根據官方指南,GMAT 數學中可能出現的考點可歸為四大類:算術、代數、幾何、應用題。具體涉及的概念如下:
算術:整數性質、分數、小數、實數、比值及比例、百分比、次方及次方根、描述性統計、集合、排列組合、離散概率;
代數:代數式化簡、方程、解一元一次方程、解二元一次方程組、因式分解、解二次方程、指數運算、不等式、絕對值、函數;
幾何:直線、相交線及角度、垂線、平行線、凸多邊形、三角形、四邊形、圓、長方體及圓柱體、座標幾何;
應用題:速率問題、工作效率問題、混合物問題、利率問題、打折問題、利潤問題、集合問題、幾何問題、單位換算問題、圖表數據理解。
對於廣大中國考生而言,GMAT 數學通常不是一項特別高要求的挑戰,然而這並不意味著考試中所有題目都易如反掌:首先,GMAT 數學部分不允許參試者使用計算器 ,這一方面對手算的可靠度提出了要求,另一方面也迫使考生在某些原本可依賴計算器的題目中必須動腦筋巧算;其次,數論、集合容斥原理、排列組合、概率等幾個概念可稱得上是相對的難點,尤其對於數學基礎本不雄厚的文科生而言,更可能帶來不小困難;另外,GMAT 數學特有的題型——數據充分性解題思路比較特別,需要考生擁有十分清晰的邏輯思維。
下面就看一看上述幾個難點的例題:
1.數論
例1
If n=20!+17, then n is divisible by which of the following?
I. 15
II. 17
III. 19
A. None
B. I only
C. II only
D. I and II
E. II and III
答案為 C。
例2
When positive integer x is divided by positive integer y, the remainder is 9. If x/y=96.12, what is the value of y?
A. 96
B. 75
C. 48
D. 25
E. 12
答案為 B。
例3
If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?
A. 10
B. 12
C. 14
D. 16
E. 18
答案為 C。
例4
If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?
A. One
B. Two
C. Three
D. Seven
E. Ten
答案為 B。
例5
If n is a positive integer, for which of the following values of k i 25*10^n+k*10^2n divisible by 9?
A. 9
B. 16
C. 23
D. 35
E. 47
答案為 E。
例6
For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12)=2*4*6*8*10*12. What is the greatest prime factor of f(24)?
A. 23
B. 19
C. 17
D. 13
E. 11
答案為 E。
例7
The function f is defined for each positive three-digit integer n by f(n)=(2^x)(3^y)(5^z), where x, y, and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), then m-v=
A. 8
B. 9
C. 18
D. 20
E. 80
答案為 D。
例8
If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is
A. 6
B. 12
C. 24
D. 36
E. 48
答案為 B。
例9
If x and y are positive integers, what is the remainder when 10^x+y is divided by 3?
(1) x=5
(2) y=2
答案為 B。
例10
If a and b are positive integers, what is the value of the product ab?
(1) The least common multiple of a and b is 48.
(2) The greatest common factor of a and b is 4.
答案為 C。
例11
If a, b, and c are consecutive integers and 0
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