Testprep数学精解
PLE SCORE BELOW 500.
(2) THE HIGHEST GMAT SCORE IS 800 AND THE LOWEST SCORE IS 200.
MANY STUDENTS MISTAKENLY THINK THAT (1) IMPLIES THE AVERAGE IS 500. SUPPOSE
JUST 2 PEOPLE TAKE THE TEST AND ONE SCORES 700 (ABOVE 500) AND THE OTHER SCO
RES 400 (BELOW 500). CLEARLY, THE AVERAGE SCORE FOR THE TWO TEST-TAKERS IS N
OT 500. (2) IS LESS TEMPTING. KNOWING THE HIGHEST AND LOWEST SCORES TELLS US
NOTHING ABOUT THE OTHER SCORES. FINALLY, (1) AND (2) TOGETHER DO NOT DETERM
INE THE AVERAGE SINCE TOGETHER THEY STILL DON’T TELL US THE DISTRIBUTION OF
MOST OF THE SCORES. THE ANSWER IS E.
7. THE SET S OF NUMBERS HAS THE FOLLOWING PROPERTIES:
I) IF X IS IN S, THEN 1/X IS IN S.
II) IF BOTH X AND Y ARE IN S, THEN SO IS X + Y.
IS 3 IN S?
(1) 1/3 IS IN S.
(2) 1 IS IN S.
CONSIDER (1) ALONE. SINCE 1/3 IS IN S, WE KNOW FROM PROPERTY I THAT 1/(1/3)
= 3 IS IN S. HENCE, (1) IS SUFFICIENT.
CONSIDER (2) ALONE. SINCE 1 IS IN S, WE KNOW FROM PROPERTY II THAT 1 + 1 = 2
(NOTE, NOTHING IN PROPERTY II PREVENTS X AND Y FROM STANDING FOR THE SAME N
UMBER. IN THIS CASE BOTH STAND FOR 1.) IS IN S. APPLYING PROPERTY II AGAIN S
HOWS THAT 1 + 2 = 3 IS IN S. HENCE, (2) IS ALSO SUFFICIENT. THE ANSWER IS D.
8. WHAT IS THE AREA OF THE TRIANGLE ABOVE?
(1) A = X, B = 2X, AND C = 3X.
(2) THE SIDE OPPOSITE A IS 4 AND THE SIDE OPPOSITE B IS 3.
FROM (1) WE CAN DETERMINE THE MEASURES OF THE ANGLES: A + B + C = X + 2X + 3
X = 6X = 180
DIVIDING THE LAST EQUATION BY 6 GIVES: X = 30
HENCE, A = 30, B = 60, AND C = 90. HOWEVER, DIFFERENT SIZE TRIANGLES CAN HAV
E THESE ANGLE MEASURES, AS THE DIAGRAM BELOW ILLUS