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9) Andres bought exactly two sorts of donuts, old-fashioned donuts and jelly donuts. If each old-fashioned donut costs $0.75 and each jelly donut costs $1.20, how many jelly donuts did Andres buy? (1) Andres bought a total of eight donuts. (2) Andres spent exactly $7.35 on donuts.

12) In nine independent trials, what is the probability that Outcome A happens at least once?

Statement #1: The probability that Outcome A does not happen even once in any of the nine trials is 0.026 Statement #2: the probability of Outcome A resulting in a single trial is 1/3.

13) A class contains boys and girls. What is the probability of selecting a boy from a class? Statement #1: there are 35 students in the class Statement #2: the ratio of boys to girls is 3:4

14) From a group of M employees, N will be selected, at random, to sit in a line of N chairs. There are absolutely no restrictions, either in the selection process nor in the order of seating — both are entirely random. What is the probability that the employee Andrew is seated somewhere to the right of employee Georgia? Statement #1: N = 15 Statement #2: N = M

15) From a group of J employees, K will be selected, at random, to sit in a line of K chairs. There are absolutely no restrictions, either in the selection process nor in the order of seating — both are entirely random. What is the probability that the employee Lisa is seated exactly next to employee Phillip? Statement #1: K = 15 Statement #2: K = J

16) Bert has $1.37 of loose change in his pocket —- pennies ($0.01), nickels ($0.05), dimes ($0.10), and quarters ($0.25). He reaches into his pocket and pulls out one coin at random. What is the probability that the coin is a nickel?

Statement #1: There are exactly seven pennies in his pocket Statement #2: There are exactly three quarters in his pocket

17) In a single Epsilon trial, the probability of Outcome T is 1/4. Suppose a researcher conducts a series of n independent Epsilon trials. Let P = the probability that Outcome T occurs at least once in n trials. Is P > 1/2? Statement #1: n > 3 Statement #2: n < 6

18) Suppose A and B are two events that are not independent. Is the probability P(A and B) > 1/3? Statement #1: P(A) = 0.8 and P(B) = 0.7 Statement #2: P(A or B) = 0.9

19) A group of N students will be randomly seated in a row of N chairs. What is the probability that Beth, one of the students, will be at the extreme right-hand end of the row? Statement #1: N is an odd prime number Statement #2: the probability that Steve, another one of the students, is at the extreme left-hand end of the row is 1/13

20) K is a rectangular solid. Find the volume of K (1) a diagonal line across the front face of K has a length of 40 (2) a diagonal line across the bottom face of K has a length of 25

21)M is a rectangular solid. Find the volume of M (1) The bottom face of M has an area of 28, and the front face, an area of 35. (2) All three dimensions of M are positive integers greater than one.

22) Q is a cube. Find the volume of the cube. (1) The total surface area of Q is 150 sq cm (2) The distance from one vertex of Q to the catty-corner opposite vertex is 5*sqrt(3)

23) A certain lighthouse is a tall thin cylinder of brick, with a light chamber at the top. The brick extends from the ground to the floor of the light chamber. The brick siding of lighthouse is in need of painting. How many square feet of brick does it have?

(1) The outer diameter of the brick portion of the lighthouse is 28 ft (2) There are 274 steps from ground level to the floor of the light chamber, and each one is 8 inches high.

33) In a card game named Allemande, each of four players has a hand of 8 cards from a standard deck of 52. Through a series of discards, players try to maximize the point value of their final hand. Suits are irrelevant. Cards Ace through 10 have a point value of the number of their card: for example, the five of any suit would be worth 5 points. Face cards (Jack, Queen, and King) are worth 20 points each. Does Charles have the highest value final hand? Statement #1: Charles’ hand is worth 117 points. Statement #2: No other player besides Charles has more than four face cards in his hand.

34) Each of three students is given fifteen tokens to spend at a fair with various tents to visit. Some tents cost 3 tokens to enter, and some, 4 tokens. How many tents did Amelia visit?

Statement #1: Amelia bought one token from another classmate, and spent all the tokens in her possession. Statement #2: Not all of the tents Amelia visited were the same token-price.

35) A group of five friends have $87 dollars between them. Each one only has bills, that is, whole dollar amounts, no coins. Dolores has $29: does she have the most money of the five of them?

Statement #1: Three of the friends are tied for the median value, and one has two dollars less. Statement #2: Two of the friends, Andie and Betty, have $30 between them, and each has more than $5 herself.

36) Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 20 machines produce in 6 minutes?

37) Jane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?

38) Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars?

