1. Most Intelligent GuyA father wants his daughter to marry the smartest of 3 extremely intelligent young guys, and so the father devised an intelligence test.The guy’s are gathered into a room and seated, facing one another, and are shown 2 black hats and 3 white hats. They are blindfolded, and 1 hat is placed on each of their heads, with the remaining hats hidden in a different room.The father tells them that the first guy to deduce the color of his hat without removing it or looking at it will marry his daughter. A wrong guess will mean death. The blindfolds are then removed.You are one of the guys. You see 2 white hats on the other guy's heads. After some time you realize that the other guy's are unable to deduce the color of their hat, or are unwilling to guess. What color is your hat?Answer: White.The father would not select two white hats and one black hat. This would mean two guys would see one black hat and one white hat. You would be at a disadvantage if you were the only guy wearing a black hat.If you were wearing the black hat, it would not take long for one of the other guy to deduce he was wearing a white hat.If an intelligent guy saw a white hat and a black hat, he would eventually realize that the king would never select two black hats and one white hat. Any guy seeing two black hats would instantly know he was wearing a white hat. Therefore if a guy can see one black hat, he can work out he is wearing white.Therefore the only fair test is for all three guys to be wearing white hats. After waiting some time just to be sure, you can safely assert you are wearing a white hat.

2. Camille is older than Eric. Cliff is older than Camille. Eric is older than Cliff. If the first two statements are true, the third statement is

A. true

B. false

C. uncertain

Answer: Option B

Explanation:

Because the first two statements are true, Eric is the youngest of the three, so the third statement must be false.

3. The Stark Raving Boss

A stark raving boss tells his 100 wisest workers he is about to line them up and that he will place either a black or brown hat on each of their heads. Once lined up, they must not communicate amongst themselves. Nor may they attempt to look behind them or remove their own hat.The boss tells the wise men that they will be able to see all the hats in front of them. They will not be able to see the color of their own hat or the hats behind them, although they will be able to hear the answers from all those behind them.The boss will then starts with the wise worker in the back and ask "what color is your hat?" The wise worker will only be allowed to answer "black" or "brown," nothing more. If the answer is incorrect then the wise man will be fired. If the answer is correct then the wise worker may be promoted but must remain absolutely silent.The boss will then move on to the next wise worker and repeat the question.The boss makes it clear that if anyone breaks the rules then all the wise workers will be fired, and then allows the wise workers to consult before lining them up. The boss listens in while the wise workers consult each other to make sure they don't devise a plan to cheat. To communicate anything more than their guess of black or brown by coughing or shuffling would be breaking the rules.What is the maximum number of workers they can be guaranteed to save?Answer: 99.You can save about 50% by having everyone guess randomly.You can save 50% or more if every even person agree to call out the color of the hat in front of them. That way the person in front knows what color their hat is, and if the person behind also has the same colored hat then both will be promoted.So how can 99 people are saved? The first wise worker counts all the red hats he can see (Q) and then answers "brown" if the number is odd or "black" if the number is even. Each subsequent wise man keeps track of the number of red hats known to have been saved from behind (X), and counts the number of red hats in front (Y).If Q was even, and if X&Y are either both even or are both odd, then the wise man would answer blue. Otherwise the wise man would answer red.If Q was odd, and if X&Y are either both even and are both odd, then the wise man would answer red. Otherwise the wise man would answer blue.There can be any number of black hats, as the following examples show...Prisoner

Hat he wears

Number of red hats he sees (Y)

Red hats saved for sure (X)

He says

1 Black 6 even (Q) N/A Black2 Brown 6 even 0 even Brown3 Black 5 odd 0 even Black4 Brown 5 odd 1 odd Brown5 Brown 5 odd 1 odd Brown6 Black 4 even 1 odd Black7 Black 3 odd 2 even Black8 Black 2 even 3 odd Black9 Black 1 odd 4 even Black10 Black 0 even 5 odd Black

4. Class A has a higher enrollment than Class B. Class C has a lower enrollment than Class B. Class A has a lower enrollment than Class C.If the first two statements are true, the third statement is

A. true

B. false

C. uncertain

Answer: Option BExplanation:From the first two statements, we know that of the three classes, Class A has the highest enrollment, so the third statement must be false.

5. The Cashier

Three women in a cafe order a meal the total cost of which is 1500. They each contribute 500. The waiter takes the money to the chef who recognizes the three as friends and asks the waiter to return 500 to the men.

The cashier is not only poor at mathematics but dishonest and instead of going to the trouble of splitting the 500 between the three she simply gives those 100 each and pockets the remaining 200 for himself.

Now, each of the women effectively paid 400, the total paid is therefore 1200. Add the 200 in the waiters pocket and this comes to 1400.....where has the other 100 gone from the original 1500?

