Quantitative Wrong Questions

A certain rectangular crate measures 8 feet by 10 feet by 12 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume? 4 5 6 8 10

B. Yes. Backsolve/Draw a picture: Geometry. If a cylinder is put into a crate, then the diameter of the cylinder will have to be equal to or smaller than the dimensions of the floor of the crate. If the radius of the cylinder is 5, then the floor of the crate could have dimensions . This means that the third crate dimension, 8, is the height of both the crate and the cylinder. If , then . The volume is , or . This is the largest volume we can accommodate.

A recent survey of the residents in Reytown showed that 4,500 people owned a VCR, a DVD player, or both. How many residents of Reytown own neither a VCR nor a DVD player? (1) There are 4,200 people in Reytown that own either a VCR or a DVD player, but not both. (2) Ninety percent of the residents of Reytown own a VCR, a DVD player, or both. Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

B. Yes. One way to do this problem is to consider the formula: Group 1 + Group 2 - Both + Neither = Total. The question already supplies Group 1 + Group 2. It asks for Neither. Statement (1) allows to you figure out that Both = 300. You have no way to figure out the Total, and thus, no way to figure out Neither. Statement (1) is not sufficient. Statement (2), however, tells you that 90 percent own a VCR, a DVD player, or both. You could find the total: 4,500 = T. Total = 5,000. If 90 percent own a VCR, a DVD player, or both, then 10 percent of the total own neither. You can solve for the number of people who own neither:5,000 = 500. The correct answer is B.

What is the average (arithmetic mean) of integers j, k, and l? (1) The sum of j and k is 9. (2) The sum of j and l is 10. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT

C. No. Combining Statements 1 & 2 will not shed any light on this situation. At best, you could come up with the equation: . But, without knowing the value for j, we cannot draw any conclusions concerning the average of . If , and , then the average is 5, but if , and , then the average is 6. E. Yes. It is impossible to answer this question using any of the information offered by Statements 1 & 2 or any combination thereof.

m and n are the x and y coordinates, respectively, of a point in the coordinate plane. If the points (m, n) an both lie on the line defined by the equation , what is the value of p? 1 2 5 8

C. Yes. Algebraic Manipulation and Coordinate Geometry. For this problem, in the coordinates (m,n), m is the x coordinate and n is the y coordinate. Thus, using the line equation from the question and substituting our coordinates (m, n), . The coordinates can be substituted into the same equation, so that . Now combine these two equations by substituting the value of m in the first equation into the second equation: . Now start solving. Add to both sides and now . Multiply both sides of the equation by 2: . Subtract n from both sides: . Solve: .

In a certain apartment building, 20 percent of the apartments are rented, of the apartments are owned, and of the apartments are vacant. If the remaining 5 apartments are reserved as model apartments, how many apartments are in the building? 100 75 60 50 30

D. Yes. Backsolve. If there 50 apartments in the building, then there are 20% x 50 = 10 rented, x 50 = 15 owned, and x 50 = 20 vacant. This leaves 50 - 10 - 15 - 20 = 5 apartments to be models. That matches the 5 models given in the problem.

During a sale, an automotive parts center offers a fourth tire free with the purchase of three tires at full price. If the sale were discontinued, by what percent would each tire have to be discounted if the total cost of four tires were to remain the same? 80% 75% 33% 25% 20%

D. Yes. Plug In. Let's suppose that, during the sale, a person bought 3 tires (and received the last one free). We'll Plug In a price per tire sold: $20. Which means that 3 * $20 = $60 for four tires (3 paid for, 1 thrown in for free). Now, if the sale were discontinued, the same person would have to pay for all 4 tires. But the problem asks us to discount the price per tire so that the overall package costs the same ($60). So now our equation would read: 4 * $15 = $60. We now know that each tire will come down from $20 to $15 in price. Note: the problem asks us to solve for the actual discount per tire incurred, however. To do that, we simply use our percentage change formula: difference/original= 5/20=25%

If a is the largest of three consecutive numbers, what is the product of these numbers in terms of a ? a^3-a a^2 + 2a + 1 a^2 - 2a + 1 a^3 + 3a + 2a a^3 - 3a^2 + 2a

E. Yes. Did you plug in? Try 2, 3, 4. Their product is 24 and the product of (E) is

Is xy < 100? (1) x < 10 (2) y < 10 Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

E. Yes. Let x = 5, y = 5 and xy = 25. Let x = -10, y = -10 and xy = 100. The correct answer is E.

A certian club has 10 members including harry. One of the ten is chosen to be prez. One of the remaining 9 is chosen to be secretary. One of the remaing 8 is chosen to be treasurer. what is the prob that harry will be either sec or treasurer?