39) The number of boxes in a warehouse can be divided evenly into 6 equal shipments by boat or 27 equal shipments by truck. What is the smallest number of boxes that could be in the warehouse? (A) 27 (B) 33 (C) 54 (D) 81 (E) 162

43) If n is a positive integer, then n(n + 1)(n – 1) is (A) even only when n is even (B) odd only when n is even (C) odd only when n is odd (D) always divisible by 3 (E) always one less than a prime number

44) Of the 80 houses in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool, and 35 have both a two-car garage and an in-the-ground swimming pool. How many houses in the development have neither a two-car garage nor an in-the-ground swimming pool? A. 10 B. 15 C. 20 D. 25 E. 30

45) A certain school has three performing arts extracurricular activities: Band, Chorus, or Drama. Students must participate in at least one, and may participate in two or even in all three. There are 120 students in the school. There are 70 students in Band, 73 in the Chorus, and 45 in the Drama. Furthermore, 37 students are in both the Band and Chorus, 20 are in both the Band and the Drama, and 8 students are in all three groups. Twenty-five students are just in the chorus, not in anything else. How many students participate in only the drama? A. 11 B. 12 C. 14 D. 17 E. 21

46) In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree and is female? (A) 1/20 (B) 1/10 (C) 1/5 (D) 2/5 (E) 3/4

47) In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree or is female? (A) 1/20 (B) 1/10 (C) 1/5 (D) 2/5 (E) 3/4

Simplify the question to the absolute basics… translate information as to what the question seeks to ask. Most of the DS questions can be simplified.

Do not assume anything. For example, if a number is not mentioned to be an integer, don’t assume it to be so.

In geometrical figures, do not assume that a figure is what it looks like. If it is not mentioned that two lines are parallel, don’t assume so. If a figure looks like a square but is not mentioned to be so, please do not assume it to be so.

The same applies to right angles. An angle of 89.9º or 90.1º will look like a right angle to the unaided eye, but if it’s not an exact right angle, none of the special right angle facts (like the Pythagorean Theorem) will apply.

While evaluating Statement (2), don’t “mentally” carry forward the information from Statement (1) to Statement (2). Statement (2) is independent of Statement (1) and vice-versa.

In “WHAT” questions, a unique numerical value is required. There should be NO AMBIGUITY.

In “IS” or “Does” type of questions, you must get a unique YES or a unique NO. There should be NO AMBIGUITY.

An unambiguous “NO” is as acceptable as an unambiguous “YES”.

Intentionally try to create a yes / no situation: don’t try to prove or disprove alone… you should try both.

There is no need to calculate the answer in most cases. Avoid calculations, wherever possible.

In a “WHAT” question, if two statements are not independently sufficient, but, on combining, result in a unique common value, then the common value will be the answer. The two statements never contradict each other.

In questions involving the solving of two simultaneous equations, usually only one statement will be sufficient.

9) Andres bought exactly two sorts of donuts, old-fashioned donuts and jelly donuts. If each old-fashioned donut costs $0.75 and each jelly donut costs $1.20, how many jelly donuts did Andres buy? (1) Andres bought a total of eight donuts. (2) Andres spent exactly $7.35 on donuts.

12) In nine independent trials, what is the probability that Outcome A happens at least once?

Statement #1: The probability that Outcome A does not happen even once in any of the nine trials is 0.026 Statement #2: the probability of Outcome A resulting in a single trial is 1/3.

13) A class contains boys and girls. What is the probability of selecting a boy from a class? Statement #1: there are 35 students in the class Statement #2: the ratio of boys to girls is 3:4

14) From a group of M employees, N will be selected, at random, to sit in a line of N chairs. There are absolutely no restrictions, either in the selection process nor in the order of seating — both are entirely random. What is the probability that the employee Andrew is seated somewhere to the right of employee Georgia? Statement #1: N = 15 Statement #2: N = M

15) From a group of J employees, K will be selected, at random, to sit in a line of K chairs. There are absolutely no restrictions, either in the selection process nor in the order of seating — both are entirely random. What is the probability that the employee Lisa is seated exactly next to employee Phillip? Statement #1: K = 15 Statement #2: K = J

16) Bert has $1.37 of loose change in his pocket —- pennies ($0.01), nickels ($0.05), dimes ($0.10), and quarters ($0.25). He reaches into his pocket and pulls out one coin at random. What is the probability that the coin is a nickel?

Statement #1: There are exactly seven pennies in his pocket Statement #2: There are exactly three quarters in his pocket

17) In a single Epsilon trial, the probability of Outcome T is 1/4. Suppose a researcher conducts a series of n independent Epsilon trials. Let P = the probability that Outcome T occurs at least once in n trials. Is P > 1/2? Statement #1: n > 3 Statement #2: n < 6

18) Suppose A and B are two events that are not independent. Is the probability P(A and B) > 1/3? Statement #1: P(A) = 0.8 and P(B) = 0.7 Statement #2: P(A or B) = 0.9

19) A group of N students will be randomly seated in a row of N chairs. What is the probability that Beth, one of the students, will be at the extreme right-hand end of the row? Statement #1: N is an odd prime number Statement #2: the probability that Steve, another one of the students, is at the extreme left-hand end of the row is 1/13

20) K is a rectangular solid. Find the volume of K (1) a diagonal line across the front face of K has a length of 40 (2) a diagonal line across the bottom face of K has a length of 25

21)M is a rectangular solid. Find the volume of M (1) The bottom face of M has an area of 28, and the front face, an area of 35. (2) All three dimensions of M are positive integers greater than one.

