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QUESTION: 1

In the “Big-Reds” parking lot there are 56 vehicles, 18 of them are buses and the rest are private cars. The color of 32 vehicles is red, from which 17 are buses. How many private cars can be found in the parking lot, which are not colored red?

Solution:

The best answer is B.

Out of 56 vehicles, 32 are colored red, therefore 24 are in different color.

17 of the red vehicles are buses, therefore (18 – 17 = 1) are in different color.

(24 – 1 = 23) private cars are in the parking lot with a different color than red.

QUESTION: 2

In Sam’s hanger there are 23 boxes, 16 out of the boxes are filled with toys and the rest are filled with electrical appliances. 8 boxes are for sale, 5 of them are filled with toys. How many boxes with __electrical appliances__ are in Sam’s hanger that are __not for sale__?

Solution:

The best answer is D.

8 boxes are for sale, 5 of them are with toys, and therefore 3 of them are with electrical appliances.

Out of 23 boxes, 16 are with toys, therefore, and therefore 7 of them are with electrical appliances.

(7 – 3 = 4) is the number of electrical appliances boxes, which are not for sale.

QUESTION: 3

In the fifth grade at Parkway elementary school there are 420 students. 312 students are boys and 250 students are playing soccer. 86% of the students that play soccer are obviously boys. How many girl student are in Parkway that are not playing soccer?

Solution:

The best answer is B.

There are (420 – 312 = 108) girls in Parkway.

86% of 250 are boys, therefore 14% of 250 are girls that play soccer, which is 35 girls.

The number of girls that do not play soccer is (108 – 35 = 73).

QUESTION: 4

In the quiet town of “Nothintodo” there are 600 inhabitants, 400 are unemployed and 300 are somnambulists. If half of the somnambulists are unemployed, how many are employed and are not somnambulists?

Solution:

The best answer is A.

There are 300 people that are not somnambulists. There are (600 – 400 = 200) people that are employed in the town, half of the somnambulists are employed (150), therefore (200 – 150 = 50) is the number of people that are employed which are also not somnambulists.

QUESTION: 5

In the youth summer village there are 150 people, 75 of them are not working, 50 of them have families and 100 of them like to sing in the shower. What is the largest possible number of people in the village, which are working, that doesn’t have families and that are singing in the shower?

Solution:

The best answer is C.

The number of people that work is 75.The number of people that doesn’t have families is (150 – 50 =100).

100 of the people like to sing in the shower.

The largest possible number of people that belong to all three groups is the smallest among them, Meaning 75.

QUESTION: 6

In the junior basketball league there are 18 teams, 2/3 of them are bad and ½ are rich. What __can’t__ be the number of teams that are rich and bad?

Solution:

(2/3 x 18 = 12) teams are bad and 9 are rich.

The number of teams which are rich and that are bad must be between 9 and (9+12-18 = 3).

The only answer, which is not in that range, is C.

QUESTION: 7

In the third grade of Windblow School there are 108 students, one third of them failed the math test and 1/6 failed that literature test. __At least__ how many students failed both tests?

Solution:

The best answer is A.

(1/3 x 108 = 36) failed the math test.

(1/6 x 108 = 18) failed that literature test.

The least amount of people that failed both tests is (18 + 36 –108 = -54), there cant be an negative Overlapping between the groups so the least amount of people who failed both tests is zero.

QUESTION: 8

If 1/X = 2.5, then what is the value of 1/(X – 2/3)?

Solution:

The best answer is C.

If 1/X is 2.5 or 5/2 then X = 2/5.

1/(2/5 – 2/3) is 1/(6/15 – 10/15) = -15/4 = -3.75.

QUESTION: 9

Travis is working as a programmer of IBW. Travis earns $3,500 annually.

If Travis pays 2.5% of that amount quarterly to support groups and he paid $525 so far, for how many years now has Travis been paying?

Solution:

Travis pays 2.5% of 3500, which is $87.5 every 3 months (quarterly).

(525/87.5 = 6), therefore Travis has been paying for (6 x 3 = 18) months now, that is 2.5 years.

QUESTION: 10

Dana borrows 5500 pounds annually for her college education. If Dana gives her parents 3% of that amount back each month, how much will she still owe her parents after four years of college?

Solution:

Dana takes 5500 each year and returns (0.03 x 5500 = 165) each month, which is (165 x 12 = 1980) each passing year. That means that each year Dana owes her parents (5500 – 1980 = 3520) pounds.

After 4 years in college she will owe them (4 x 3520 = 14,080) pounds.