1.) Must calc prob of being chosen as sec. (1-prob(president)) * (prob(sec))= 1-1/10 * 1/9 = 1/10 2.) must calc prob that he will be chosen for treasurer. 1-1/10=9/10 for prob not prez 1-1/9=8/9 for prob not being sec Prob(treasurer) = (9/10)(8/9)(1/8)=1/10 3.) Add either or probs so 1/10+1/10=1/5

What is the sum of interior angles of any polygon?

180(n-2) where n is the number of sides

Bart currently sells 40 chairs each month. If he were to decrease the price per chair by $10.00, how many more chairs per month would he have to sell in order to earn the same gross revenue as he did before he lowered his prices? (1) A decrease of $10.00 would represent a 20 percent decrease in the price of a chair. (2) Bart currently has gross revenues of $2000 a month from the sale of chairs. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT.

First, consider Statement (1) alone. The percent decrease is equal to the change in the price divided by the original price, multiplied by one hundred. Therefore, if x is equal to the original (pre-discount) price, you can solve for the pre-discount price: ×100 = 20 so 10 × 100 = 20x, 1000 = 20x, and x = 50. If Bart currently sells 40 chairs a month, then his gross revenue is 40 × 50 = $2000 per month. If Bart were to decrease the price by $10, he would now sell chairs at $40 each and would therefore need to sell 50 chairs to maintain revenue of $2000. Statement (1) is sufficient; eliminate choices B, C, and E. Next, consider Statement (2) alone. If Bart sells 40 chairs and has gross revenues of $2000, you can determine that he sells chairs for $50 each. From here, you can determine how many chairs he must sell at $40 each, just as you did for Statement (1). Therefore, Statement (2) is sufficient. The correct answer is D.

If in the equation , x is an integer, x > 0, and m is expressed as a decimal, what is the value of the tenths digit of m ? (1) x < 5 (2) x > 3 Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT.

To solve this problem, plug in some values for x and see what you get for m. Consider Statement (1): If x = 1, then m = 0.5 and the tenths digit of m is 5. If x = 2, then m = 0.25 and the tenths digit of m is 2. Statement (1) is therefore insufficient since you get at least 2 different values for the tenths digit. Therefore you are left with B, C, and E. Consider Statement (2): If x = 4, then m = 0.0625 and the tenths digit is 0. If x = 5, then m = 0.03125 and the tenths digit is also 0. You should notice a pattern here that as x increases, m will continue to decrease and the tenths digit will always be 0. Statement (2) is therefore sufficient. The final answer is B.

What is 20 percent of x? (1) Sixty percent of is less than 2x. (2) Forty percent of 8x is 16. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT

B. Yes. This statement could be translated as , and you could solve for x.

For all integers a and b, the operation # is defined as a # b = (-a + b)(b + a). If a = 2 and b = 5, then b # a = -25 -21 -7 21 25

B. Yes. Try plugging the numbers into the function: 5 # 2 = (-5 + 2)(2 + 5) = (-3)(7) = -21.

If a @ b @ c = (a - b) (b - c), then which of the following is equal to 5 @ 4 @ 3? 5 @ 3 @ 4 1 @ 1 @ 1 3 @ 4 @ 5 6 @ 4 @ 3 10 @ 8 @ 6

C. Yes. The first step is to calculate 5 @ 4 @ 3, which equals (5 - 4) (4 - 3), or 1. This answer choice equals (3 - 4) (4 - 5), which equals 1. So the answer is C.

Is 96 divisible by integer x? (1) x is divisible by 8. (2) x is divisible by 12. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT

E. Yes. Plug in. If x = 24, then 96 is divisible by x. If x = 72, then 96 is not divisible by x.

(sqrt(10)+sqrt(10)/sqrt(2))^2 10 20 50 100 200

First, rewrite the terms inside parenthesis to get (2sqrt(10)/sqrt(2))^2 Then, distribute the exponent, which yields 4x10/2 . Simplify to 20.

