下面是三道
Mathematics > Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
1、At Central High School, the math club has members and the chess club hasmembers. If a total of students belong to only one of the two clubs, how many students belong to both clubs?
Answer Choices
(A)
(B)
(C)
(D)
(E)
The correct answer is C
Explanation
Let stand for the number of students who belong to both clubs. The members of the math club can be broken down into two groups: those who are in both clubs (there are students in this category) and those who are in the math club only (there are students in this category).
The members of the chess club can also be broken down into two groups: students who are in both clubs and students who are in the chess club only.
Since a total of students belong to only one of the two clubs, you know that . Solving this equation gives , so students belong to both clubs。
2、If is divisible by , , and , which of the following is also divisible by these numbers?
Answer Choices
(A)
(B)
(C)
(D)
(E)
The correct answer is D
Explanation
Since is divisible by , , and , must be a multiple of , as is the least common multiple of , , and . Some multiples of are , , , , and .
If you add two multiples of , the sum will also be a multiple of . For example, and are multiples of and their sum, , is also a multiple of .
If you add a multiple of to a number that is not a multiple of , the sum will not be a multiple of . For example, is a multiple of and is not. Their sum, , is not a multiple of .
The question asks which answer choice is divisible by , , and ; that is, which answer choice is a multiple of . All the answer choices are in the form of "plus a number." Only choice (D), , has added to a multiple of . The sum ofand is also a multiple of , so the correct answer is choice (D).
3、In an solution of water and alcohol, the ratio by mass of water to alcohol is to . If grams of a solution consisting of grams water for each gram of alcohol is added to the solution, what fraction by mass of the new solution is alcohol?
Answer Choices
(A)
(B)
(C)
(D)
(E)
The correct answer is B
Explanation
To find what fraction by mass of the new solution is alcohol, you can find how many grams of alcohol are in the final solution of grams. Since the solution is part alcohol to parts water, it is alcohol. So it contains grams of alcohol. Similarly, the solution is alcohol by mass, so it contains grams of alcohol. Thus, the final 20-gram solution contains grams of alcohol, so , or , of it is alcohol.
以上就是这三道SAT数学题的全部内容，每一道SAT数学题后都附有答案解析，非常详细。SAT数学备考的过程就是大家不断做题熟悉考试形式的过程，所以大家在备考SAT数学考试的时候，重点一定要放在掌握SAT数学出题方式上。