QUESTION: 11

Mr. Rusty owes the bank $1,040,000, he returns $40,000 quarterly to the bank. If the tax on the money Rusty owes is compounded quarterly by 0.25% starting before Rusty paid the first payment, how months would it take poor Rusty to reach a point where he owes the bank no more than 1 million dollars?

Solution:

The best answer is B.

Every three months Rusty gives the bank $40,000.

After the first quarter the bank took (0.0025 x 1040000 = 2600) and Rusty paid $40,000 so the new Debt is now (1,040,000 - 40,000 + 2,600 = 1,002,600).

After the second quarter the bank took (0.0025 x 1002600 = 2506.5) and Rusty paid again $40,000 so the new Debt is now (1,002,600 – 40,000 + 2506.5 < 1 million dollars).

QUESTION: 12

Simba borrowed $12,000 from his brothers so he can buy a new sports car. If Simba returns 4.5% of that amount every 2 weeks, after how many months Simba wouldn’t owe his brothers any more money?

Solution:

The best answer is B.

Simba gives (0.045 x 12,000 = 540) to his brothers every 2 weeks, in a month he gives (540 x 2 = 1080). (12,000/1,080 is a little over 11), therefore after 12 months he won’t owe any more money.

QUESTION: 13

If A and B are two roots of the equation X^{2} –6.5X – 17, then what is the value of A x B?

Solution:

The best answer is D.

The roots of the equation are 8.5 and (-2).

The multiplication of the roots is equal to (-17).

QUESTION: 14

If A,B and C are roots of the equation X^{3} – 16X^{2} +48X, what is the sum of the roots?

Solution:

The best answer is A.

The equation can be written as: X(X^{2} – 16X +48) = X(X – 12)(X – 4).

The roots of the equation are: 0,4 and 12. The sum of the roots is 16.

QUESTION: 15

If R is a root of the equation X2 +3X – 54, than which of the following equations have also the root R ?

Solution:

The best answer is D.

The original equation is X^{2} + 3X – 54, it can be written as (X – 6)(X + 9). The roots are 6 and (-9).

We are looking for an equation that has one of the same roots.

Answer D: X^{2} – 15X +54 = (X – 6)(X – 9) à This equation has the root 6.

All the other answers have different roots than the original equation

QUESTION: 16

If P is a root of the equation X^{3} +10X^{2} + 16X, than which of the following equations have also the root P ?

Solution:

The best answer is B.

The original equation is X^{3} +10X^{2} + 16X, it can be written as X(X + 8)(X + 2). The roots are (-8),0 and (-2).

We are looking for an equation that has one of the same roots.

Answer B: X + 8 à This equation has the root (-8).

All the other answers have different roots than the original equation.

QUESTION: 17

If X is a root of the equation a^{3} +8a^{2} – 20a, than which of the following equations __Don’t__ have the root X as one of their roots?

Solution:

The best answer is E.

The original equation is a^{3} +8a^{2} – 20a, it can be written as a(a – 2)(X + 10). The roots are 2,0 and (-10).

We are looking for an equation that has none of the same roots.

Answer E: X^{2} – 10X +16 = (X + 2)(X + 8) à This equation has none of the original roots. All the other answers have one or more of the same original roots.

QUESTION: 18

Gwen has to divide her money between her three sons. If the older brother received 65% of the total amount and the other two received the same amount of money, how much money did the median brother get?

(1) The combined amount of money of the older brother and the small one is $45,000.

(2) The older brother received $35,454.5.

Solution:

The best answer is D.

The data gave us the ratio of the amounts each one got (65 : 17.5 : 17.5), therefore all we need is one number to know how much each of the brothers received. Each of the statements above gives us enough information to solve the problem.

QUESTION: 19

Little Timmy spends half of his allowance on his favorite pet Din and the other half on candies. How much money did Timmy spend on Din?

(1) Din eats 1.5Kg of food every day.

(2) Timmy buys 110 gr. Of candies each day. One Kg of candies costs $7.5.

Solution:

The best answer is B.

From the question we know the ratio of the money that Timmy is spending on Din and on candies.

In order to know how much Timmy spends on each, we need to know one of the expanses in real

Amount of money and not in percent terms. The first statement doesn’t provide us any sufficient information but the second one gives us the exact amount of money that Timmy spends on Candies, which is equal to the amount that he spends on Din.

QUESTION: 20

A, B, C and D are four consecutive points on a straight line. What is the distance between A to D?

(1) AC = 6.

(2) BD = 8.

Solution:

The best answer is E.

First, draw the line with the points marked.

