Analytical
Three division office managers, Fred, Al, and Cynthia draw office assistant each day from the clerical and typing pools available to them. The clerical pool consists of Lyndia, Jim, Dennis, and Sylvia. The typing pool consists of Edra, Gene, and Helen. The office assistants are selected according to the following conditions:Fred always needs at least one typist, but never more than two assistants.
Al always needs at least two assistants, but never more than three.
Sylvia or Gene and one other assistant always work for Cynthia.
Gene and Lyndia always work together.
Dennis and Edra will not work together
No more than two typists work for the same manager, but all three typists must work each day.
Question:
A blue eyed, brown haired male and a green eyed, red haired female have a child. All of the following are possible characteristics of the child except
A. Green Eyes, Brown Hair
B. Red Hair, Blue Eyes
C. Green Eyes, Red Hair
D. Blue Eyes, Brown Hair
E. All Are Possible
Correct Answer C
Explanation:
Only girls can have both green eyes and red hair. But any girl from a blue eyed, brown haired father must have at least one of his characteristics. Therefore, green eyes and re hair are not possible characteristics of his child.
Question:
A green eyed male
I. May have red hair
II. May have brown hair
III. Must have red hair
IV. Must have brown
A. I Only
B. II Only
C. III Only
D. IV Only
E. I And II
Correct Answer D
Explanation:
every male must have at least one f the following characteristics: blue eyes, brown hair. Therefore, a green eyed male must have brown hair.
Question:
Two blue eyed people get married. If their child has red hair. It MUST be true that
A. The Child Has Brown Eyes
B. The Mother Has Red Hair
C. The Child Is A Male
D. The Child Is Female
E. None Of The Above Must Be True
Correct Answer B
Explanation:
If two blue eyed people get married, the female must have red hair because all females have at least one of the following characteristics: green eyes and/ or red hair. Note that the father could also have blue eyes and red hair; therefore, the child could be either a boy or girl.
Question:
All of the children of a couple have brown hair, and the children are both boys and girls. Therefore, the mother
A. Must Have Brown Hair
B. Must Have Red Hair
C. Must Have Blue Eyes
D. Must Have Green Eyes
E. Non The Above
Correct Answer D
Explanation:
If all the children of a couple have brown hair, then the girls must have green eyes, brown hair. Thus, if the girls get their brown hair from their mother, then the other characteristic of their mother must be green eyes (since all females have at leas tone of green eyes/red hair). Or the girls could get their green eyes from their mother. Either way, their mother must have green eyes
Question:
A blue eyed, brown haired male and a blue eyed, red haired female marry (1st generation)and many years later are blessed with one grandchild. This grandchild (3rd generation) has red hair and green eyes. Which of the following MUST be true?
I. The child of the 1st generation is a female
II. The father from the 2nd generation has green eyes
III. The grandchild is a female
A. I
B. II
C. III
D. I And III
E. I,II And III
Correct Answer E
Explanation:
This is a difficult problem. Your chart should look like this:
1st Generation: Father Mother
blues eyes blues eyes
brown hair red hair
2nd Generation: If Male Child If Female child Child’s Spouse
blues eyes blues eyes ?
brown hair red hair
3rd Generation Grandchild
red hair
Green eyes
Since the grandchild has red hair and green eyes, she must be a girl (III). And since she is a girl, she must get one characteristic from each of her parents (the 2nd generation). Therefore, the only person from whom she could get green eyes would be the other spouse of the second generation (II). The red hair must thus come from the 2nd generation female (I).
There are five flagpoles in a row.
Each flagpole flies one flag and one pennant.
The flags are either red, white, or blue.
The pennants are either green, white, or blue.
On a given flagpole, the pennant and the flag can not be the same color.
Two adjacent flagpoles can not fly the same color flags.
Two adjacent flagpoles can not fly the same color pennants.
No more than two of any color flag or pennant may fly at one time.
Question:
If the 2nd and 5th pennants are blue, the 2nd and 5th flags are red, and the 3rd flag is whit, then which of the following must be true?