If the area of a right triangle with legs of 4 and 6 increases 25% to form a larger right triangle and the larger triangle has a base of length 2, what is the height of the larger triangle? 4.75 7.5 10 14 15

Yes. The area of the smaller triangle is × 4 × 6 = 12. Increasing 12 by 25% gives us a larger triangle with an area of 15. If we plug a base of 2 into the area formula, we get: × 2 × h = 15. Solving for h, we get a height of 15. The correct answer is E.

In the figure above, the perimeter of rectangle ABCD is 30, and the ratio of length to width is 2:1. If CE = CD, what is the area of triangle AED ? 30 25 20 15 10

D. Yes. Try making CE equal to 2 and CD equal to 5. That makes ED equal to 3, and the 2:1 ratio tells you that AD is equal to 10. Is the perimeter of ABCD 30? Yes. So, in triangle ADE, the base is equal to 10, and the height is equal to 3, and since the area of any triangle is equal to one-half the base times the height, the area of triangle ADE is 15.

A florist prepares bouquets of which 24 contain roses, 32 contain lilacs, and 16 contain both roses and lilacs. If every bouquet contains roses, lilacs, or both, how many bouquets did the florist prepare? 34 36 38 40 42

A. No. Since all of the bouquets contain roses, lilacs, or both, you can use the Group Equation: Total = Group1 + Group2 + Neither - Both. Hence, T = 24 + 32 + 0 - 16 = 40. B. No. Since all of the bouquets contain roses, lilacs, or both, you can use the Group Equation: Total = Group1 + Group2 + Neither - Both. Hence, T = 24 + 32 + 0 - 16 = 40. C. No. Since all of the bouquets contain roses, lilacs, or both, you can use the Group Equation: Total = Group1 + Group2 + Neither - Both. Hence, T = 24 + 32 + 0 - 16 = 40. D. Yes. Since all of the bouquets contain roses, lilacs, or both, you can use the Group Equation: Total = Group1 + Group2 + Neither - Both. Hence, T = 24 + 32 + 0 - 16 = 40. E. No. Since all of the bouquets contain roses, lilacs, or both, you can use the Group Equation: Total = Group1 + Group2 + Neither - Both. Hence, T = 24 + 32 + 0 - 16 = 40.

If x not equal to 0, what percent of x is y ? (1) x + y = 120 (2) x = 5y Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT

A. No. This statement allows for too many possibilities (x = 100 and y = 20, x = 119 and y = 1, etc.). B. Yes. This statement gives us a ratio, so we can find the percent.

A triangular sign was cut from a rectangular piece of paper. If the paper was cut so as to yield a sign of the greatest possible area, then what is the area of the remaining piece (or pieces) of paper? (1) The rectangular piece of paper originally had dimensions 16 inches by 24 inches. (2) The height of the triangle is 16 inches. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT

A. Yes. A triangle of the greatest possible area would have the largest possible base and height; in other words it would have the same base and height as the original rectangle. This statement gives us the base and height of the original rectangle.

One-fifth of the students at a nursery school are 4 years old or older. If 16 students have not yet reached their third birthday, and a total of 40 students are not between 3 years old and 4 years old, how many children are in the nursery school? 120 96 70 60 24

A. Yes. Backsolve! If the school has 120 children, then 120/5=24 children 4 years old or older. 16+24=40.

If 1/y= 7/2, then 1/y+2= 7/16 2/7 7/9 7/8 16/7

A. Yes. First, convert the right hand side of the equation into a fraction, 1/y=7/2. Next, cross-multiply to find out the value of y, 7y = 2, so y = 2/7 . Then put the value of y into the second equation, and solve, and you come up with 7/16 .

In order to modernize billing operations, a company bought a total of 60 computers and 20 printers. If the price of each computer was three times the price of each printer, what percent of the total cost of the purchase was the cost of one computer and one printer? 2 % 3 % 4 % % 12 %

A. Yes. Plug in for the "invisible variables": the unknown price of the printers and computers. Let's say printers cost $2 each; thus computers cost $6 each. Total cost of 20 printers is $40, and of 60 computers is $360. The total cost overall is thus $400. The question asks" what percent of the total cost was the cost of one computer and one printer?" One computer and one printer together cost $8, so the question is $8 is what percent of $400, or 8 = . The answer is 2%.

