
The
correct answer is Choice D
, 
the relationship cannot be determined from the
information given
. 
The strategy of simplifying the comparison works most efficiently when you note that a 
simplification step is reversible while actually taking the step. Here are some common steps 
that are always reversible: 
•
Adding any number or expression to both sides of a comparison
•
Subtracting any number or expression from both sides
•
Multiplying both sides by any nonzero number or expression
•
Dividing both sides by any nonzero number or expression
Remember that if the relationship is an 
inequality
, multiplying or dividing both sides by 
any 
negative
number or expression will yield the 
opposite
inequality. Be aware that some 
common operations like squaring both sides are generally not reversible and may require 
further analysis using other information given in the question in order to justify reversing 
such steps.