I. The 4th flag is blue
II. The 3rd pennant is green
III. If the 1st flag is white, then the 1st pennant is green
A. I And II
B. I And III
C. II And III
D. I,II, And III
E. None Of These
Correct Answer D
Explanation:
1 2 3 4 5 6
b/w R W b R (flag)
w/b B g w B (pennant)
The 3 pennant can not be blue or white, so therefore it is green. The 4th flag can not be white or red, so it must be blue. The 4th pennant can not be green or blue, so it must be white. The 1st flag can not be red, so it is either blue or white. The 1st pennant can not be blue, so it must be green or white. Thus statement I is true, statement II is true, and statement III is true.
Question:
if the 1st flag is red and the 2nd pennant is blue, then which of the following is not necessarily true?
A. The 2nd Flag Is White
B. If The 5th Flag Is Red, Then The 3rd Flag Is Blue
C. If The 4th Pennant Is Green, Then The 1st Pennant Is White
D. If The 1st And 5th Flags Are The Same Color, Then The 3rd Flag Is Blue
E. If The 4th Pennant Is Green And The 5th Pennant Is White, Then The 1st And 3rd Pennants Are Different Colors.
Correct Answer C
Explanation:
1 2 3 4 5
R w r/b (flag)
g/w B g/w (pennant)
(A) Is clearly true. If the 5th flag is red, then the 3rd flag can not be, since the 1st flag is red and we can have only two of any one color. Thus,(B) is true. If the 4th pennant is green, then the 3rd pennant must be white. But that does not determine the color of the 1st pennant. Thus, (C) is not necessarily true. (D) is the same as (A) and is also true. If the 4th pennant is green, this implies that the 3rd pennant must be white. If the 5th pennant is white, then the 1st pennant can not be. Therefore (E) is true.
Question:
if the 1st and 3rd flags are white and the 2nd and 4th pennants are blue, then which of the following is false?
A. The 4th Flag Is Red
B. The 1st Pennant Is Green
C. The 3rd Pennant Is Not Red
D. The 5th Pennant Is Green
E. There Is One Blue Flag
Correct Answer D
Explanation:
1 2 3 4 5
W r W b (flag)
g B g B w (pennant)
the facts in this problem determine the complete configuration of flags and pennants. (D) is the one statement that is false.
Question:
If the 1st and 4th flags are blue and the 3rd pennant is white, then which of the following must be true?
<="">I. If the 5th pennant is white, then the 1st pennant is green
II. If the 1st pennant is green, the 5th pennant is white
III. The 2nd flag I white
A. I And II
B. I And III
C. I,II And III
D. II Only
E. III Only
Correct Answer B
Explanation:
1 2 3 4 5
B W r B (flag)
w g (pennant)
statement I is true since the 1st pennant can not be blue or white. Statement II is false since the 5th pennant could be blue or white. Statement III is true; the 2nd flag can not be blue since two other flags are already blue, and it can not be red since the 3rd flag must be red.
Question:
If the 1st and 3rd flags are blue and the 1st and 4th pennants are white, then which of the following must be true?
I. The 2nd pennant is blue
II. The 5th flag is white
III. The 2nd flag is red
A. I And II
B. I And III
C. II And III
D. II, II And III
E. II Only
Correct Answer A
Explanation:
1 2 3 4 5
B r/W r w (flag)
W b g w g/b (pennant)
since the 3rd flag is blue and the 4th pennant is white, the 3rd pennant must be green and the 4th flag must be red. Since the 1st pennant is white, the 2nd pennant must be blue; thus I is true. Since the 1st and 3rd flags are blue, the 5th flag can not be blue. Since the 4th flag is red, the 5th flag must be white; thus II is true. Since the 2nd flag could be red or white, III is false.
Question:
If the 2nd flag is red and the 3rd flag is white, and the 4th pennant is blue, then which of the following must be true?
A. If The 5th Flag Is White, Then Two Of The Pennants Are Blue
B. If The 1st Flag Is With, Then The 2nd Flag Is White
C. If The 1st Pennant Is Blue, Then The 5th Pennant Is Green
D. If The 1st Pennant The 5th Flag Is Not Blue
E. If The 1st And 5th Flags Are The Same Color, Then The 1st And 5th Pennants Are Not He Same Color
Correct Answer A
Explanation:
1 2 3 4 5
R W r (flag)
g B (pennant)
if the 5th flag is white, then the 5th pennant must be green. Thus the 1st and 2nd pennants can not be green and can not be the same color, so one o them is blue. Therefore, (A) is true. All the other statements are false.