We know AC and BD but it’s not sufficient to know the length of AD.

If the question said the points are evenly spaced than the answer would be solvable.

QUESTION: 21

A, B, C, D and E are five consecutive points with equal spacing on a straight line. What is the distance between A to E?

(1) AB = 3.

(2) BE = 9.

Solution:

The best answer is D.

First, draw the line with the points marked.

Because the points are evenly spaced on the straight line, only one measurement is needed to answer the question. Both statements give us a measurement of some kind therefore each of them, by itself is sufficient.

QUESTION: 22

A, B and C are 3 consecutive points on an arc with a constant radius. What is the distance between A and C?

(1) The radius of the arc is 25 Cm.

(2) The length of AB is 5 Cm.

Solution:

The best answer is E.

In order to know the distance between two points on an arc you need to know the angle that the points make and the radius of the arc.

Statement (1) gives us the radius.

Statement (2) gives us the length of AB, but the question didn’t mention that there is equal spacing and therefore the length of BC can’t be found with both of the statements taken together.

QUESTION: 23

If X and Y are positive integers, is X greater than Y?

(1) X > Y – 2.

(2) X > 2.

Solution:

The best answer is E.

Take some numbers for example.

Y= 8 à from statement (1) we know that X > 6 and from statement (2) we know that X >2, but X can be 7 or even 24 and he will still fit the equation properly, therefore both statements, taken together are not sufficient.

QUESTION: 24

If X and Y are positive integers, is X greater than Y?

(1) X > 2.

(2) Y < 3.

Solution:

The best answer is C.

From statement (1) we learn that X is 3 or bigger and from statement (2) we learn that Y is 2 or smaller. Therefore both statements are sufficient to answer the question.

QUESTION: 25

If X, Y and Z are positive integers, is X greater than Z – Y?

(1) X – Z – Y > 0.

(2) Z^{2} = X^{2} + Y^{2}.

Solution:

The best answer is A.

From statement (1) we learn that X > Z + Y therefore X must be bigger than Z – Y (positive integers).

From statement (2) we learn that X^{2} = Z^{2} – Y^{2} and that tells us nothing relevant.

QUESTION: 26

(x, y) are the coordinates of the intersection of the following lines:

(3x – 2y = 8) and (3y + x = 10). What is the value of (x/y)?

Solution:

The best answer is B.

There is no need to draw the lines. There are two equations with two variable that you have to solve.

Take the second equation and multiply it by (-3) to get: -9y –3x = -30 add this equation to the first and You’ll get: -11y = -22 à y=2 and x=4. (x/y) is 2

QUESTION: 27

A(a, b) is the coordinates of the intersection between the lines:

(x + y –1 = 0) and (4x – 2y = 5). What is the shortest distance between A(a, b) and the coordinate B(25/6, 23/6)?

Solution:

The best answer is E.

There is no need to draw the two lines. Multiply equation (1) by 2 and then add the equations to get:

6x = 7 à x = 7/6, y = -1/6.

Draw a rectangular axis system and mark the point A and B.

Complete the two points to a triangle so one of sides is 3 and the other is 4, the hypotenuse, which is also the requested length is 5.

QUESTION: 28

P(x, y) is the intersection point between the circle (x2 + y2 = 4) and the line (y = x +2). Which of the following can be the point P?

Solution:

The best answer is D.

First, draw the circle and the line. The circle is centered at (0, 0) with a radius of 2.

You can see that the line and the circle intersect at two points: (-2, 0) and (0, 2). Another way is to insert y = x+2 into the equation of the circle and solve it.

QUESTION: 29

Is the intersection of the two lines: (x + y = 8) and (4y – 4x = 16) inside the circle: x^{2} + y^{2} = r^{2}?

(1) r = 81.

(2) The center of the circle is at the coordinate (-99, -99).

Solution:

The best answer is A.

The intersection point of the two lines is easy to find, its (2, 6).

In order for us to know if the point is inside the circle we need to know the exact location of the circle. Statement (1) clears the problem by giving us the radius so all the sufficient data is know.

Statement (2) is not sufficient because it tells us nothing about the radius of the circle.

QUESTION: 30

. Is there an intersection between the line (Y = aX - b) and the parabola (Y = X^{2} + b)?

(1) a < 0.

(2) 0 > b.

Solution:

The best answer is B.

First, draw the parabola and the line.

We can see that the thing that determines if the two intersect is b and not a.

If b > 0 there is no intersection but if b<0 there is an intersection no matter what the value of a is.

Therefore statement (2) is sufficient and (1) is not.

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