GRE数学比大小题型的解题思路
GRE数学比较两个数的大小,一般可以用作差法,作商法,代数法以及列表达式等方法。
作差法是指两数相减,将相减之后的结果与0比较大小就行,例如x-y>0,就可以判断x>y。
3<x<5
Quantity A:(3+x)/3 Quantity B:(5+x)/x
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.
【解析】两数做差(3+x)/3-(5+x)/x=x/3-5/x=(x^2-15)/3x,因为3<x<5,所以分母3x>0,但是分子x^2-15可能的符号无法确定,所以(x^2-15)/3x与0无法比较大小,所以选D。
作商法是指两数相除,将相除之后的结果与1比较大小就行,例如x/y>1,就可以判断x>y>0或者x<y<0,所以这个方法一般是在确定两数的符号的时候用。
The average(arithmetic mean)height for a group of m men is 70 inches and the average(arithmetic mean)height for a group of f woman is 64 inches.When the groups are combined ,the average height is 66 inches.
Quantity A:m Quantity B:f
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.
【解析】利用十字交叉法可以将两数做商,m/f=(66-64)/(70-66)=1/2<1,而且m,f指的是人数,都为正整数,所以m<f,选B。
代数法即带入不同的数字,一般适用于无法比较大小的情况,通过列举不同的数字,发现两数的大小无法判断。
n is a positive integer.
n is not divisible by 4.
n is not divisible by 5.
Quantity A:The remainder when n is divided by 4 Quantity B:The remainder when n is divided by 5
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.
【解析】举例:6除以4余2,除以5余1,2>1即QA>QB;9除以4余1,除以5余4,1<4即QA<QB,所以选D。
|x|≥1
|y|<(1/2)
Quantity A:X/Y
Quantity B:Y/X
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.
【解析】x≤-1或者x≥1 -1/2<y<1/2
举例:x=1,y=1/4,那么x/y=4,y/x=1/4,QA>QB
x=1,y=-1/4,那么x/y=-4,y/x=-1/4,QA<QB
无法比较x/y和y/x,所以选D。
列表达式是指把题干描述的信息用表达式列出来,或者将几个未知数都用同一个未知数来表示,从而比较大小。
Yesterday, Carl had 40 percent more CDs than Karen had. Today, Carl gave 20 percent of his CDs to Karen.
Quantity A:Number of CDs that Carl now has
Quantity B:Number of CDs that Karen now has
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.
【解析】假设Carl原来有CDs的数量是C,Karen原来有CDs的数量是K。那么C=1.4K
QA:C(1-20%)=0.8*1.4K=1.12K
QB:K+20%C=K+0.2*1.4K=1.28K
所以QA<QB,选B。
以上就是GRE数学比大小题型的解题思路分享了,希望对大家有所帮助!



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