Answer: The payments should equal the receipts. It does not make sense to add what was paid by the women (1200) to what was received from that payment by the waiter (200)

Although the initial bill was 1500 pesos, one of the five hundred notes gets changed into five hundred. The total the three women ultimately paid is 12000, as they get three one hundred back. So from the 1200 the women paid, the owner receives $10 and the cashier receives the 200 difference. 1500 - 300 = 1000 + 200

6. On the day the Jacob triplets are born, Jenna weighs more than Jason.Jason weighs less than Jasmine.Of the three babies, Jasmine weighs the most.If the first two statements are true, the third statement is

A. true

B. false

C. uncertain

Answer: Option C

Explanation:

We only know that Jasmine weighs more than Jason. There is no way to tell whether Jasmine also weighs more than Jenna.

7. The Husband

A wife is 21 years older than her child. In exactly 6 years from now, the wife will be exactly 5 times as old as the child.

Where's the husband?

Answer:

With the wife. If you do the math, you find out the child will be born in 9 months.

8. Battery A lasts longer than Battery B. Battery B doesn't last as long as Battery C. Battery C lasts longer than Battery A.If the first two statements are true, the third statement is

A. true

B. false

C. uncertain

Answer: Option C

Explanation:

The first two statements indicate that Battery B lasts the least amount of time, but it cannot be determined if Battery C lasts longer than Battery A.

9. The Grasshopper

A Grasshopper is at the bottom of a 30 meter well. Each day he summons enough energy for one 3 meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?

Note: Assume after the first leap that his hind legs are exactly three meters up the well. His hind legs must clear the well for him to escape.

Answer: 28

Each day he makes it up another meter, and then on the twenty seventh day he can leap three meters and climb out.

10. Manila is north of Caloocan.Caloocan is east of Valenzuela.Valenzuela is northwest of Manila.If the first two statements are true, the third statement is

A. true

B. false

C. uncertain

Answer: Option B

Explanation:

Because the first two statements are true, Valenzuela is west of Caloocan and southwest of Manila. Therefore, the third statement is false.

11. The Fake Coin

You have twelve coins. You know that one is fake. The only thing that distinguishes the fake coin from the real coins is that its weight is imperceptibly different. You have a perfectly balanced scale. The scale only tells you which side weighs more than the other side.What is the smallest number of times you must use the scale in order to always find the fake coin?Use only the twelve coins themselves and no others, no other weights, no cutting coins, no pencil marks on the scale. Etc.These are modern coins, so the fake coin is not necessarily lighter.Presume the worst case scenario, and don't hope that you will pick the right coin on the first attempt.Answer: 3.If you knew the fake coin was lighter, then the solution would have an easy explanation. But you do not. So....Number the coins 1 through 12.1. Weigh coins 1,2,3,4 against coins 5,6,7,8.1.1. If they balance, then weigh coins 9 and 10 against coins 11 and 8 (we know from the first weighing that 8 is a good coin).1.1.1. If the second weighing also balances, we know coin 12 (the only one not yet weighed) is the counterfeit. The third weighing indicates whether it is heavy or light.

1.1.2. If (at the second weighing) coins 11 and 8 are heavier than coins 9 and 10, either 11 is heavy or 9 are light or 10 are light. Weigh 9 against 10. If they balance, 11 are heavy. If they don't balance, you know that either 9 or 10 are light, so the top coin is the fake.1.1.3 If (at the second weighing) coins 11 and 8 are lighter than coins 9 and 10, either 11 is light or 9 are heavy or 10 are heavy. Weigh 9 against 10. If they balance, 11 are light. If they don't balance, you know that either 9 or 10 are heavy, so the bottom coin is the fake.

1.2. Now if (at first weighing) the side with coins 5,6,7,8 is heavier than the side with coins 1,2,3,4. This means that either 1,2,3,4 are light or 5,6,7,8 are heavy. Weigh 1, 2, and 5 against 3, 6, and 9.1.2.1. If (when we weigh 1, 2, and 5 against 3, 6 and 9) they balance, it means that either 7 or 8 are heavy or 4 are light. By weighing 7 and 8 we obtain the answer, because if they balance, then 4 have to be light. If 7 and 8 do not balance, then the heavier coin is the counterfeit.

1.2.2. If (when we weigh 1,2, and 5 against 3,6 and 9) the right side is heavier, then either 6 is heavy or 1 is light or 2 is light. By weighing 1 against 2 the solution is obtained.1.2.3. If (when we weigh 1, 2, and 5 against 3, 6 and 9) the right side is lighter, then either 3 are light or 5 are heavy. By weighing 3 against a good coin the solution is easily arrived at.1.3 If (at the first weighing) coins 1,2,3,4 are heavier than coins 5,6,7,8 then repeat the previous steps 1.2 through 1.2.3 but switch the numbers of coins 1,2,3,4 with 5,6,7,8.

12. A fruit basket contains more orange than lemons.There are more lemons in the basket than there is strawberry.The basket contains more orange than strawberry.If the first two statements are true, the third statement is

A. true

B. false

C. uncertain

Answer: Option AExplanation:There is less strawberry than either orange or lemons, so the statement is true.