If r and s are non-negative, what is the ratio of r to s? (1) r is 60 percent of s. (2) r is 42 less than s. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT

A. Yes. Plug in. If s = 100, then r = 60, so the ratio of r to s is 60:100, which reduces to 3:5. If s=15, then r=12, so the ratio of r to s is 12:15, which again reduces to 3:5, so Statement 1 alone is sufficient to answer the question.

* + # = @ In the addition problem above, each of the symbols *, # and @ represents a positive single-digit number. If * > #, and if * and # are both odd, what is the value of *? (1) (2) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT

A. Yes. Statement (1) is sufficient. If then . * and # are positive and odd, so since , we know * and # must be 5 and 1. . Eliminate B, C, and E. Statement (2) is not sufficient. If , the * could be any odd positive number greater than 1. Eliminate D. The answer is A.

If ABCD shown above is a rectangle, what would be the length of a straight line drawn from point B to point D ? (1) The length of BC is 6, and the length of AB is the length of AD. (2) AD + AB = 10. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT

A. Yes. You can use the Pythagorean theorem to find the answer with this information. You should not, however, waste your time trying to find sqrt(52).

If # represents either addition, subtraction, multiplication, or division, and 4 # 0 = 4, which operation does # stand for? (1) 0 # 0 = 0 (2) 0 # 4 = 4 Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT

B. Yes. Statement 2 alone is sufficient since the only operation the # in the statement could be is addition.

For any values of a and b, s(a, b) represents the sum of a and b and p(a, b) represents the product of a and b. Is p(x, y) = 0 ? (1) s(x, y) = 0 (2) s(-x, y) = 0 Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT.

Because you are working with variables, plugging in may be a good strategy to use for this question. First, consider Statement (1). If s(x, y) = 0, then x + y = 0. Plug values in that make the equation true. For example, if x = 2 and y = -2, then p(2, -2) = 2 × -2 = -4 and the answer to the question is "no." However, if x = 0 and y = 0, then p(0, 0) = 0 × 0 = 0 and the answer to the question is "yes." Because you can get two different answers depending on what values you plug in, Statement (1) is not sufficient. Your remaining answers are B, C, and E. Now, consider Statement (2) If s(-x, y) = 0, then -x + y = 0. Plug values in that make the equation true. For example, if x = 2 and y = 2, then p(2, 2) = 2 × 2 = 4 and the answer to the question is "no." However, if x = 0 and y = 0, then p(0, 0) = 0 × 0 = 0 and the answer to the question is "yes," so Statement (2) is not sufficient. Your remaining answers are C and E. Finally, consider Statements (1) and (2) together. With this information x + y = 0 and -x + y = 0. Add these equations to get 2y = 0 and y = 0. Now you know that p(x, y) will always equal 0, since anything multiplied by 0 equals 0. In this case, p(x, 0) = x × 0 = 0, and the correct answer is C.

If x<0 and 0<x/y + 1< 1 , which of the following must be true? I. y>0 II. x/y>-1 III. 1/x + 1/y <0 I only I and II only I and III only II and III only I, II, and III

E. Yes. , so plug in -2 for x. This means that y must be positive, so plug in 3 for y. Therefore, Statement I is true. Eliminate D. Statement II is true, too, since . Eliminate A and C. Statement III is also true, since . Eliminate B, so the answer is E.

If x and y are positive integers, then what is the ratio of x to y? (1) x = 200 (2) y is 30 percent of x. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT

C. No. If you picked this answer choice you fell for their trap. The question asks you for the ratio, not actual numbers. So the relationship given in Statement 2 is enough by itself. The question is asking for . Translate "y is 30 percent of x" as ; you can solve this for .

