Voltage SAT Quiz 1 (Chapter 1 to 4 Quiz Explanations)

Voltage Tutoring Test Preparation

QUIZ 1

1. Courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $1.55 ?

A. 1155

B. B. 1145

C. C. 1040

D. D. 950

E. E. 259

Correct Answer: B

Explanation:

The weight will be 250g plus (1.55 - 0.65)/0.10 units of 100g

250 + 900 = 1150

This is the maximum weight that can be sent at that price. But, weights exceeding

250 + 800 will also get charged this amount (that is what the ‘part thereof’ implies).

Hence a package weighing 1145 (ans. B) will be charged $1.55

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2. AB and DE are parallel. Angle BAC = 30 , angle CDE = 50. What is the measure of angle ACD ?

A. 100

B. B. 90

C. C. 80

D. D. 70

E. E. cannot be determined from the information

Correct Answer: C

Explanation:

Imagine a third parallel line drawn through C. The angle ACD will be made of two angles, one alternate to BAC, and therefore = 30. The other is alternate to CDE and therefore = 50. Total for angle ACD = 80

3. If x / y is an integer, which of the following statements must be true?

A. both x and y are integers

B. B. x is an integer

C. C. either x or y is negative

D. D. y / x is an integer

E. E. x = ny where n is an integer

Correct Answer: E

Explanation:

You can eliminate answer choices by picking numbers.

In case (A), x and y could, for example, both be equal fractions and x/y would be an integer.

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For the same reason (B) does not have to be correct.

There is no reason for either of them to be negative.

Answer (D) does not need to be correct. Consider x/y = 6/3. Then y/x = 3/6, which is a fraction not an integer.

But rearranging x/y = n, we get x = ny which is therefore always true.

4. What is the average of four tenths and five thousandths?

A. 25002

B. B. 2502

C. C. 0.225

D. D. 0.2025

E. E. 0.02025

Correct Answer: D

Explanation:

Four tenths = 0.4

Five thousandths = 0.005

The average is (0.4 + 0.005)/2 = 0.2025

5. What is the simplified result of following the steps below in order?

(1) add 5y to 2x(2) multiply the sum by 3(3) subtract x + y from the product

A. 5x + 14y

B. B. 5x + 16y

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C. C. 5x + 5y

D. D. 6x + 4y

E. E. 3x + 12y

Correct Answer: A

Explanation:

Step one 2x + 5y

Step two 3(2x + 5y) = 6x + 15y

Step three (6x + 15y) - (x +y) = 6x + 15y - x - y (watch that last minus sign!)

This gives 5x + 14y

6. If the equation of a line p in the coordinate plane is y = 3x + 2, what is the equation of line q which is a reflection of line p in the x-axis?

A. y = -3x + 2

B. B. y = -3x - 2

C. C. y = 3x - 2

D. D. y = -1/3x - 5

E. E. y = -1/3x + 5

Correct Answer: B

Explanation:

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The reflection of the line in the x-axis will change the signs for the slope and the intercept but the absolute value of the intercept and slope will be unchanged.

7. If y ¤ x = y2x for all positive integers, then (3 ¤ 4) ¤ 2 =

A. 38

B. B. 312

C. C. 316

D. D. 324

E. E. 332

The strange sign tells us what operation to carry out on x and y

Carry out the same procedure on 3 and 4 first. So 38 is the result.

Now carry out the procedure on 38 and 2. So (38)4 is the result, which is equivalent to 332

8. The first term in a sequence is 1 and the second term is 5. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 25th term in the sequence?

A. 2.5

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B. B. 3

C. C. 5

D. D. 25

E. E. 50

Correct Answer: B

Explanation:

Start constructing the sequence until you see the pattern

1...5...(average of 1 and 5 = 3)...(average of 1, 5, and 3 = 3)...(average of 1,5,3 and 3 = 3)

now you can see that all subsequent terms will be 3

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9. The solid brick shown is made of small bricks of side 1. When the large brick is disassembled into its component small bricks, the total surface area of all the small bricks is how much greater than the surface area of the large brick?

A. 32

B. B. 40

C. C. 60

D. D. 72

E. E. 80

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Correct Answer: B

Explanation:

Surface area of one small brick = 6; total number of bricks = 12; total surface when disassembled = 6 x 12 = 72

Surface of whole big block= area of four larger faces + area of the two smaller faces = (4 x 6) + (2 x 4) = 24 + 8 = 32

The increase is 40 units

10. (3x + 2) (2x - 5) = ax² + kx + n .

What is the value of a - n + k ?

