Tables for difficult problem solving questions

[Shenz0r]

Hey guys, I'm having trouble making tables for a few problem solving questions and some help would be appreciated right now.

Q1: James has three jugs with capacities of 11, 13 and 17 cups. Each jug contains 9 cups of water. By pouring jug to jug, and not spilling any water, James aims to measure exactly 8 cups of water.

What is the minimum number of pours required?
A. 3
B. 4
C. 5
D. 6

Q2: The number of false statements in this paragraph is one. The number of false statements in this paragraph is two. The number of false statements in this paragraph is three. The number of false statements in this paragraph is four.

How many false statements in the above paragraph?
A. 1
B. 2
C. 3
D. 4

Q3: Agnes, Becky, Cindy & Delia crossed a lake in a canoe that held only two people. The canoe held two people on each of the three forward trips across the lake and one person on each of he two return trips. Agnes was unable to paddle when someone else was in the canoe with her. Becky was unable to paddle when anybody else except Cindy was in the canoe with her. Each person paddled continuously for at least 1 trip.

The person who paddled twice is:

A. Agnes
B. Becky
C. Cindy
D. Delia

[paulsterio]

I'll do Q2 first because it's the easiest, the answer is three false!
This is because the 1st, 2nd and 4th statements are false and the 3rd statement is true (comes from experience really)

So Q2 is C

[Shenz0r]

I'll do Q2 first because it's the easiest, the answer is three false!
This is because the 1st, 2nd and 4th statements are false and the 3rd statement is true (comes from experience really)

So Q2 is C

Oh true, I see it now lol

If the first statement is true, it states that there is only 1 false statement but since there are 3 statements that say there is at least 1 false statement, it indicates that the 1st statement cannot be true, and the same logic goes for the 2nd and 4th statements.

If the third statement is true, it states there are 3 false statements and this coincides perfectly as the 1st, 2nd and 4th statements cannot be true at the same time

Cheers!

[paulsterio]

That's one way of thinking about it, the other, faster way, is to couple the statements. Now we know that you have to have 3 false statements because you have a set of 4 statements which are contradictory meaning that 2 or more statements cannot be true together. (For example, you cannot have 1 false statement and 2 false statements at the same time - it makes no logical sense) - thus you must have 3 false statements.

(You can also have 4 false statements - but it's irrelevant in this case)

[Stick]

Question 3 can be solved using a diagram:

Becky paddles, Cindy sits
-------------------------------->
(We will use this scenario first since it is a combination we've been given exactly.)

Cindy paddles
<--------------------------------
(We know that either Becky or Cindy must return with the canoe. - Read part 3.)

Cindy paddles, Agnes sits
-------------------------------->
(Agnes must sit in this leg and Becky does not paddle when anyone except Cindy is in the boat with her. Hence, we know Cindy must have paddled back in order to get Agnes. Cindy has paddled twice.)

<--------------------------------

-------------------------------->

Without even knowing the last two legs, we know the answer is C.

[Shenz0r]

I just found a solution to Q1:
Original: 9 9 9
9 13 5
0 13 14
8  5  14
Therefore 3 pours required.
But my friend says that:
"you have to do it by filling the top of the jug
cause he doesn't know what 8 cups is exactly
so you cant just do it from 0 13
to 8 5

9 9 9
9 13 5
0 13 14
0 10 17
11 10 6
8 13 6"
Therefore 5 cups required, I think this is a more logical solution?

Just found a few more questions I had trouble with:

A lock is made of a combination of 4 digits randomly chosen from the numbers 0 to 9 inclusive. The only clues given to find the correct combination are:
1. No digit is repeated.
2. The sum of all the four digits is 21.
3. The sum of the first and third digit is twice the sum of the remaining digits.
4. Adjacent digits cannot have a highest common factor above 1.
5. The first and last digits cannot have a highest common factor above 1.

Which number cannot be third in the combination?
A. 0 and 7
B. 5 and 9
C. 0
D. 7

When all the digits of each possible combination are multiplied to gain the product, the number is:
A. 0
B. 315
C. 420
D. 540

[pi]

Which number cannot be third in the combination?
A. 0 and 7
B. 5 and 9
C. 0
D. 7

0 can't be in third position because otherwise the sum would be two small (remember that  0+x must be double the sum of the other two numbers)

7 can't either, because then the sum will be too big

Ideally you want 2x+x=21, therefore x=7. Hence, 2x=14. If 7 was the third digit, then 7 must also be the first digit, which is not allowed. If 0 was the third digit, the other one would have to be 14, which is not allowed

Therefore A

When all the digits of each possible combination are multiplied to gain the product, the number is:
A. 0
B. 315
C. 420
D. 540

D

Just find any combo that works, eg. 9453

[Shenz0r]

When all the digits of each possible combination are multiplied to gain the product, the number is:
A. 0
B. 315
C. 420
D. 540

D

Just find any combo that works, eg. 9453

It can't be D, the first and last digits have a highest common factor of 3.

