PSAT Math : PSAT Mathematics
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Example Questions
Example Question #11 : Evaluating Expressions
Let x&y = xy – x + y. Which of the following is equal to 5&3 ?
11&(0&2)
3&(5&2)
2&(8&1)
4&(3&4)
8&(2&0)
11&(0&2)
First, we need to evaluate 5&3.
Since x&y = xy – x + y, we can find 5&3 as follows:
5&3 = 5(3) – 5 + 3
= 15 – 5 + 3
= 13
Now, we need to go through each of the choices and determine which one equals 13.
Let's start with 2&(8&1). Remember that we must first evaluate inside the parantheses.
2&(8&1) = 2&(8(1) – 8 + 1)
= 2&(8 – 8 + 1)
= 2&(1)
= 2(1) – 2 + 1 = 1, which doesn't equal 13.
Next, let's evaluate 4&(3&4).
4&(3&4) = 4&(3(4) – 3 + 4)
= 4&(13) = 4(13) – 4 + 13 = 61.
Next, we can evaulate 8&(2&0).
8&(2&0) = 8&(2(0) – 2 + 0)
= 8&(–2) = 8(–2) – 8 + 2 = –22.
Next, let's find 3&(5&2).
3&(5&2) = 3&(5(2) – 5 + 2)
= 3&(7) = 3(7) – 3 + 7 = 25.
Finally, lets evaluate 11&(0&2).
11&(0&2) = 11&(0(2) – 0 + 2)
= 11&(2) = 11(2) – 11 + 2 = 13.
The answer is 11&(0&2).
Example Question #12 : Evaluating Expressions
x is 75% of y, which is 8 times the amount of 150% of z. What is x in terms of z?
7.5z
12z
6z
None of the other answers
9z
9z
Just take this step by step. First write out each equation:
x = 0.75y
y = 8(1.5z)
First, simplify the second equation:
y = 12z
Then, substitute y from this equation into the first:
x = 0.75(12z) = 9z
Example Question #2492 : Sat Mathematics
2x + 6y = 44
What is x + 3y + 33?
81
55
77
The answer cannot be determined
23
55
The key to solving this question is noticing that we can factor out a two:
2x + 6y = 44 is the same as 2(x + 3y) = 44
Therefore, x + 3y = 22
In this case, x + 3y + 33 is the same as 22 + 33 or 55
Example Question #13 : Evaluating Expressions
John has four more dollars than four times the amount of dollars that Sandy has.
Peter has three times that of John.
Sandy has $20.
How much money does Peter have?
252
60
84
288
64
252
Let's make 3 equations based on our data:
J = 4S + 4
P = 3J
S = 20
All we have to do is sequentially replace values.
Substitute 20 for S in the J equation:
J = 4 * 20 + 4 = 84
Now, we can calculate P: P = 3 * 84 = 252
Example Question #21 : Expressions
There are 42 marbles in a bag. Half are red. The remaining ones are green and blue. There are five more blue marbles than green ones. How many marbles are there of each type?
21 Red, 16 Blue, 5 Green
None of the other answers
21 Red, 13 Blue, 8 Green
21 Red, 8 Blue, 13 Green
4 Red, 15 Blue, 21 Green
21 Red, 13 Blue, 8 Green
Rewrite our question as a set of equations:
R + G + B = 42
R = 42/2 = 21
Therefore, we already know:
G + B = 21
Also, we know that B = 5 + G
Replace that value into the B + G equation:
G + 5 + G = 21 → 2G + 5 = 21 → 2G = 16; G = 8
Therefore, we know that there are 5 + 8 or 13 blue marbles.
The total is therefore 21 Red, 13 Blue, 8 Green
Example Question #22 : Expressions
The operation x || y is evaluated as: 3x – 14y
What is the value of 5 || (6 || 2)?
140
–10
155
None of the other answers
–235
155
The operation x || y is evaluated as: 3x – 14y
What is the value of 5 || (6 || 2)?
Do this in parts. Start with 6 || 2:
6 || 2 = 3 * 6 – 14 * 2 = 18 – 28 = –10
This leaves us with:
5 || –10 = 3 * 5 – (14 * –10) = 15 – (–140) = 15 + 140 = 155
Example Question #1051 : Psat Mathematics
If the first term of a sequence is 15 and each term is 8 more than the previous term, what is the 24th term of the sequence?
184
191
199
207
199
Taking 23 terms * 8 = 184; adding the original term of 15 yields 199.
Example Question #12 : Expressions
If f(x) = 5x/a, and g(x) = ax/10, what is f(2) + g(5)?
a/10
a
(20+a2)/2a
5a
10
(20+a2)/2a
(20+a2) / 2a is the answer. Find a common denominator to add the 2 fractions after plugging in the values. So we get 10/a + a/2 after plugging in the values. The lowest common denominator would be 2a. Mutiply 10/a by 2/2, and multiply a/2 by a/a. The new equation appears as 20/2a + a2/2a. Add them together to get (20 + a2)/2a.
Example Question #18 : Evaluating Expressions
(√(4) + √(16))2 = ?
√30
20
6
36
√20
36
If we use order of operations (PEMDAS), the answer is 36.
Example Question #19 : Evaluating Expressions
x * y = –a, a – x = 2a. What is y?
-2
a
-a
1
Insufficient Information.
1
Use the second equation to find x in terms of a. Plug it back in the second equation, that will give you 1 = y.
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