A. 5

B. B. 8

C. C. 9

D. D. 10

E. E. 11

Correct Answer: A

Explanation:

This is a quadratic equation. To find n we multiply the last terms in each bracket together (2 times -5) = -10

To find ‘a’ we multiply the first terms in each bracket together (3x times 2x) = 6x2, So a = 6.

Thus a - n = 16

To find k we multiply the first term in the first bracket by the second term in the second bracket and add the result to the product of the second term in the first bracket and the first term in the second. (-15x + 4x) = -11x. So k = -11

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16 - 11 = 5

QUIZ 2 1. Of the following, which is greater than ½ ? Indicate ALL such fractions.

A. 2/5B. 4/7C. 4/9D. 5/11E. 6/13F. 8/15G. 9/17

Correct Answer: BFG

Explanation:

One way to deal with fractions is to convert them all to decimals. In this case all you would need to do is to see which is greater than 0.5.Otherwise to see which is greater than ½, double the numerator and see if the result is greater than the denominator. In B, one of the correct answers, doubling the numerator gives us 8, which is bigger than 7. In F, doubling 8 gives 16, which is greater than 15. In G doubling 9 gives 18, which is greater than 17.

2. If an object travels at five feet per second, how many feet does it travel in one hour?

A. 30 B. 300 C. 720 D. 1800 E. 18000

Correct Answer: E

Explanation:

If an object travels at 5 feet per second it covers 5x60 feet in one minute, and 5x60x60 feet in one hour. Answer = 18000 (E)

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3. What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?

A. 90 B. 95 C. 100 D. 105 E. 110

Correct Answer: C

Explanation:

You could add up all the multiples of 10 (10 + 20 + 30 ....+190), and divide by the number of terms (19). Or you could realize that the average of an evenly spaced series of numbers is equal to the value of the middle term (or the average of the two middle terms if there are an even number of terms). The middle term out of 19 is the tenth term in the series = 100.

4. A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?

A. 48 B. 32 C. 24 D. 18 E. 12

Correct Answer: A

Explanation:

If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8. Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48.

5. In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?

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A. 6 B. 15 C. 24 D. 33 E. 54

Correct Answer: C

Explanation:

You could solve this by drawing a Venn diagram. A simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking French to find the number taking only French. Likewise find those taking only German. Then we have:Total = only French + only German + both + neither78 = (41-9) + (22-9) + 9 + neither. Not enrolled students = 24

6. A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following could be the length of the fence in feet? (12 inches = 1 foot). Indicate ALL such answers.

A. 17B. 28C. 35D. 39E. 50

Correct Answer: ABDE

Explanation:

The fence will consist of one more post than there are chains. (e.g. P-c-P-c-P).Therefore, a total length has to be a multiple of the length of the chain plus one post (5.5) plus one post extra.We have length = (5.5n + 0.5), where n can be any positive whole number. If n= 3, length =17; if n= 5, length = 28, etc.but there is no whole number that can give 35. Hence all the answers except C are correct.

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7. ( √2 - √3 )² =

A. 5 - 2√6 B. 5 - √6 C. 1 - 2√6 D. 1 - √2 E. 1

Correct Answer: A

Explanation:

Expand as for (a + b)2.(√2 - √3)(√2 - √3) = 2 - 2(√2 + √3) + 3 = 5 - 2 √6

8. 230 + 230 + 230 + 230 =

A. 8120 B. 830 C. 232 D. 230 E. 226

Correct Answer: C

Explanation:

All four terms are identical therefore we have 4 (230).But 4 = 22, and so we can write 22. 230 Which is equivalent to 232

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9. Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?

A. 10 B. 8 C. 6 D. 4 E. 2

Correct Answer: B

Explanation:

Amy can travel clockwise or anticlockwise on the diagram.Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.Similarly, anticlockwise she has four different routes.Total routes = 8

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10. In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?

A. 18 B. 13.5 C. 9 D. 4.5 E. 3

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Correct Answer: D

Explanation:

If we take AE as the base of triangle AEC, then the height is CD.The height of the triangle is therefore, 9 (given).To find the base we need to see that triangles AEB and CDE are similar. The ratio AB: CD, is therefore equal to the ratio AE: ED. The given information shows that the ratio is 3:9, or 1:3. Now dividing AD (4) in this ratio gives us AE as 1.The area of AEC = ½ base x height =1/2 x 9 = 4.5

QUIZ 3

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1. Which of the following could be a value of x, in the diagram above?

A. 10

B. B. 20

C. C. 40

D. D. 50

E. E. any of the above

Correct Answer: B

Explanation:

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The marked angle, ABC must be more than 90 degrees because it is the external angle of triangle BDC, and must be equal to the sum of angles BDC (90) and DCB.

Also ABC is not a straight line and must be less than 180.