[Milkshake]

I got 0, using 8067

[pi]

When all the digits of each possible combination are multiplied to gain the product, the number is:
A. 0
B. 315
C. 420
D. 540

D

Just find any combo that works, eg. 9453

It can't be D, the first and last digits have a highest common factor of 3.

Yep, my bad.

Milkshake is correct

[Shenz0r]

Two of Anthony, Bernard and Charles are in a boxing match with each other. The shorter of Anthony and Bernard is the older of the two boxers. The younger of Bernard and Charles is the shorter of the two brothers. The taller of Anthony and Charles is the younger of the two brothers.

Who is not in the boxing match?
A. Anthony
B. Bernard
C. Charles.
D. Insufficient information.

Mike has a number of pencils in his case. He has at least 2 black pencils, 2 blue pencils, 2 red pencils, 2 orange pencils, but has no more than 3 pencils of a particular colour.

Without looking at the colours, what is the minimum number of pencils he must remove to guarantee he has two pairs, each of the same colour?

A. 5
B. 7
C. 9
D. None of the above

Lee, Dale and Terry are related to each other. Among the three are Lee's spouse, Dale's spouse and Terry's sister-in-law. Lee's spouse and Dale's sibling are of the same sex. No one if married to a person of the same sex. Who is the married man?

A. Lee
B. Dale
C. Terry
D. Cannot be determined.

Alan wants to call his friend Jameson whose phone number is 238. Unfortunately, many of the numbers on his phone are labelled incorrectly. The following rules apply:

1. The number 7 is labelled correctly.
2. The true numbers 1, 2 and 3 have an identical pitch when pressed.
3. The true numbers 4, 5 and 6 have an identical pitch when pressed.
4. The true numbers 7, 8 and 9 have an identical pitch when pressed.
5. No number is labelled correctly unless specified by another Rule
6. Alan has access to perfect pitch-recognition techology.

What are the chances that he dials the correct number on his first attempt?

A. 1/24
B. 1/80
C. 1/116
D. 1/504

Which of the following changes will result in the chances of him dialling the correct number on his first attempt becoming 1/108?

A. The deletion of Rule 1
B. The changing of any of Rules 2, 3 or 4 such that each number referred in the rule has a distinct pitch.
C. Both A and B
D. None of the above.

The island Folkel has three types of inhabitants: Yokels, Bokels and Dokels. Yokels always tell the truth, Bokels always lie and Dokels sometimes lie and sometimes tell the truth. On this island, a man and a woman only marry if they are both Dokels, or if one of them is a Yokel and one is a Bokel. Mr and Mrs X, who live on the island, claim the following:

Mr X: "My wife is not a Dokel"
Mrs. X: "My husband is not a Dokel".

What type of people are Mr. and Mrs X?

A. Mr X is a Dokel, Mrs X is not a Dokel
B. Mr X is not a Dokel, Mrs X is a Dokel
C. Both are Dokels
D. Both are not Dokels

(Will post more Qs soon)

[illuminati]

Two of Anthony, Bernard and Charles are in a boxing match with each other. The shorter of Anthony and Bernard is the older of the two boxers. The younger of Bernard and Charles is the shorter of the two brothers. The taller of Anthony and Charles is the younger of the two brothers.

Who is not in the boxing match?
A. Anthony
B. Bernard
C. Charles.
D. Insufficient information.

I'd say D but usually there's an answer (so don't take my word for it). I think your question just has no information, because only one sentence there refers to a boxer. The other two just refer to the height and age, doesn't give us any information about the other boxer :S....

Mike has a number of pencils in his case. He has at least 2 black pencils, 2 blue pencils, 2 red pencils, 2 orange pencils, but has no more than 3 pencils of a particular colour.

Without looking at the colours, what is the minimum number of pencils he must remove to guarantee he has two pairs, each of the same colour?

A. 5
B. 7
C. 9
D. None of the above

So this one should be B. Let's assume that he has 3 of each pencil, because the more pens he has the harder it will be to get 2 pairs. If he picks. We are trying to find the minimum number that is necessary. So lets say we draw 1 pencil of each colour. We have no pairs and 4 pencils have been taken out. The next one has to be a pair. so thats 5. If we then draw another pencil of the same colour (we now have 3 of the same colour and 3 different ones), we still don't have two pairs. The last pencil we draw will have to be a pair so then we need a minimum of 7.

Lee, Dale and Terry are related to each other. Among the three are Lee's spouse, Dale's spouse and Terry's sister-in-law. Lee's spouse and Dale's sibling are of the same sex. No one if married to a person of the same sex. Who is the married man?

