¡¡¡¡4. What is the value of the two-digit number x£¿
¡¡¡¡£¨1£© The sum of its digits is 4.
¡¡¡¡£¨2£© The difference of its digits is 4.
¡¡¡¡Considering £¨1£© only£¬ x must be 13£¬ 22£¬ 31£¬ or 40. Hence£¬ £¨1£© is not suffici
¡¡¡¡ent to determine the value of x.
¡¡¡¡Considering £¨2£© only£¬ x must be 40£¬ 51£¬ 15£¬ 62£¬ 26£¬ 73£¬ 37£¬ 84£¬ 48£¬ 95£¬ or 5
¡¡¡¡9. Hence£¬ £¨2£© is not sufficient to determine the value of x.
¡¡¡¡Considering £¨1£© and £¨2£© together£¬ we see that 40 and only 40 is common to th
¡¡¡¡e two sets of choices for x. Hence£¬ x must be 40. Thus£¬ together £¨1£© and £¨2£©
¡¡¡¡are sufficient to uniquely determine the value of x. The answer is C.
¡¡¡¡5. If x and y do not equal 0£¬ is x/y an integer£¿
¡¡¡¡£¨1£© x is prime.
¡¡¡¡£¨2£© y is even.
¡¡¡¡£¨1£© is not sufficient since we don't know the value of y. Similarly£¬ £¨2£© is
¡¡¡¡not sufficient. Furthermore£¬ £¨1£© and £¨2£© together are still insufficient sin
¡¡¡¡ce there is an even prime number¡ª¡ª2. For example£¬ let x be the prime number
¡¡¡¡2£¬ and let y be the even number 2 £¨don't forget that different variables can
¡¡¡¡stand for the same number£©¡£ Then x/y = 2/2 = 1£¬ which is an integer. For al
¡¡¡¡l other values of x and y£¬ x/y is not an integer. £¨Plug in a few values to v
¡¡¡¡erify this.£© The answer is E.
¡¡¡¡6. Is 500 the average £¨arithmetic mean£© score on the GMAT£¿
¡¡¡¡£¨1£© Half of the people who take the GMAT score above 500 and half of the peo
¡¡¡¡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.