Therefore 90 < 5x < 180

The only value of x which satisfies this relation is 20.

2. Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes per hour, or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?

A. 10

B. B. 15

C. C. 20

D. D. 25

E. E. 30

Correct Answer: A

Explanation:

20 large cakes will require the equivalent of 10 helpers working for one hour. 700 small cakes will require the equivalent of 20 helpers working for one hour. This means if only one hour were available we would need 30 helpers. But since three hours are available we can use 10 helpers.

3. Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?

A. 5 : 1

B. B. 10 : 5

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C. C. 15 : 2

D. D. 20 : 2

E. E. 25 : 2

Correct Answer: E

Explanation:

Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.

US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2.

Now US : Indian = 25 : 10, and Indian : British = 10 : 2

Hence the two ratios can be combined and US : British = 25 : 2

4. A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?

A. 2.5π

B. B. 3π

C. C. 5π

D. D. 4π

E. E. 10π

Correct Answer: C

Explanation:

Draw the diagram. The diagonal of the rectangle is the diameter of the circle. The diagonal is the hypotenuse of a 3,4,5 triangle, and is therefore, 5.

Circumference = π.diameter = 5π

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5. Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?

A. 4

B. B. 7

C. C. 8

D. D. 12

E. E. it cannot be determined from the information given.

Correct Answer: D

Explanation:

If two sets of four consecutive integers have one integer in common, the total in the combined set is 7., and we can write the sets as

n + (n + 1) + (n + 2) + (n + 3 ) and

(n + 3) + (n + 4) + (n + 5) + (n + 6)

Note that each term in the second set is 3 more than the equivalent term in the first set. Since there are four terms the total of the differences will be 4 x 3 = 12

6. If f(x) = (x + 2) / (x-2) for all integers except x=2, which of the following has the greatest value?

A. f(-1)

B. B. f(0)

C. C. f(1)

D. D. f(3)

E. E. f(4)

Correct Answer: D

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Explanation:

You can solve this by back solving – substitute the answer choices in the expression and see which gives the greatest value.

A (-1 + 2) / (-1-2) = -2 / 2 = -1;

B (0 + 2) / (0-2) = 2/ -2 = -1;

C (1 + 2) / (1-2) = 3/-1 = -3;

D (3 + 2) / (3-2) = 5/1 = 5;

E (4+ 2) / (4-2) = 6/2 = 3

If you had just chosen the largest value for x you would have been wrong. So although it looks a long method, it is actually quick and accurate since the numbers are really simple and you can do the math in your head.

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7. ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilateral EBFD ?

A. 2.25

B. B. 3

C. C. 4

D. D. 4.5

E. E. 6

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Correct Answer: D

Explanation:

(Total area of square - sum of the areas of triangles ADE and DCF) will give the area of the quadrilateral

9 - (2 x ½ x 3 x 1.5) = 4.5

8. If n ≠ 0, which of the following must be greater than n?

I 2nII n²III 2 - n

A. I only

B. B. II only

C. C. I and II only

D. D. II and III only

E. E. None

Correct Answer: E

Explanation:

Remember that n could be positive negative or a fraction. Try out a few cases:

In case I, if n is -1, then 2n is less than n.

In case II, if n is a fraction such as ½ then n2 will be less than n.

In case III, if n is 2, then 2-n = 0, which is less than n.

Therefore, none of the choices must be greater than n

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9. After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce?

A. 20

B. B. 15

C. C. 8

D. D. 5

E. E. 3.2

Correct Answer: C

Explanation:

If after each bounce it reaches 2/5 of the previous height, then after the second bounce it will reach 2/5 x 125. After the third it will reach 2/5 x 2/5 x 125. After the fourth it will reach 2/5 x 2/5 x 2/5 x 125. This cancels down to 2 x 2 x 2 = 8

10. n and p are integers greater than 1

5n is the square of a number

75np is the cube of a number.

The smallest value for n + p is

A. 14

B. B. 18

C. C. 20

D. D. 30

E. E. 50

Correct Answer: A

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Explanation:

The smallest value for n such that 5n is a square is 5.

75np can now be written as 75 x 5 x p.

This gives prime factors.... 3 x 5 x 5 x 5 x p

To make the expression a perfect cube, p will have to have factors 3 x 3 , and hence p =9

n + p = 5 + 9 = 14

QUIZ 4

1. If a² = 12, then a4 =

A. 144

B. B. 72

C. C. 36

D. D. 24

E. E. 16

Correct Answer: A

Explanation:

a4 = a2 x a2 = 12 x 12 = 144

2. If n is even, which of the following cannot be odd?

I n + 3II 3nIII n² - 1

A. I only

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B. B. II only

C. C. III only

D. D. I and II only

E. E. I, II and III

Correct Answer: B

Explanation:

In case I , even plus odd will give odd

In case II, odd times even will give even

In case III even squared is even, and even minus odd is odd.

