（1） ABC is the base word.

　　（2） If C immediately follows B， then C can be moved to the front of the code

　　word to generate another word.

　　From （1）， we cannot determine whether CAB is a code word since （1） gives no

　　rule for generating another word from the base word. This eliminates A and D

　　……

　　Turning to （2）， we still cannot determine whether CAB is a code word since n

　　ow we have no word to apply this rule to. This eliminates B.

　　However， if we consider （1） and （2） together， then we can determine whether

　　CAB is a code word：

　　From （1）， ABC is a code word.

　　From （2）， the C in the code word ABC can be moved to the front of the word：

　　CAB.

　　Hence， CAB is a code word and the answer is C.

　　UNWARRANTED ASSUMPTIONS

　　Be extra careful not to read any moresintosa statement than what is given.

　　？The main purpose of some difficult problems is to lure¹ yousintosmaking an u

　　nwarranted assumption.

　　If you avoid the temptation， these problems can become routine.

　　Example 6： Did Incumbent² I get over 50% of the vote？

　　（1） Challenger C got 49% of the vote.

　　（2） Incumbent I got 25，000 of the 100，000 votes cast.

　　If you did not make any unwarranted assumptions， you probably did not find t

　　his to be a hard problem. What makes a problem difficult is not necessarily

　　its underlying³ complexity⁴； rather a problem is classified as difficult if ma

　　ny people miss it. A problem may be simple yet contain a psychological trap

　　that causes people to answer it incorrectly.

　　The above problem is difficult because many people subconsciously⁵ assume tha

　　t there are only two candidates. They then figure that since the challenger

　　received 49% of the vote the incumbent received 51% of the vote. This would

　　be a valid⁶ deduction⁷ if C were the only challenger （You might ask， “What if

　　some people voted for none-of-the-above？“ But don't get carried away with fi

　　nding exceptions. The writers of the GMAT would not set a trap that subtle）。

　　But we cannot assume that. There may be two or more challengers. Hence， （1）

　　is insufficient⁸

Now， consider （2） alone. Since Incumbent I received 25，000 of the 100，000 vo

　　tes cast， I necessarily received 25% of the vote. Hence， the answer to the q

　　uestion is “No， the incumbent did not receive over 50% of the vote.” Therefo

　　re， （2） is sufficient to answer the question. The answer is B.

　　Note， some people have trouble with （2） because they feel that the question

　　asks for a “yes” answer. But on Data Sufficiency questions， a “no” answer is

　　just as valid as a “yes” answer. What we're looking for is a definite answe

　　r.

　　CHECKING EXTREME CASES

　　？When drawing a geometric figure or checking a given one， be sure to include

　　drawings of extreme cases as well as ordinary ones.

　　Example 1： In the figure to the right， AC is a chord and B is a point on the

　　circle. What is the measure of angle x？

　　Although in the drawing AC looks to be a diameter， that cannot be assumed. A

　　ll we know is that AC is a chord. Hence， numerous cases are possible， three

　　of which are illustrated⁹ below：

　　In Case I， x is greater than 45 degrees； in Case II， x equals 45 degrees； in

　　Case III， x is less than 45 degrees. Hence， the given information is not su

　　fficient to answer the question.

　　Example 2： Three rays emanate¹⁰ from a common point and form three angles with

　　measures p， q， and r. What is the measure of q + r ？

　　It is natural to make the drawing symmetric as follows：

　　In this case， p = q = r = 120， so q + r = 240. However， there are other draw

　　ings possible. For example：

　　In this case， q + r = 180. Hence， the given information is not sufficient to

　　answer the question.

　　Problems：

　　1. Suppose 3p + 4q = 11. Then what is the value of q？

　　（1） p is prime.

　　（2） q = -2p

　　（1） is insufficient. For example， if p = 3 and q = 1/2， then 3p + 4q = 3（3）

　　+ 4（1/2） = 11. However， if p = 5 and q = -1， then 3p + 4q = 3（5） + 4（-1） = 1

　　1. Since the value of q is not unique， （1） is insufficient.

　　Turning to （2）， we now have a system of two equations in two unknowns. Hence

　　， the system can be solved to determine the value of q. Thus， （2） is suffici

　　ent， and the answer is B

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