A. Lee
B. Dale
C. Terry
D. Cannot be determined.

B. Dale and Lee must be married to each other because there are two spouses. The fact that Terry has a sister in law means that they are the sibling of the husband. So Dale has a sibling which presumably is Terry, and if Terry has a SISTER-IN-LAW then Dale must be the man of the relationship

Alan wants to call his friend Jameson whose phone number is 238. Unfortunately, many of the numbers on his phone are labelled incorrectly. The following rules apply:

1. The number 7 is labelled correctly.
2. The true numbers 1, 2 and 3 have an identical pitch when pressed.
3. The true numbers 4, 5 and 6 have an identical pitch when pressed.
4. The true numbers 7, 8 and 9 have an identical pitch when pressed.
5. No number is labelled correctly unless specified by another Rule
6. Alan has access to perfect pitch-recognition techology.

What are the chances that he dials the correct number on his first attempt?

A. 1/24
B. 1/80
C. 1/116
D. 1/504

I'd say A, but the question is really not so great. If the guy knows that 7 is labelled correctly and knows the pitch of 7, he therefore knows the pitch of 8 and 9. So he has a 1/6 chance of hitting the 2 with his first shot (in theory it should be 1/5 because he knows that 2 is not correctly labelled, if he knows the rule exists at all?), then he has a 1/2 chance of hitting the 3 and then a 1/2 chance of hitting the 8. Not a great question at all.

Which of the following changes will result in the chances of him dialling the correct number on his first attempt becoming 1/108?

A. The deletion of Rule 1
B. The changing of any of Rules 2, 3 or 4 such that each number referred in the rule has a distinct pitch.
C. Both A and B
D. None of the above.

A. Without rule 1, the chance that he hits the 2 initially is 1/9. Since he knows the 3 is of the same pitch then he has a 1/2 chance of hitting it. Knowing that the 8 is of different pitch than the 1, 2, 3 means he has a 1/6 chance of hitting it. Again, up for dispute.

The island Folkel has three types of inhabitants: Yokels, Bokels and Dokels. Yokels always tell the truth, Bokels always lie and Dokels sometimes lie and sometimes tell the truth. On this island, a man and a woman only marry if they are both Dokels, or if one of them is a Yokel and one is a Bokel. Mr and Mrs X, who live on the island, claim the following:

Mr X: "My wife is not a Dokel"
Mrs. X: "My husband is not a Dokel".

What type of people are Mr. and Mrs X?

A. Mr X is a Dokel, Mrs X is not a Dokel
B. Mr X is not a Dokel, Mrs X is a Dokel
C. Both are Dokels
D. Both are not Dokels

C. A and B are impossible since Dokels must marry eachother. D does not work because if they are both not Dokels, then they must be Yokel and Bokel, making both their statements true. If they are Yokel and Bokel then one of their statements has to be false, so therefore they are both Dokels by elimination

[Shenz0r]

Every person in their genetic make-up has two chromosomes, one inherited from each parent. Chormosomes are comprised of genes, which code for certain traits. The sequence of genes inherited on chromosomes from each parent are identical but the genes can have different forms (alleles). In some cases, certain alleles can code for disease states, or genetic disorders.

Disease A is a recessive genetic disorder. This means that for somebody to have the disease they must have inherited two diseased alleles, one from each parent. Individuals who have one faulty gene are termed "carriers" as they do not suffer the disorder themselves, but have the potential to pass on the faulty gene to their child. Hence, both parents must be carriers for a child to suffer from this disorder.

Disease B is a dominant genetic disorder. This means that for someone to have the disease, they need only one faulty gene. Hence, a person with a dominant genetic disorder must have a parent whi is also suffering from the same disorder. In the case of disease B, an individual born with two faulty alleles will not survive bast adulthood.

Both grandmothers of a child suffer from disease A, both grandfathers neither suffer from disease A or are they carriers. One grandfather of the child suffers from disease B.

A. The child has 0.50 chance of having disease A and 0.25 chance of having disease B.
B The child has 0.25 chance of having disease A and 0.50 chance of having disease B.
C. The child has 0.25 chance of having disease A and 0.25 chance of having disease B.
D. The child has 0.50 chance of having disease A and 0.50 chance of having disease B.

Art, Bob, Cab and Ida are guards in a museum. Each of Art, Bob and Cab stands guard on exactly four days a week. Exactly two persons stand guard together every day. No person stands guard 3 days in a row. Here is a partial listing that shows when they stand guard every week.

Sun    Mon   Tues   Wed    Thurs    Fri    Sat
Art     Cab    Ida     Art       Bob     Cab   Ida
Bob    ?        ?       ?           ?        ?       ?

Who does not stand guard with Ida?

A. Art
B. Bob
C. Cab
D. Not possible to determine.

Amos, Bert and Clem are brothers. Amos has exactly two brothers with grey eyes. Bert has exactly two brothers with grey or hazel eyes. Clem has exactly two brothers who do not have blue eyes. At least one of the three has hazel eyes and at least one of the three has blue eyes.

It is possible to determine the eye colour of
A. Amos
B. Bert
C. Clem
D. None of the three brothers

[BlueSky_3]

Does anyone know the kind of scores required on the individual sections to get an overall score of percentile of 95 on the Medentry trial exams?

[BlueSky_3]

Bump! Anyone?