Question:
If the 1t flag and the 2nd pennant are the same color, the 3rd flag and the 4th pennant are the same color and the 4th flag and the 5th pennant are the same color, then which of the following must be true?
I. The 1st pennant is white
II. The 2nd flag is not white
III. The 5th flag is re
A. I Only
B. II Only
C. III Only
D. I And III
E. I, II And III
Correct Answer C
Explanation:
1 2 3 4 5
W B W B r (flag)
g w B W B (pennant)
1 2 3 4 5
B W B W r
g B W B W
since blue and white are the two common colors between flags and pennants, the above are the only two arrangements possible. In bother cases, the 5th flag is red and the 1st pennant is green. Thus III is the only statement the must be true.
Art, Dash, Aggie and Phil are taking part in a mystery role-playing game. Each has been assigned a method of committing a murder—poison, a knife, a tire iron or piano wire—and a set of rules regarding their use. The following rules and conditions are in effect:
• The tire iron cannot be used by a woman.
• Art has a broken arm, so he cannot use piano wire or the tire iron.
• Aggie and her husband are the same size and the smallest people in the game.
• For appearances, only the largest person is allowed to use the tire iron.
• Phil is the second largest person in the game.
• Neither Dash nor Aggie can use the poison.
• Neither Phil nor Aggie can use the knife.
Question:
Based on the information in the argument, which of the male contestants is married to Aggie?
A. Art
B. Dash
C. Phil
D. None Of Them
Correct Answer A
Explanation:
One of the initial conditions given in the passage that sets up the analytical exercise is that Aggie is the same size as her husband, and they are tied for the smallest person in the game. Since they are the smallest people in the game, and there are four players, the condition that identifies Phil as the second-largest person in the game eliminates him from consideration, which eliminates Statement C. Since Aggie’s husband is explicitly identified as playing the game, Statement D can be rejected out of hand. Additionally, since the initial conditions state that only the largest person can use the tire iron, and Art, Phil and Aggie have been eliminated from its use, that leaves Dash, which thus eliminates him as a possibility for Aggie’s husband, thus removing Statement B. Only Art can be Aggie’s husband, making A correct.
Question:
Which of the contestants has the least potential freedom in possible murder weapons based on the initial conditions and rules?
A. Phil
B. Dash
C. Art
D. Aggie
Correct Answer D
Explanation:
Of all the contestants, Aggie had the largest amount of information directly provided about her; in addition, the specificity of the information was greatest when applied to her. The rules and conditions were explicit in defining that Aggie could not use poison or the knife, but another condition stated that a woman could not use the tire iron, and as Aggie was explicitly identified as a woman by another condition, the choice of weapon was restricted to one by the primary information provided. All the other contestants were restricted by deduction and application of the other conditions, leaving Aggie with the greatest confinement; thus, D is the correct answer.
Question:
Which contestant has the least direct information provided about him or her?
A. Phil
B. Dash
C. Art
D. Aggie
Correct Answer B
Explanation:
Phil and Aggie are each mentioned directly in at least two of the initial conditions, which allows for more deductions to be made concerning them in the role-playing game; Aggie, in fact, is directly mentioned in three conditions, and another condition is about women in the game, of which Aggie is the only one, so yet more information is available. Art and Dash are directly mentioned only once apiece, but in the condition where Art is mentioned, the reader is given a good deal of information, including the statement that Art can’t use two of the possible four weapons. The condition which mentions Dash only states that he can’t use one of the four possible weapons, and that condition is shared with Aggie. Thus, of the game contestants, Dash has the least amount of direct information made available about him, which makes B correct.
Question:
Which weapon does Aggie use in the game?
