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## Question Explanations For

##
*PRACTICE TEST 1 (Calculator Math Test)*

## 1.

The Correct Answer is (C) —
Multiplying through gives . Simplifying the right side gives -6

*x*+ 2*c*= -6*c*- 3*x*+ 5*c*, which can be further simplified to -6*x*+ 2*c*= -*c*– 3*x*. Rearranging gives 3*c*= 3*x*, so*c*=*x*.## 2.

The Correct Answer is (D) —
If the mean of 6 integers is 30, their sum must be 180. Similarly, if the mean of 5 integers (since one was removed) is 34, their sum must be 170. The difference between these two numbers is 10, which must be the number that was removed.

## 3.

The Correct Answer is (D) —
The

*y*-intercept is defined as the value of*y*when*x*is zero. Plugging zero in for*x*in the equation gives 6.## 4.

The Correct Answer is (A) —
The slope of the line is 1/3 and the

*y*-intercept is 0, so the equation is .## 5.

The Correct Answer is (D) —
Plugging in 6 for

*x*gives 6/2 + 3 ≤ 2(6) – 9, or 6 ≤ 3, which is false.## 6.

The Correct Answer is (C) —
Scenario I can be represented as

*y*= 5*x*+*b*. Scenario III can be represented as*y*= 3*x*+*b*. Scenario II, however, would require an exponential term.## 7.

The Correct Answer is (B) —
Based on the graph, the total number of students enrolled in 2009 was 2500.

## 8.

The Correct Answer is (B) —
Between 2007 and 2008, the number of students in the public sector increased, but the number of students in the private sector and the number of students overall decreased.

## 9.

The Correct Answer is (D) —
For every gray finch, there are two black finches, and for every two black finches, there are four spotted finches. So out of every seven finches (1 gray + 2 black + 4 spotted), four will be spotted.

## 10.

The Correct Answer is (C) —
This is the only equation that satisfies all values of

*x*for*f*(*x*).## 11.

The Correct Answer is (C) —
Rearranging gives 0 =

*x*^{2}+*x*– 20 and factoring gives 0 = (*x*+ 5)(*x*– 4), so*x*= -5 or*x*= 4. Plugging these values into*x*^{2}–*x*gives 12 and 30, and both of these values are between 11 and 31.## 12.

The Correct Answer is (C) —
If the number of events had held steady at

*a*, the events over the 28 days would have totaled 4*a*. Since events decreased by 25%, only 75% of the events will occur. 75% of 4*a*is 3*a*.## 13.

The Correct Answer is (A) —
A company saw an increase in stock price if its

*y*-coordinate (stock price in 2011) is greater than its*x*-coordinate (stock price in 2010); in other words, if a company lies above the line*y*=*x*, it saw an increase. The company at (25, 25) saw neither an increase nor a decrease.## 14.

The Correct Answer is (B) —
30 correct answers would give 60 points; the remaining 15 incorrect or unanswered questions give -15 points. 60 – 15 = 45.

## 15.

The Correct Answer is (C) —
70 milliliters are dumped on the ground 60 times per minute, for a total of 4200 milliliters dumped per minute. Over 5 minutes this will result in 21000 milliliters, or 21L, dumped on the ground.

## 16.

The Correct Answer is (A) —

*x*+*y*= 9 can be rewritten as*y*= 9 –*x*. Plugging this value in for*y*in the equation*x*^{2}+*y*^{2}= 45 gives us*x*^{2}+ (9 –*x*)^{2}= 45. Expanding and simplifying gives us 2*x*^{2}– 18*x*+ 36 = 0, and dividing both sides by two gives us*x*^{2}– 9*x*+ 18 = 0. Factoring gives (*x*– 3)(*x*– 6) = 0, so the possible values of*x*are 3 and 6.## 17.

The Correct Answer is (C) —
Setting the two equations equal to each other gives –

*x*^{2}+ 4 = 2*x*+ 1. Rearranging gives 0 =*x*^{2}+ 2*x*– 3, and factoring gives (*x*– 1)(*x*+ 3) = 0, so the possible values for*x*are 1 and -3. Since (*a*,*b*) is in quadrant 1, we must use 1 as the value of*x*. Plugging this back in to either equation gives us*y*= 3, so*ab*= 1 × 3 = 3.## 18.

The Correct Answer is (B) —
The question can be written as

*a*+*b*= 2|*a*—*b*|. Let*a*= 6. Then setting*b*= 2, we can see that 6 + 2 = 2|6 — 2|, so (A) is not the correct answer. Similarly, 18 + 6 = 2|18 — 6|, so (C) is not the correct answer. However, 12 + 6 ≠ 2|12 — 6|, so 12 is not a possible value.## 19.