A merchant has selected two items to be placed on sale, one of which currently sells for 30 percent less than the other. If he wishes to raise the price of the cheaper item so that the two items are equally priced, by what percentage must he raise the price of the less expensive item? 22 % 30% 42(6/7)% 70% 130%

C. Yes. Plugging In. Suppose the prices for the more expensive item is $100. So, the less expensive item is 30% less, or $70. To make them equal, you must raise the less expensive price by $30. Using the percent change formula you get . You can Ballpark this by looking for a number a little less than 50%. *PLUG IN HYPOTHETICAL ANSWERS*

What is the value of (x+y)/(x-y) ? (1) x = y + 4 (2) y = 8 - x Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

C. Yes. Statement 1 tells you the value of x - y, and Statement 2 tells you the value of x + y.

ABCDE is a regular pentagon with F at its center. How many different triangles can be formed by joining 3 of the points A, B, C, D, E and F? 10 15 20 25 30

C. Yes. There are two ways to approach this question. The first is to redraw the figure, then draw all the possible triangles. The second is to approach it as a combination problem. You have six possible points, A-F, and order does not matter, so your equation is: (6x5x4)/(3x2x1)=20

A retailer bought 4 cartons of product A and 2 cartons of product B for a total of $440. If a carton of product B costs 25 percent less than a carton of product A, how much does one carton of product A cost? $60.00 $73.33 $75.00 $80.00 $86.33

D. Yes. Plug in the answers. Start with (C): if A = 75, then 75 x 4 = 300; B would cost 75% of A, or , so two of these would = 112.50; add 300 and 112.50 and you get 412.50, which is too small. Eliminate (A), (B), and (C). Try (D): if A = 80, then 80 x 4 = 320; B would cost 75% of A, or , so two of these would = 120; add 320 and 120 and you get 440. Bingo.

By how many dollars has the cost of tuition increased since last year? (1) This year, tuition is 10 percent higher than it was last year. (2) Two years ago, tuition was $11,000. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT

E. Yes. Reading carefully, you'll notice that they tell you the tuition from two years ago, but the increase from last year.

A student bought both pens and notebooks. Did she buy more pens than notebooks? (1) The student spent a total of $4.00. (2) Pens cost $0.50 each and notebooks cost $1.00 each. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT

E. Yes. The two statements together do not allow us to answer the question in only one way; for instance, perhaps she bought two pens and three notebooks, or perhaps she bought four pens and two notebooks.

If x > 0 and y < 0, what is the value of x + y? (1) abs(x)= abs(y) (2) x^2=y^2 Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT.

First, consider Statement (1) alone. Since x is positive and y is negative, plug-in x = 2. The only value of y that satisfies the conditions of the question and the statement is y = - 2; x must be positive and y must be negative. The absolute value of 2 and that of −2 is 2. Hence x + y = 2 - 2 = 0. Plug in a second value for x. Consider a ZONE F number: plug-in x = 0.25. If x = 0.25, then y = - 0.25. Again, x + y = 0.25 - 0.25 = 0. Thus, for every possible value of x and y, x + y = 0. Statement (1) is sufficient. Eliminate BCE. Your remaining choices are AD. Next, consider Statement (2) alone. Plug in a value for x: x = 7. Since = 49, the value of y could only be −7; the only squared negative value that equals 49 is −7. Notice that the absolute values of x and y must be equal in order for the squares of x and y to be equal. Since the absolute values of x and y must be equal, x must be positive, and y must be negative, x + y = 0. Therefore, Statement (2) is sufficient. Eliminate A. The correct answer is D.

In an arithmetic sequence, each term after the first is the sum of the term before it plus a constant. In the arithmetic sequence a, b, c, d, e, each term after the first is the sum of the preceding term and the constant k. Which of the following is NOT an arithmetic sequence? a, b − 1, c − 2, d − 3, e − 4 a - 1, b - 1, c - 1, d - 1, e − 1 a − 1, b - 2, c - 3, d − 4, e − 5 a, 2b, 3c, 4d, 5e 3a, 3b, 3c, 3d, 3e

