加(add, plus)→和(sum)
减(subtract)→差(difference)
乘(multiply, times)→积(product)
除(divide)→商(quotient)
例: The sum of the numbers x, 3x-y and 2y+4 is subtracted from 15. In terms of x and y, what is the result?
(A) 11-4x-3y
(B) 11-4x-y
(C) 11+2x-3y
(D) 19-4x-y
(E) 19+2x-3y
分析: “ A is subtracted from B ”这一常见表达表示从B中减去A,故选择B。
例: If 13 is added to 2 more than one-half of a certain number, the result is 37. What is the original number?
(A) 24
(B) 40
(C) 44
(D) 61
(E) 80
分析: “add”和“add to”都有加上的意思,但add仅是加上后面的数,而add to是加上后面的整个部分。比如“1 add 2 minus 3”表示“1+2-3”,而“1 is added to 2 minus 3”表示“1+(2-3)”。因此,本题有13+ =37x=44,选C。
例: If a number x is increased by 2 and the result is squared, the final value will be 49. Which of the following could be the value of x?
(A) -9
(B) -7
(C) -5
(D) -3
(E) -1
分析: “A is increased/decreased by B”表示A增加/减少 了 B,另一个容易与之混淆的表达是“A is increased/decreased to B” A增加/减少 到 B,请大家注意区分。
“A is squared”是将A平方的意思,等价的表达有“square A”,“the square of A”等。由此题目所要表达的是(x+2) 2 =49,两边开方。从所给选项看x+2为负,故选择A。
例: If 8+x is 4 more than 16, what is the value of 2x?
分析: “A more/less than B”表示比B多/少A,故得到8+x=16+4, x=24。
例: If multiplying k by 7 gives the same result as squaring k, which of the following must be true?
(A) 7+k 2
(B) k 2 +k=7
(C) k 2 +7k=1
(D) 7k=1
(E) 7k=k 2
分析: “multiply A by B”表示用B乘以A,另一种等价的表达是“A is multiplied by B”。故选择E。
练习题
1. If 5 times t is decreased by 8, which of the following represents the result?
(A) 8-5t
(B) 5t-8
(C) 5(t-8)
(D) 5(8-t)
(E) 8(t-5)
2. If 6 times j is 1 more than the square of k, where k is an integer, what is the smallest possible value of j?
(A) -5
(B)
(C) 0
(D)
(E) It cannot be determined form the information given.
3. A number is added to 9 less than the number. If the result is 181, what is the number?
4. The product of 3, 5, 7 is equal to one-half the sum of 20 and x. What is the values of x?
5. By Saturday afternoon, 375 tickets had been sold for a Saturday evening performance at a theater with a capacity of 500 seats. After those 375 tickes were sold, half the members of a group of 210 people each purchased a ticket. If no other tickets were sold prior to the performance, how many tickets remained unsold at the time of the performance?
6. Prime numbers k and n are each greater than 2, and they differ by 4. If there is no prime number between k and n, what is the least possible value of k+n?
习题解答
1. B
2. D
分析: 由题意可得6j=k 2 +1≥1 (k为整数),故当k=0, 6j=1最小。
3. 95
分析: x+(x-9)=181x=95
4. 190
分析: =3·5·7=10520+x=210x=190
5. 20
分析: 该题只是一道简单的减法题,对于这种较长的题目强烈建议大家在读题时及时地将题目中反映出的相关数据和信息转换成数学表达,这样就避免了反复读题浪费时间。
6. 18
分析: “differ by”是相差多少的意思,并不表明量与量之间确切的大小关系,即|k-n|=4。
要使k+n的值最小,则k和n的值都要尽可能小。令k为相对较小的素数,当k=3时,n=7,中间还有素数5不符合题意;当k=5时,n=9,不是素数;当k=7时,n=11, 是素数,且中间没有别的素数,故k+n的最小值为18。