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Word Problems Posts

Multiple Choice on the SAT: How to Use the Answer Choices

Contrary to what you may think, the answer choices on the SAT are not designed to trap or trick you! We may describe them as “tricky” or “tempting” but seeing the answer choices can actually be a huge asset on Test Day. After all, we know that 1 of the 5 must be correct! Unlike grid-ins, we can often utilize the answer choices in problem solving questions to help us find the solution and get better SAT scores overall. Here are 5 ways you can make the answer choices work for you on your SAT Test!

For Writing question, remember that “No Error” is a strong option. For Identifying Sentence Error test questions, parts of a sentence are underlined. For this SAT question, Choice (E) is “No Error.” There is not always going to be an error. In fact, about 1/4th of the time, “No Error” is correct! Trust your instincts. If a sentence “sounds” okay, and you’ve checked the other four choices and found no grammatical mistake, the SAT alternative is choice E.

Eliminate (-) or (+) choices in Sentence Completions using your prediction. On test day, don’t simply read the sentence and plug in the answer choices, re-reading the SAT sentence five times. Identify the keywords that relate to the blank and write in your OWN word for the blanks, or at least predict whether the blank is a (+) or (-) word. Ace these tricky SAT questions by then eliminating answer choices that contain words with the opposite word charge!

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SAT Math Practice: Data Interpretation

Interpreting data on the SAT may come in many forms: charts, graphs, tables, or extrapolating information from a reading passage. Mastering all the different ways to interpret data will be an important part of scoring well on the SAT. Only by getting enough test prep, including spending some time in Grockit’s interactive games with trained instructors, will ensure you get the score you want. Make sure to remember the following tips and strategies when faced with a data interpretation question. Then, use them to solve the sample problem below.

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Tips and Strategies for data interpretation questions:

  1. Read the passage before looking at any questions. Reading the question(s) first may mislead you when you’re examining the passage. Although it may seem like you’re targeting your reading, the chances you’ll make a mistake are much greater if you read the question(s) first.
  2. Carefully examine any chart, graph or table. Make sure you know what information the chart, graph or table is relaying. Carefully examine the title and what the x- and y-axes represent. And try to analyze the information in the chart, graph or table.
  3. Don’t be afraid to take notes and/or write out the math. You should never try to compute a data interpretation question without writing down the figures. Although it may take a few seconds longer, the chances you’ll correctly answer the question are much greater if you write out the math.
  4. Look for patterns. If numbers and figures come easily to you, look to see if you can see a pattern in the data. But even if you think you know the answer because there’s a pattern, do the math just to be sure.

Now, keep these tips and strategies in mind as you examine the following example:

What is the average (arithmetic mean) height, in inches, of the 5 students’ mothers?

  1. 60
  2. 62.5
  3. 65
  4. 70
  5. 72

After you examine the graph carefully, you should notice that the y-axis has the height of each student’s mother in inches. That means you will only refer to the information on the y-axis, as the x-axis (height of father) is not relevant to this question. With this in mind, we see that two mothers are 60 inches tall, one is 65 inches tall, and the other two are 70 inches tall. To find the average, we need to add all their heights together and then divide by 5, the total number of mothers. Let’s do the math:

60 + 60 + 65 + 70 + 70 = 325 (all heights together)

325 ÷ 5 = 65 (average height—or arithmetic mean—of the mothers)

Now that we’ve done the math, we can see that C is the right answer!

(There’s another, faster way to solve this problem. If you’re good at noticing patterns, you would’ve seen that the average of the two mothers at 60 inches tall and the other two mothers at 70 inches tall would’ve been 65 inches. This is the same height as the other remaining mother, meaning the average height for all the mothers would be 65. Looking for patterns like this can save you time when completing data interpretation questions, but if you’re stuck, just do the math to get the correct answer.)

Data interpretation questions on the SAT require you to read and examine any charts, graphs or tables closely. Getting enough test prep, which you can get in Grockit’s interactive games, will ensure you’re ready for any data interpretation questions that come your way on test day.

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Inequalities

We can break SAT inequalities questions down into three types: those involving a word problem, those involving algebra and those involving absolute values. Let’s tackle the word problems first.

Word Problems

Do you remember this question on Grockit?