(You can check this by using an easy even number like 2 in place of n)

Only case II cannot be odd.

3. One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?

I 24II 20III 5

A. I only

B. B. II only

C. C. III only

D. D. II and III only

E. E. I, II and III

Correct Answer: D

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Explanation:

The maximum area of the triangle will come when the given sides are placed at right angles. If we take 8 as the base and 5 as the height the area = ½ x 8 x 5 = 20

We can alter the angle between the sides to make it less or more than 90, but this will only reduce the area. (Draw it out for yourself). Hence the area can be anything less than or equal to 20.

4. A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 91 pounds?

A. 12

B. B. 11

C. C. 10

D. D. 9

E. E. 8

Correct Answer: E

Explanation:

Food consumed per day = 39/6.

In the remaining days it will consume 91 - 39 pounds = 52 pounds

Now divide the food by the daily consumption to find the number of days

52 / (39/6) = 52 x (6 / 39) = 8

5. A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?

A. 8p

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B. B. pq

C. C. pq + 27

D. D. -p

E. E. (p - q)6

Correct Answer: C

Explanation:

A perfect cube will have prime factors that are in groups of 3; for example 125 has the prime factors 5 x 5 x 5 , and 64 x 125 will also be a cube because its factors will be 4 x 4 x 4 x 5 x 5 x 5

Consider the answer choices in turn.

8 is the cube of 2, and p is a cube, and so the product will also be a cube.

pq will also be a cube as shown above.

pq is a cube and so is 27, but their sum need not be a cube. Consider the case where p =1 and q = 8, the sum of pq and 27 will be 35 which has factors 5 x 7 and is not a cube.

-p will be a cube.

Since the difference between p and q is raised to the power of 6, this expression will be a cube (with cube root = difference squared).

6. Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 7, how many people got on at the first stop?

A. 128

B. B. 64

C. C. 32

D. D. 16

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E. E. 8

Correct Answer: B

Explanation:

Work backwards. If one person got off at stop 7, as the bus approached the stop there must have been two people on board. As it approached the previous stop (no. 6) there were four on board. Approaching stop 5, there were 8. Approaching stop 4, there were 16 on board. Approaching stop 3, there were 32. Approaching stop 2, there were 64. As stop 2 was the first stop at which people got off there must have been a total of 64 people who boarded at the first stop. (We are assuming that no people could have been on the bus before the first official stop.)

7. n is an integer chosen at random from the set

{5, 7, 9, 11 }

p is chosen at random from the set{2, 6, 10, 14, 18}

What is the probability that n + p = 23 ?

A. 0.1 B. B. 0.2 C. C. 0.25 D. D. 0.3 E. E. 0.4

Correct Answer: A

Explanation:

Each of the integers in the first set could be combined with any from the second set, giving a total of 4 x 5 = 20 possible pairs.

Of these the combinations that could give a sum of 23 are (5 + 18), and (9 + 14)

This means that the probability of getting a sum of 23 is 2/20 = 1/10

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8. A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?

A. 0.75D

B. B. 0.76D

C. C. 0.765D

D. D. 0.775D

E. E. 0.805D

Correct Answer: C

Explanation:

If the price is reduced by 15 %, then the new price will be 0.85D

If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85D = 0.765D

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9. All the dots in the array are 2 units apart vertically and horizontally. What is the length of the longest line segment that can be drawn joining any two points in the array without passing through any other point ?

A. 2

B. B. 2√2

C. C. 3

D. D. √10

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E. E. √20

Correct Answer: E

Explanation:

The longest line segment that can be drawn without passing through any dots other than those at the beginning and end of the segment, such a line could go from the middle dot in the top row to either the bottom left or right dot. In any case the segment will be the hypotenuse of a right triangle with sides 2 and 4. Using Pythagoras theorem the hypotenuse will be √(2 ² + 4 ² ) = √20

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10. If the radius of the circle with centre O is 7 and the measure of angle AOB is 100, what is the best approximation to the length of arc AB ?

A. 9

B. B. 10

C. C. 11

D. D. 12

E. E. 13

Correct Answer: D

Explanation:

If the radius is 7, the circumference = 14π

The length of the arc is 100/360 of the circumference

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Taking π as 22/7 we get

(100 x 14 x 22) / (360 x 7) which reduces to 440/ 36 = 12.22 (i.e. approx. 12)

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Voltage SAT Quiz 1 (Chapter 1 to 4 Quiz Explanations)

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