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## Question Explanations For

##
*ONLINE PRACTICE TEST (Calculator Math Test)*

## 1.

The Correct Answer is (D) —
Using FOIL, (3

*x*– 2)(*x*+ 1) = 3*x*^{2}+ 3*x*– 2*x*– 2. This simplifies to 3*x*^{2}+*x*– 2.## 2.

The Correct Answer is (C) —
-16(5)

^{2}+ 128(5) = 240## 3.

The Correct Answer is (A) —
2(-3) – 3(4) = -18

## 4.

The Correct Answer is (A) —
To figure out depreciation, we first calculate the difference in value $930 - $570 = $360. The computer has lost $360. Since this was over the course of three years, divide $360/3 to arrive at a linear yearly depreciation of $120.

## 5.

The Correct Answer is (D) —
Since each inch represents 2 feet, 5 by 6 inches represents 10 by 12 feet. 10 × 12 = 120 square feet.

## 6.

The Correct Answer is (D) —
There are 20 + 70 + 90 + 40 = 220 students who are involved in clubs, according to the graph. With 250 total students, this leaves 250 – 220 or 30 students who are not involved in a club.

## 7.

The Correct Answer is (A) —
The scatterplot trend line is a parabola, and so is represented by a quadratic formula — C) and D) are eliminated because they are linear equations. Plugging in the value of 3 for

*x*,*y*= 11 for B). This is incorrect, so answer A) must be the correct answer. 3(3^{2}) + 1 = 28, so this checks out.## 8.

The Correct Answer is (A) —
Cost for a drill and electric saw from John’s tools = 0.90 × ($50 + $30) = $72. Cost for a drill and electric saw from Lin’s tools = 0.85 × ($55 + $25) = $68. $72 - $68 = $4.

## 9.

The Correct Answer is (C) —
Reading the chart, only two sets have more even than negative numbers.

## 10.

The Correct Answer is (B) —
200,000 × (0.75 – 0.50) = 50,000

## 11.

The Correct Answer is (C) —
. . 15.6 seconds × 5 files = 78 seconds. This is equal to 78 seconds/(60 seconds/minute) or 1.3 minutes.

## 12.

The Correct Answer is (C) —
The value of Offer 1 = 20 × 5 + 15 × 10 + 4 × 25 = 350 cents. The value of Offer 2 = 25 × 5 + 5 × 10 + 8 × 25 = 375 cents. Because Maria is evaluating the coins based on worth, C) is the correct answer.

## 13.

The Correct Answer is (C) —
Since the newborn’s increases by 30% in the first month, a weight of

*w*at the end of the first month implies a weight of*w*/1.3 at the beginning of the month. Since*w*× 1.3/1.3 =*w*, this equation checks out.## 14.

The Correct Answer is (B) —
The only answer choice that adds to 25% according to the demographic pie chart is B), since we know that Europe is itself equal to 25% and that Other is equal to half or 50% of the chart.

## 15.

The Correct Answer is (B) —
25% of the immigrants in the city come from Europe, and 20% of the European immigrant come from France. Since there are a total of 1500 immigrants, 0.25 × 0.20 × 1500 = 75.

## 16.

The Correct Answer is (B) —
0.10 × number = 12. Solving this, number = 120. 0.05 × 0.5 × 120 = 3.

## 17.

The Correct Answer is (C) —

*b*–*a*= -24 can be rearranged as –*a*= –*b*– 24. Adding this to the first equation, you get 0 = -3*b*– 27, or*b*= -9. Plugging this back into the equation gives –*a*= 9 – 24, or*a*= 15.*a*+*b*= 15 – 9 or 6.## 18.

The Correct Answer is (C) —
The sum of three consecutive odd integers can be expressed as

*n*+ (*n*+ 2) + (*n*+ 4), where*n*is an odd integer. This simplifies to 3*n*+ 6. 290 – 6 = 284, which is not divisible by three and D) is incorrect. 26 – 6 is not divisible by three and B) is incorrect. 23 – 6 = 17, which is not divisible by three and A) is incorrect. 105 – 6 = 99, which is divisible by three, so C) is the answer.## 19.

