*Read the following SAT test question and then select the correct answer.*

For all math problems, read the problem carefully. Identify your bottom line, and assess your options for reaching that bottom line. Select the most efficient method to work the problem, and attack the problem. Your last step is to loop back and make sure that the answer addresses the bottom line.

*On the line above, if AB < BC < CD < DE, which of the following must be true?*

(A)

*AC*<*CD*
(B)

*AC*<*CE*
(C)

*AD*<*CE*
(D)

*AD*<*DE*
(E)

*BD*<*DE*
You must decide which of the answer choices is true. This is a “which of the
following” question, and it would be really difficult to predict an answer
choice, so start with answer choice (

*E*).
(E)

*BD*<*DE*
Normally you cannot depend on a drawing that has the words "Note: Figure not drawn to scale" underneath it, but this particular line follows the rule that each line segment is longer than the last. Once you have ascertained that the image matches the information that you have been given, you can use the image to draw conclusions. You can look at the line provided and see that this does not have to be true:

*BD*actually looks longer than*DE.*You can also think of*BD*as*BC*+*CD*. You don’t have any information to compare*BC*+*CD*and find out whether it is less than*DE*. One way of proving this is to imagine that*AB*is 1,*BC*is 2,*CD*is 3 and*DE*is 4. That fits*AB < BC < CD < DE*. However, 2 + 3 is not less than 4. Eliminate (E).
(D)

*AD < DE*
Look back at the line. You can clearly see that

*AD*is longer than*DE*. Eliminate (D).
(C)

*AD < CE*
This one is not obvious
from a glance at the line. Think of

*AD*as*AB + BC + CD*and*CE*as*CD + DE*. Both equations share*CD*, but do we know that*AB + BC*is smaller than*DE*? No. Think about what would happen if*AB*had a high value. Suppose that*AB*= 10,*BC*= 11,*CD*= 12 and*DE*= 13. In that case*AD*would be 33 while*CE*would only be 25, and this answer choice would be false. Eliminate (C).
(B)

*AC < CE*
Think of

*AC*as*AB + BC*and*CE*as*CD + DE*. Compare the two. You know that*AB*must be smaller than*CE*and*BC*must be smaller than*DE*. What you really have is: small number + small number < big number + big number. Is that always true? Yes. You do not have to check the last answer choice.
The correct answer is (B).

On sat.collegeboard.org, 70% of
the responses were correct.

For more help with math, visit www.myknowsys.com!

For more help with math, visit www.myknowsys.com!