Notice that this question is testing a new mathematical definition. Although this does not appear obvious, by giving you a rule set to follow with variables, the question is testing functions. So, the best way to approach this question is to plug in some values and follow the instructions within the question stem. Plug 3 in for k and 2 for a, making a, b, c, d, and e equal to 2, 5, 8, 11, and 14 respectively. Then, plug into the answers. Choice A: With your numbers, a, b − 1, c − 2, d − 3, and e − 4 become 2, 4, 6, 8, and 10 respectively. This is an arithmetic sequence because there is a constant difference of 2 between consecutive terms. You're asked which answer choice is NOT an arithmetic sequence, so eliminate A. Choice B: With your numbers, a - 1, b - 1, c - 1, d - 1, and e - 1 become 1, 4, 7, 10, and 13 respectively. This is an arithmetic sequence because there is a constant difference of 3 between consecutive terms. You're asked which answer choice is NOT an arithmetic sequence, so eliminate B. Choice C: With your numbers, a − 1, b - 2, c - 3, d − 4, and e − 5 become 1, 3, 5, 7, and 9 respectively. This is an arithmetic sequence because there is a constant difference of 2 between consecutive terms. You're asked which answer choice is NOT an arithmetic sequence, so eliminate C. Choice D: With your numbers, a, 2b, 3c, 4d, and 5e become 2, 10, 24, 44, and 70 respectively. There is no constant difference between the elements in the set, so this is NOT an arithmetic sequence. Keep choice D. Choice E: With your numbers, 3a, 3b, 3c, 3d, and 3e become 6, 15, 24, 33, and 42 respectively. This is an arithmetic sequence because there is a constant difference of 9 between consecutive terms. You're asked which answer choice is NOT an arithmetic sequence, so eliminate E. Since only choice D is left, the correct answer is D.

If x and y are positive integers, what is the largest integer of which they are both multiples? (1) x is a multiple of 8, but y is not. (2) x and y are both multiples of 7. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT.

Start by assessing the question. The answer to this question will be a number that divides evenly into both x and y (making them multiples of the number) and that you can know for certain is the largest possible number that divides evenly into them. Another term for such a number is the greatest common factor. Now, evaluate Statement (1). You know that the answer to the question is not 8, but there are still many possibilities. Consider some actual numbers. If x = 8 and y = 5, then 1 is the greatest common factor. If x = 8 and y = 4, then 4 is the greatest common factor. Since multiple answers are possible, Statement (1) is insufficient. Write down BCE. Now, evaluate Statement (2). Again, you should choose numbers to prove that multiple answers are possible. If x and y are both 7, the n 7 is greatest common factor. If x = 14 and y = 28, then 14 is the greatest common factor. Since multiple answers are possible, Statement (2) is insufficient. Eliminate B. Now, evaluate the statements together. Notice that there are no restrictions limiting how big x and y might be, so it seems unlikely that you know with certainty the largest number that divides into them. Again, it is possible to find actual numbers that show that multiple answers are possible. If x = 56 and y = 7, then 7 is the greatest common factor. If x = 56 and y = 14, then 14 is the greatest common factor. Therefore the Statements together are insufficient. The correct answer is E.

If the average (arithmetic mean) of a group of numbers is 57, how many of the numbers are not equal to 57 ? (1) None of the numbers is less than 57. (2) None of the numbers is greater than 57. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT.

Start by evaluating Statement (1). If none of the numbers, which have an average of 57, are less than 57, then it is also impossible for any of the numbers to be greater than 57; changing even one number would change the mean from 57 to something higher. For example, if the mean is 57 and there are 10 numbers, all of the numbers must add up to 570. If none of the numbers are less than 57, then if some of the numbers are larger, the 10 numbers would not add up to 570. In fact, if all of the numbers are not less than 57, then the 10 numbers must all equal 57 in order for them to add up to 570. Statement (1) is therefore sufficient. Write down AD. Next, evaluate Statement (2). If there are eight numbers, and none of the numbers, which have an average of 57, can be greater than 57, it is impossible for any of the eight numbers to be lower than 57 without changing the average. The reasoning in this case is exactly the same as in the first statement. Thus, Statement (2) is also sufficient. The answer is D.

In a jar of marbles, the ratio of red marbles to green marbles is 9 to 5, and the ratio of red marbles to blue marbles is 1 to 3. If the ratio of the number of green marbles to the number of yellow marbles is 1 to 6, then what is the ratio of the number of red marbles to the number of yellow marbles? 3 to 10 10 to 27 9 to 5 10 to 3 5 to 9

Start by plugging in numbers for the number of marbles that work for this problem. You need to plug in numbers that make all of the numbers of marbles whole numbers. Start with the first ratio given: the ratio of red marbles to green marbles is 9 to 5. You must have a whole number of marbles, so the number of green marbles must be a multiple of 5. You can plug in 5 for the number of green marbles. There are 9 red marbles for every 5 green marbles, so the number of red marbles is 9. Next, you can figure out the number of yellow marbles. The ratio of green marbles to yellow marbles is 1 to 6, so there are six times as many yellow marbles as green marbles, Therefore, there are 30 yellow marbles. You now know that for every 9 red marbles, there are 30 yellow marbles. If you simplify the ratio by dividing both sides by 3, then the ratio becomes 3 red marbles to 10 yellow marbles. The correct answer is choice A, 3 to 10.