22) Q is a cube. Find the volume of the cube. (1) The total surface area of Q is 150 sq cm (2) The distance from one vertex of Q to the catty-corner opposite vertex is 5*sqrt(3)

23) A certain lighthouse is a tall thin cylinder of brick, with a light chamber at the top. The brick extends from the ground to the floor of the light chamber. The brick siding of lighthouse is in need of painting. How many square feet of brick does it have?

(1) The outer diameter of the brick portion of the lighthouse is 28 ft (2) There are 274 steps from ground level to the floor of the light chamber, and each one is 8 inches high.

33) In a card game named Allemande, each of four players has a hand of 8 cards from a standard deck of 52. Through a series of discards, players try to maximize the point value of their final hand. Suits are irrelevant. Cards Ace through 10 have a point value of the number of their card: for example, the five of any suit would be worth 5 points. Face cards (Jack, Queen, and King) are worth 20 points each. Does Charles have the highest value final hand? Statement #1: Charles’ hand is worth 117 points. Statement #2: No other player besides Charles has more than four face cards in his hand.

34) Each of three students is given fifteen tokens to spend at a fair with various tents to visit. Some tents cost 3 tokens to enter, and some, 4 tokens. How many tents did Amelia visit?

Statement #1: Amelia bought one token from another classmate, and spent all the tokens in her possession. Statement #2: Not all of the tents Amelia visited were the same token-price.

35) A group of five friends have $87 dollars between them. Each one only has bills, that is, whole dollar amounts, no coins. Dolores has $29: does she have the most money of the five of them?

Statement #1: Three of the friends are tied for the median value, and one has two dollars less. Statement #2: Two of the friends, Andie and Betty, have $30 between them, and each has more than $5 herself.

36) Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 20 machines produce in 6 minutes?

37) Jane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?

38) Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars?

39) The number of boxes in a warehouse can be divided evenly into 6 equal shipments by boat or 27 equal shipments by truck. What is the smallest number of boxes that could be in the warehouse? (A) 27 (B) 33 (C) 54 (D) 81 (E) 162

43) If n is a positive integer, then n(n + 1)(n – 1) is (A) even only when n is even (B) odd only when n is even (C) odd only when n is odd (D) always divisible by 3 (E) always one less than a prime number

44) Of the 80 houses in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool, and 35 have both a two-car garage and an in-the-ground swimming pool. How many houses in the development have neither a two-car garage nor an in-the-ground swimming pool? A. 10 B. 15 C. 20 D. 25 E. 30

45) A certain school has three performing arts extracurricular activities: Band, Chorus, or Drama. Students must participate in at least one, and may participate in two or even in all three. There are 120 students in the school. There are 70 students in Band, 73 in the Chorus, and 45 in the Drama. Furthermore, 37 students are in both the Band and Chorus, 20 are in both the Band and the Drama, and 8 students are in all three groups. Twenty-five students are just in the chorus, not in anything else. How many students participate in only the drama? A. 11 B. 12 C. 14 D. 17 E. 21

46) In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree and is female? (A) 1/20 (B) 1/10 (C) 1/5 (D) 2/5 (E) 3/4

47) In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree or is female? (A) 1/20 (B) 1/10 (C) 1/5 (D) 2/5 (E) 3/4

Simplify the question to the absolute basics… translate information as to what the question seeks to ask. Most of the DS questions can be simplified.

Do not assume anything. For example, if a number is not mentioned to be an integer, don’t assume it to be so.

In geometrical figures, do not assume that a figure is what it looks like. If it is not mentioned that two lines are parallel, don’t assume so. If a figure looks like a square but is not mentioned to be so, please do not assume it to be so.

The same applies to right angles. An angle of 89.9º or 90.1º will look like a right angle to the unaided eye, but if it’s not an exact right angle, none of the special right angle facts (like the Pythagorean Theorem) will apply.

While evaluating Statement (2), don’t “mentally” carry forward the information from Statement (1) to Statement (2). Statement (2) is independent of Statement (1) and vice-versa.

In “WHAT” questions, a unique numerical value is required. There should be NO AMBIGUITY.

In “IS” or “Does” type of questions, you must get a unique YES or a unique NO. There should be NO AMBIGUITY.

An unambiguous “NO” is as acceptable as an unambiguous “YES”.

Intentionally try to create a yes / no situation: don’t try to prove or disprove alone… you should try both.

There is no need to calculate the answer in most cases. Avoid calculations, wherever possible.

In a “WHAT” question, if two statements are not independently sufficient, but, on combining, result in a unique common value, then the common value will be the answer. The two statements never contradict each other.

In questions involving the solving of two simultaneous equations, usually only one statement will be sufficient.