A pulley can handle no more than 800 lbs of weight. It is currently holding 4 steel frames that weigh 112 lbs each. Amanda wants to load as many bricks onto it as she can without it breaking. If x represents the total weight of bricks, in lbs, that she can add, which of the following inequalities could be used to determine possible values of x?

From the question, I have deduced the following information:
• I can have a MAXIMUM of 800 lbs
• I have 4 frames, each weighing 112 lbs. That means, all 4 frames weight 4*112 = 448 lbs
• In addition to the 4 frames, I want to load x lbs in bricks.
I can thus conclude that x + 448 lbs must not exceed 800 lbs or my pulley will break.
In mathematical notation, x + 4(112) < 800 Don’t get tricked if the answer is written as 800 > x + 4(112). This statement is exactly the same as the statement above. 800 is greater than x + 4(112) is the same as x + 4(112) is less than 800.

Algebraic Inequalities

Another type of inequality involves algebra.  Suppose y = 2x + 4 and x < 3 and you need to find an inequality involving y.

  1. Start with the inequality you have x < 3
  2. Look at the equation involving y.  There is a 2x in it.  Since x < 3, that means 2x < 6
  3. If 2x < 6, that means 2x + 4 < 6 + 4 = 10.  Thus 2x + 4 < 10
  4. But 2x + 4 is simply y, so we can conclude that y < 10

The trick is to make your inequality look like the equation.  Can you work the next two examples out on your own?

If 2y = 2x + 4 and x < 3, find an inequality involving y

Answer: Like before, we have 2x < 6 and 2x + 4 < 10.  But now we have 2y < 10, meaning y < 5

If y = -2x + 4 and x < 3, find an inequality involving y

Hint: Don’t forget, that when multiplying an inequality by a negative number, you have to switch the signs.

Answer: If x < 3 , then -2x > -6.  That means that -2x + 4 > -2 so we get y > -2

Absolute Value Problems

The last type of question tests your knowledge of absolute values.  Absolute values are denoted by two straight lines | |.  Absolute values make negative numbers positive.

So |10| = 10 and |-10| = 10 too.

Now that we’ve established what absolute values do, we can solve absolute value inequalities.  Here’s a Grockit question:

A theater company is auditioning for actors to portray the leading character in a new play. The company is looking for actors between the ages of 20 and 40 (inclusive). Which of the following inequalities can be used to determine whether an actor of age a is eligible to audition for the part?

  1. | a-10 | ≤ 40
  2. | a-20 | ≤ 40
  3. | a-30 | ≤ 20
  4. | a-30 | ≤ 10
  5. | a-35 | ≤ 5

The answer is 20 ≤ a ≤ 40. But how do we make that look like one of the inequalities above?

  1. Take the average of 20 and 40.  That’s 30.
  2. Subtract 30 from everything to get 20 – 10 ≤ a – 30 ≤ 40 – 30
  3. You get -10 ≤ a – 30 ≤ 10  Note that the left and right side of the inequality is the same number, except that the one of the left is negative
  4. Now we can say, | a – 30 | ≤ 10

So the answer is clearly choice D.

Can you work out the lower and upper bounds of the other choices?   I’ll do Choice A for you.

Choice A says | a – 10 | ≤ 40.

=> -40 ≤ a – 10 ≤ 40

=> -40 + 10 £ a – 10 + 10 £ 40 + 10

Thus Choice A is effectively saying -30 ≤ a ≤ 50, which is not the answer at all.

Tackling SAT Word Problems

Even the strongest SAT Math student can be troubled by the occasional tough SAT word problem. It’s important not to rush when you read these types of questions. Make sure to read methodically and be confident you understand each part of the problem before you move on. Many students find themselves setting up equations and solving algebraically before they’ve even understood what the question is really asking!

Make sure to circle the question at the end of the word problem. Ask yourself: what do the answer choices represent? Practice will make you faster but when it comes to perfecting your strategy, slow and steady wins the race!

One of the ways you can quickly sharpen your word problem skills is to practice translating English into Math. Certain words and phrases commonly occur in word problems and knowing the Math processes they represent will help you gain confidence. Here are a few examples:

Need more SAT practice? Try this multiple choice practice problem and see if you’re ready for test day!

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