All of the shoppers in a grocery store are either male or female. Are there more than 25 male shoppers in the store? (1) There are 10 more male shoppers than female shoppers in the grocery store. (2) 40 percent of the shoppers are female. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT.

Start with Statement (1). This tells you that there are more men than women in the store, but you don't know if there are twice as many men. There could be 5 women and 15 men, in which case the answer would be "no", or there could be 20 women and 30 men, in which case the answer would be "yes." Statement (1) is not sufficient. Eliminate answers A and D. Write down BCE. From Statement (2) you can write the following algebraic expression. Let f equal the number of female shoppers, m equal the number of male shoppers, and s equal the number of total shoppers: Statement (2) alone is not sufficient, because you still don't know how many actual men and women are in the store. Eliminate answer B. Now, try the two statements together. You now have three pieces of information. The first is from the question stem, the second is from Statement (1), and the third is from Statement (2): This is sufficient, because you have three variables and three distinct equations. On yes/no DS questions, you don't actually have to solve the question, you just need to know that it's possible to. Here's how you would do the math. First, solve the first equation for m: Now, substitute your new m into the second equation: Solve for s: Next, substitute your new s into the third equation: Now you can solve for f. First, bring the fraction to the other side and simplify: Bring 2f over to the right side: Solve for f: f = 20 Now that you know how many shoppers are female, you can solve for the number of males using the second equation: Statements (1) and (2) together are sufficient, so eliminate E. The correct answer is C.

The projected profit of the Internet Division of a company for the year 2009 was 125% greater than the actual profit in 2008. If the actual profit in 2009 was 10% less than the actual profit in 2008, the actual profit in 2009 was what percent less than the projected profit for the year 2009 ? 28% 35% 40% 60% 72%

To solve this problem, try to plug in your own number. As the question asks what percent, start with 100. Assume that the actual profit in 2008 was $100. Therefore, the projected profit for the year 2009 was 125% greater than $100. 125% of $100 is, so the profit for 2009 was 100 + 125 = $225. The actual profit in 2009 was 10% less than the actual profit in 2008. Therefore, the actual profit in 2009 was (100 10) = 90. The question asks how much less the actual profit was in 2009 than the projected profit for the year 2009 and the answers are in percent form. The actual profit was (225 90) = $135 less than the projected profit of $225, which is (135/225)*100=60% The correct answer is D.

Is the diagonal of the rectangle pictured above less than 13? (1) x < 12 (2) The diagonal of the rectangle is greater than 10. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT SUFFICIENT

Using the Pythagorean Theorem, you know that 5^2 + 12^2 = 13^2. Since Statement 1 tells you that x is less than 12, then the diagonal can never be 13 or larger. Therefore, Statement (1) helps you to answer the question always yes. Statement 2 alone is not sufficient to consistently answer the question. The correct answer is A.

After reading 3/5 of his homework on Monday night, Bernie read 1/3 of his remaining homework on Tuesday night. What fraction of his original homework would Bernie have to read on Wednesday night to complete his assignment? 1/15 2/15 4/15 2/5 4/5

Yes. When you have an unknown in a word problem, and fractions for answers, you can plug-in for the unknown. Pick a number that is easy to work with, given the fractions in the problem. In this problem, you have the fractions 3/5 and 1/3 , so 15 is a good number. If his homework assignment is 15 pages, and he read 3/5 on Monday, he read 9 pages. Then he read 1/3 of his remaining homework (he has 6 pages remaining), so he read 2 pages. How much is left? 4 pages. So the answer is 4/15.

How do you solve for star shaped with angles and figuring out the sum of the angles?

figure out polygon area figure out system of equations using polygon angles and triangle angles