The Correct Answer is (D) —
2

*x*+ 7*x*+ 3*x*= 12*x*= 180.*x*= 15. The largest angle is 7*x*or 7(15) = 105 degrees.## 20.

The Correct Answer is (C) —
The average of Set A is 85 and the number of elements in the set is 5, so the sum of all elements in Set A is 85 × 5. The average of Set A and Set B is the sum of both sets divided by the total number of elements in both set. Let

*n*= the number of elements in set B, then 5(85 + 13 ×*n*) = 70 × (*n*+ 5). Simplifying, 85 + 13*n*= 14*n*+ 70 and*n*= 15.## 21.

The Correct Answer is (C) —
The shark spends 1/4, or 2/8 of its time sleeping, leaving 3/4 of time remaining. 1/2 of 3/4 is 3/8; this is the amount of time the shark spends hunting. 1 – 2/8 – 3/8 = 3/8. The shark has (3/8)

*d*remaining.## 22.

The Correct Answer is (C) —
The sample contains 370/750 or 49.3% females. Out of a population of 31,000 people we would expect 31,000 × 49.3% = 15,283 females, so A) is wrong. The sample contains 275/750 or 36.7% females 65 years or younger; this equates with 31,000 × 36.7% or 11,377 for the population, so B) is wrong. There are 225/750 females between 19 and 65 years of age or 30% of the sample; this equate to 31,000 × 30% or 9,300 females for the population, so C) is correct.

## 23.

The Correct Answer is (A) —
2

*x*^{2}– 2*y*^{2}= 72, simplifies to (*x*–*y*)(*x*+*y*) = 36. Since*x*=*y*= 18,*x*–*y*is equal to 2.## 24.

The Correct Answer is (A) —
(10

*x*+ 35)^{0.5}=*x*+ 6 simplifies to 10*x*+ 35 =*x*^{2}+ 12*x*+ 36. Rearranging this we get 0 =*x*^{2}+ 2*x*+ 1. This equation factors to 0 = (*x*+ 1)(*x*+ 1), so*x*= -1.*x*/2 is equal to -1/2.## 25.

The Correct Answer is (D) —
There are 60 technicians. 30/60 have worked for 6 years or more, or 50%.

## 26.

The Correct Answer is (C) —

*f*(2) = 8 +*a*,*f*(3) = 18 +*a*, and*f*(5) = 50 +*a*. 8 +*a*+ 18 +*a*= 50 +*a*. Solving for*a*, we arrive at*a*= 24.## 27.

The Correct Answer is (D) —
Adding 3

*x*+ 4*y*= 12 to 4*x*+ 2*y*= -5 gives us 7*x*+ 7*y*= 7. Dividing the equation by 7,*x*+*y*= 1.## 28.

The Correct Answer is (3) —
According to these two equations 21/

*k*= 7. Solving this gives*k*= 3.## 29.

The Correct Answer is (7) —
The ratio of odd to even integers is 5:1. 1/6 of the integers in the group are even. 42/6 = 7 even integers.

## 30.

The Correct Answer is (587) —
The resonant frequency of the A string is 440.

*F*=*v*/2*l*. Since*v*is a constant, and the length decreased by the new length is equal to 3/4 of the original length. Balancing both sides of the equation,*F*(4/3) =*v*/(2*l*(3/4)). Multiplying 440 by 4/3 rounds to 587Hz.## 31.

The Correct Answer is (293) —
Both the A and D string lengths are decreased by half. According to the equation

*F*=*v*/2*l*, the original frequency would increase by half as per*F*(2/1) =*v*/(2*l*(1/2)). The resonant frequency on the A string is therefore 440 × 2 or 880 is the new frequency. The resonant frequency on the D string is 293.7, therefore 293.7 × 2 or 587.4 is the new frequency. |880 – 587.4|= 292.6 Hz, which rounds to 293Hz.