Before starting grab:
A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 100 seniors, 150 juniors, and 200 sophomores who applied. Each senior’s name is placed in the lottery 3 times; each junior’s name, 2 times; and each sophomore’s name, 1 time. What is the probability that a senior’s name will be chosen?
- (A) 1/8
- (B) 2/9
- (C) 2/7
- (D) 3/8
- (E) 1/2
In the Selects Univeristy SAT Prep Course, every question type is explained thoroughly first, and then later students are taught how to quickly answer these types of questions, to most efficiently use their time on the SAT Reasoning Test.
For the above question, students will learn the underlying principles of the question types:
When you see the word “probability”, immediately think of either a percentage or a fraction. In this case, all the answers are fractions, meaning we will use fractions to solve this problem.
First, we want to determine how many times a senior’s name will be entered into the draw. If there are 100 students, and each student gets entered 3 TIMES, we know we must multiply (times) these numbers. 3 x 100 seniors = 300 seniors.
The total number of students from which the draw will occur includes the juniors and sophomores as well. Using the same method as above, we determine that there are 2 x 150 juniors, and 1 x 200 sophomores. We want to know the TOTAL number of students, so we will add these values to the seniors. 300 seniors + 300 juniors + 200 sophomores = 800 total students.
Given these values, we see the probability that a senior’s name will be chosen as the number of seniors (300) in the draw over the total number of students (800). 300 seniors / 800 total students.
In its simplest form, 300/800 becomes 3/8. The answer D is correct.
Students will then learn how to streamline the solution process:
100 seniors get 3 entries each…3 x 100 = 300
150 juniors get 2 entries each…2 x 150 = 300
200 sophomores get 1 entry each…1 x 200 = 200
Total = 800
We need the total number of senior entries…300 In simplest form -> 3
And the total number of all entries…800 In simplest form -> 8
Our answer is D, 3/8.
Additional SAT Sample Questions:
Tests your comprehension of what is stated in or implied by the passage.
Sentence completion questions
Tests your vocabulary and your understanding of sentence structure.
You’re asked to solve a problem and pick the best choice offered.
You are not given answer choices. You must solve the problem and “grid in” your answers.
Tests your ability to correct faults in usage and sentence structure, and recognize effective sentences that follow the conventions of Standard Written English.
Identifying sentence errors
Tests your ability to recognize faults in usage, and recognize effective sentences that follow the conventions of Standard Written English.
Tests your ability to revise sentences in the context of a paragraph or the entire essay, organize and develop paragraphs in a coherent and logical manner, and apply the conventions of Standard Written English.
The SAT begins with an essay. You’ll be asked to present and support a point of view on a specific issue. Because you have only 25 minutes, your essay is not expected to be polished – it is meant to be a first draft.
For more information regarding SAT Practice Questions, please visit CollegeBoard.com.