PSAT Math : Expressions

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #41 : Expressions

Fred has $100 in quarters and nickels.  He initially has 260 quarters.  He then exchanges some of his nickels for the dimes of a friend.  He is left with a total of 650 coins (consisting of quarters, dimes and nickels) still worth $100.  How many nickels does Fred have now?

Possible Answers:

Correct answer:

Explanation:

Fred has $100 in quarters and nickels initially.  We are also told that he has 260 quarters.  This is worth $65.  Thus Fred initially has $35 in nickels or 700 nickels.

Fred now exchanges some of his nickels for the dimes of a friend.  He ends up with 650 coins.  We know that Fred started with 960 coins (700 nickels + 260 quarters).  He ends up with 650 coins.  The number of quarters remains unchanged, meaning he now has 390 nickels and dimes.  These must have the same value as the initial 700 nickels, though, since he didn't lose any money.

Now we can finally set up our solution:

Thus Fred has 80 nickels and 310 dimes.

An alternative solution step is to notice that turning nickels into dimes always occurs in exactly one way: 2 nickels to 1 dime.  Every time you do this conversion, you will lose exactly one coin.  We then notice that the number of coins drops from 960 to 650, or drops by 310 coins.  We thus need to get rid of 310 coins.  Since we're only allowed to change nickels into dimes (and lose 1 coin each time), we simply do this 310 times to reach the requisite number of coin losses.  We are left with the proper number of coins with the proper value immediately.  Since every replacement replaced 2 nickels, we also lost  nickels.  Our final number of nickels is thus  nickels.

Example Question #736 : Algebra

Let , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Example Question #737 : Algebra

Tim went to the hardware store to buy nails and screws.  The screws were being sold for $.07 each and the nails were being sold in packs of 40 for $1.30.

If Tim spent $14.80, how many nails did he buy?

Possible Answers:

Correct answer:

Explanation:

Nails are sold in packs of 40 for $1.30.

Screws are $0.07 each.

Since the total is $14.80, we must have a 0 in the hundredths place.  This means that the number of screws must be a multiple of 10 (otherwise it won't be a 0).  Now we are essentially dealing with screws in packs of 10 for $0.70.

Now we have 5 values of  to check.  If  is divisible by 7, then we have the right answer.

What we find is that for  is divisible by 7.

Thus our answer is 6 boxes or 240 nails.

Example Question #738 : Algebra

Twenty percent of a number, , is four greater than the product of that number and six. Which of the following algebraic equations could be used to find ?

Possible Answers:

Correct answer:

Explanation:

The "is" in the question means "equal," so whatever comes before "is" must be equal to whatever comes after. We will find an expression for the information before "is" and an expression for the information after "is," and then we will set these two expressions equal.

Twenty percent of a number can be represented as 0.2n, because 20% expressed as a decimal is 0.2, and because twenty percent "of" a number means the product of that number and twenty percent.

Four greater than the product of a number and six means that we must first find the product of that number and six, and then increase this value by 4.

The product of a number and six means that we must multiply this number by six, which can be represented by 6n. Increasing 6n by 4 can be modeled by the expression 6n + 4, or 4 + 6n (because of the commutative property of addition).

Setting the two expressions equal gives us 0.2n = 4 + 6n .

Example Question #739 : Algebra

Based on the chart, which equation represents the table data?

 

Possible Answers:

Correct answer:

Explanation:

The easiest way to solve this problem is to guess-and-check the answer choices. The equation that can be used to match the table will be correct.

We can see that the values in the table match the equation for each given value. Thus, this must be our answer.

We can also determine certain characteristics from the table itself. For example, as x increases, y(x) decreases. This tells us that there is likely a negative coefficient, which can help narrow down the answer options.

Example Question #740 : Algebra

An elementary school class consists of  boys and  girls. What fraction of the class is female?

Possible Answers:

Correct answer:

Explanation:

There are B+G total students in the elementary school class, so G out of B+G are girls.

Example Question #2512 : Sat Mathematics

What is the sixth term of the sequence: \frac{1}{3}, \frac{1}{2}, \frac{3}{4}, \frac{9}{8} ... ?

Possible Answers:

2

\frac{81}{32}

\frac{3}{2}

\frac{27}{16}

\frac{81}{16}

Correct answer:

\frac{81}{32}

Explanation:

Each term equals the previous term multiplied by \frac{3}{2}.

The fifth term in the sequence is \frac{9}{8} \cdot \frac{3}{2} = \frac{27}{16}.

The sixth term in the sequence is thus \frac{27}{16} \cdot \frac{3}{2} = \frac{81}{32}.

Example Question #2511 : Sat Mathematics

If \dpi{100} \small z-3=n, then \dpi{100} \small 2z=  ?

Possible Answers:

\dpi{100} \small n+3

\dpi{100} \small n

\dpi{100} \small 2n+6

\dpi{100} \small 3n+6

\dpi{100} \small n+6

Correct answer:

\dpi{100} \small 2n+6

Explanation:

Begin by rearranging the equation to solve for z:

\dpi{100} \small z=n+3

This means that \dpi{100} \small 2z=2\left ( n+3 \right ), which can be rewritten as \dpi{100} \small 2n+6.

Example Question #422 : Algebra

The symbol  is defined as follows:

Which of the following is equivalent to ?

Possible Answers:

Correct answer:

Explanation:

Symbols may appear scary, but these problems are often easier than they first appear. Begin by taking the numbers you are given and replacing the letters in the equation with these numbers.

 

We can now solve the equation. Be sure to perform the operations within the parentheses (PEMDAS) first.

The correct answer is 512.

 

Example Question #423 : Algebra

If , then which of the following is equivalent to ?

Possible Answers:

Correct answer:

Explanation:

Begin by solving for

First, square both sides of the equation:

Now, solve for :

Now that we know that  is equal to 6, substitute 6 into the equation we need to solve:

Using the correct order of operations (PEMDAS), we find:

The answer is 19.

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