A. Poison
B. Knife
C. Piano Wire
D. Tire Iron
Correct Answer C
Explanation:
As described in the initial conditions, Aggie can’t use either the poison or the knife for weapons in the game. Furthermore, the first of the initial conditions specifically states that the tire iron cannot be used by a woman in the game. Although Aggie is generally considered a feminine name, she is not explicitly identified as female until a later condition, where it states that Aggie and her husband are tied for the smallest people in the game. Once that identification is made, then the previous condition is applied to Aggie in the game, and the tire iron is eliminated from her use. That leaves only the piano wire for a possible weapon, which makes D the correct answer.
Question:
Which contestant is assigned poison as a murder weapon during the game?
A. Art
B. Aggie
C. Dash
D. Phil
Correct Answer D
Explanation:
By examining the information given, the reader can deduce the usage of the murder weapons by the relevant contestant. Looking at the initial conditions, Phil is explicitly identified as the second-largest of the contestants, and since another condition states only the largest contestant gets to use the tire iron, that weapon is thus ineligible for Phil to use. The last of the initial conditions explicitly states that Phil cannot use the knife, eliminating that weapon. As seen in a previous question, the reader has already deduced that Aggie was assigned the piano wire. That leaves only one weapon for Phil to use: the poison. Thus, D is the correct answer.
Jake is trying to arrange the radio station’s CD library on the new shelves according to the station manager’s instructions. However, the instructions were incomplete, and the manager is not available for clarification. The arrangement has to be done before the start of business the next day. Jake has to shelve five sets of CDs—rock, jazz, blues, Americana and metal, and has to deal with the following rules and conditions:
• The top two shelves each hold 100 CDs, and the bottom three hold 75 CDs apiece.
• Neither rock nor blues can be on the top shelf.
• There are 100 Americana, 100 blues, 75 metal CDs, 75 rock and 50 jazz CDs to shelve.
• No one genre can completely fill one shelf alone.
• Metal must come immediately after rock.
• Blues cannot be the last shelved genre.
Question:
Based on the rules and conditions set forth, what genre has to be the first one shelved?
A. Americana
B. Jazz
C. Rock
D. Blues
Correct Answer B
Explanation:
The initial conditions state explicitly that neither rock nor blues can be shelved first on the top shelf, which simultaneously eliminates both Statements C and D. Of the remaining genres, one of the initial conditions specifically says that no one genre can fill a shelf all by itself; since the top shelf holds 100 CDs, which is how many Americana CDs the library has, that disqualifies Americana from further consideration, which removes Statement A. Among the listed options (although even if metal were listed, it could not be shelved first, as the initial conditions say it must follow rock in the shelving), only jazz is allowable under the initial conditions to be shelved first, making B the correct answer.
Question:
What genre has to be the last one shelved?
A. Jazz
B. Rock
C. Metal
D. Blues
Correct Answer C
Explanation:
Since the initial conditions specifically state that blues cannot be the last genre shelved, Statement D is immediately eliminated out of hand. Similarly, the initial conditions state that metal must come after rock, which means that rock cannot be the last genre shelved; as a result, Statement B is eliminated. While there is no explicit reason that jazz cannot be last, the deduction as demonstrated in the previous question shows that jazz has to be the first genre shelved, which obviously eliminates it from consideration as the last one shelved, thus removing Statement A from consideration. Thus, only metal can be shelved last, which makes C the correct answer.
Question:
In what order must the genres be shelved based on the rules and conditions?
A. Jazz, Americana, Rock, Blues, Metal
B. Jazz, Rock, Blues, Metal, Americana
C. Jazz, Metal, Rock, Blues, Americana
D. Jazz, Americana, Blues, Rock, Metal
Correct Answer D
Explanation:
Again, examining the initial conditions will help eliminate options right away; the second condition listed states that neither rock nor blues can be on the top shelf, and since there are only 50 jazz CDs, Statement B can be eliminated because it would put rock CDs on the top shelf with the jazz CDs, which contradicts the aforementioned condition. Similarly, because one of the initial conditions states that metal must come after rock in the shelving, Statement C can be rejected as it reverses this order. Finally, since it is stated in the conditions that metal must immediately follow rock in the shelving, Statement A can eliminated, as it places blues between the two. Only Statement D meets all the conditions and completes the task as required, which makes D the correct answer.