The Correct Answer is (D) —
If Jenny has a 3 and a 6, the points from those cards is equal to (3 × 2) + (6 × 3) = 24. That means that the third card is worth 48 – 24 = 24 points. Since 24/3 = 8, her third card must have been an 8.

## 20.

The Correct Answer is (C) —
The smallest number that is divisible by both 3 and 5 is 15. That means that 1/15 of the numbers from 1 to 1000 will be divisible by both 3 and 5. 1000/15 = 66.67, but we round down to 66 to stay within the range of 1 to 1000. So 66 out of the 1000 numbers will be divisible by 3 and 5, giving us a probability of 33/500.

## 21.

The Correct Answer is (B) —
Percent increase can be calculated by dividing the newer value by the older value. Company B had an increase of $37.80/$35.80 = 1.0559 = 105.59%, the highest of the three companies.

## 22.

The Correct Answer is (B) —
The growth between 36 and 48 hours is much smaller than the growth between 12 and 24 hours and 24 and 36 hours.

## 23.

The Correct Answer is (D) —
There are three integers each with value 3

*d*, three integers each with value*e*, and six integers each with value*f*. This gives us a total of 12 integers. The total value for the first group is 9*d*(three groups of single integers, each with value 3*d*, gives 3*d*+ 3*d*+ 3*d*= 9*d*); the total value for the second group is 3*e*(one group of 3 integers, each with value*e*, gives*e*+*e*+*e*= 3*e*); the total value for the third group is 6*f*(one group of 6 integers, each with value*f*). To find the average, we can write (9*d*+ 3*e*+ 6*f*)/12. Simplifying gives (3*d*+*e*+ 2*f*)/4.## 24.

The Correct Answer is (C) —
Given that event

*v*has already occurred, we can say that the chances of*v*having happened on this Tuesday are 100%. We can get 100% by dividing 28% (the probability that*v*will happen) by 28% (the probability that*v*has happened). To find the probability of event*w*also having happened on Tuesday, given that*v*happened, we can divide 19% (the probability that*w*will happen) by 28% (the probability that*v*has happened), which gives us 67.8%. Rounding gives us 68%.## 25.

The Correct Answer is (B) —

*g*(3) can be found by plugging in 1 for*x*in the first equation:*g*(2(1) + 1) = 4*g*(1) + 1 + 1. So*g*(3) = 4*g*(1) + 2, but we know that*g*(1) = 3. So*g*(3) = 4(3) + 2 = 14.## 26.

The Correct Answer is (D) —
If the average of a set of four numbers is

*x*, their sum must be 4*x*. Similarly, if the average of a set of five numbers is*x*+ 2, their sum must be 5*x*+ 10. So adding the fifth number brought the sum from 4*x*to 5*x*+ 10, meaning that in terms of*x*, that number was*x*+ 10.## 27.

The Correct Answer is (B) —
The

*x*-intercept occurs when*y*= 0, as shown in the given ordered pairs. Setting the equation equal to zero and factoring gives -(*x*– 1)(*x*+ 5), so |*a*+*b*| = |1 – 5| = 4.## 28.

The Correct Answer is (40) —
Since vertically opposite angles are equal (“vertically” here means that they share a vertex), the internal angles of the triangle are

*x*, 51, and 89 degrees. Since the sum of the angles in every triangle is 180 degrees,*x*= 180 – (51 + 89) = 40.## 29.

The Correct Answer is (5) —
The slope of line

*s*is 3 (slope = rise/run = 9/3 = 3), so*s*also passes through (0, 5).## 30.

The Correct Answer is (460) —
Since one meter = 100 cm (1 × 10

^{2}cm), one cubic meter = 100^{3}cm^{3}(1 × 10^{6}cm^{3}). So 1.9 m^{3}= 1.9 × 10^{6}cm^{3}of ice. Since 1 cm^{3}of ice melts into 0.92 cm^{3}of water, we can multiply 1.9 × 10^{6}× 0.92 cm^{3}= 1,748,000 cm^{3}of water. To convert cm^{3}to gallons, we use the relationship given: there are approximately 3800 cm^{3}in a gallon, which we can write as 3800 cm^{3}/gallon. To cancel out the units, we need to divide our 1,748,000 cm^{3}of water by cm^{3}/gallon: .## 31.

The Correct Answer is (392) —
179.4 km

^{3}of water every year for six years = 179.4 km^{3}× 6 = 1076.4 km^{3}of water. To convert to cm of sea level rise, we use the relationship given: 1000 km^{3}leads to a 364 cm rise, so to cancel our units (km^{3}), we need to multiply by 364 cm/1000 km^{3}. 1076.4 km^{3}× (364 cm/1000 km^{3}) = 392cm.