Easy method: (Try this method to solve without any confusion) 1. A fruit basket contains more orange than lemons = Org > Lem 2. There are more lemons in the basket than there are strawberry = Lem >Str Now, Combine the above two results: Org > Lem > Str3. The basket contains more orange than strawberry (Org> ... > Str) = Yes.

Therefore, the given 3rd statement is true.

13. The Glove

Cathy has six pairs of black Glove and six pairs of white Glove in her drawer.

In complete darkness, and without looking, how many Glove must she take from the drawer in order to be sure to get a pair that match?

Answer: 3

Glove do not come in in left and right, so any black will pair with any other black and any white will pair with any other white. If you have three Glove and they are either colored black or white, then you will have at least two Glove of the same color, giving you one matching pair.

14. All spotted Gangles have long tails.Short-haired Gangles always have short tails.Long-tailed Gangles never have short hair.If the first two statements are true, the third statement is

A. true

B. false

C. uncertain

Answer: Option C

Explanation:

We know only that long-tailed Gangles have spots. We cannot know for certain if long-tailed Gangles also have short hair.

15. Four Gallons

You have a three gallon and a five gallon measuring device. You wish to measure out four gallons.

Answer: Fill the five gallon container. Pour all but two gallons into the three gallon container. Empty the three gallon container. Put the two remaining gallons from the five gallon container into the three gallon container. Fill the five gallon container one more time. Pour one gallon from the five gallon container by filling the three gallon container. Now the five gallon container contains four gallons.

16. Fact 1: Sharmaine has four children

Fact 2:Two of the children have blue eyes and two of the children have brown eyes.

Fact 3: Half of the children are girls.

If the first three statements are facts, which of the following statements must also be a fact?

I: At least one girl has blue eyes.

II: Two of the children are boys.

III: The boys have brown eyes.

A. I only

B. II only

C. II and III only

D. None of the statements is a known fact.

Answer: Option B

Explanation:

Since one-half of the four children are girls, two must be boys. It is not clear which children have blue or brown eyes.

17. Five Gallons

You are mixing cement and the recipe calls for five gallons of water. You have a garden hose giving you all the water you need. The problem is that you only have a four gallon bucket and a seven gallon bucket and nether has graduation marks. Find a method to measure five gallons.

Answer: Pour the four gallon bucket filled with water into the empty seven gallon bucket. Fill the four gallon bucket up again and poor as much as you can into the seven gallon bucket until the seven gallon bucket is fill. Now there is one gallon left in the four gallon bucket. Empty the seven gallon bucket and transfer the one gallon of water into the seven gallon bucket. Fill the four gallon bucket one more time, then pour the four gallons into the seven gallon bucket making which already has one gallon in it, making a total of five gallons.

18. Fact 1: All hats have brims.

Fact 2: There are red hats and blue hats.

Fact 3: Baseball caps are hats.

If the first three statements are facts, which of the following statements must also be a fact?

I: All caps have brims.

II: Some baseball caps are blue.

III: Baseball caps have no brims.

A. I only

B. II only

C. II and III only

D. None of the statements is a known fact.

Answer: Option D

Explanation:

All baseball caps have brims, since baseball caps are hats (Fact 3) and all hats have brims (Fact 1). This rules out statement III, but it doesn't follow that all caps, a category that may include caps that are not baseball caps, have brims (statement I). Statement II cannot be confirmed, either, since it is possible, given the information, that all baseball caps are red.

19. The Pigeon

Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet.

How many miles does the pigeon travel?

Answer: 54.

It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 18 MPH = 54 miles.

20. Four defensive football players are chasing the opposing wide receiver, who has the ball. Caleb is directly behind the ball carrier. John and Bryan are side by side behind Caleb. Zean is behind John and Bryan. Caleb tries for the tackle but misses and falls. Bryan trips. Which defensive player tackles the receiver?

A. Bryan

B. Zean

C. John

D. Caleb

Answer: Option C

Explanation:

After all the switching was done, John was directly behind the receiver. Caleb and Bryan had fallen. Zean remained in the rear.

21. Bad Boy Bubby was warned by his mother never to open the cellar door or he would see things that he was not meant to see. One day while his mother was out he did open the cellar door. What did he see?

Answer: When Bad Boy Bubby opened the cellar door he saw the living room and, through its windows, the garden. He had never seen these before because his mother had kept him all his life in the cellar.

22. Four people witnessed a mugging. Each gave a different description of the mugger. Which description is probably right?

A. He was average height, thin, and middle-aged.

B. He was tall, thin, and middle-aged.

C. He was tall, thin, and young.

D. He was tall, of average weight, and middle-aged.

Answer: Option B

Explanation:

Tall, thin, and middle-aged are the elements of the description repeated most often and are therefore the most likely to be accurate.

23. There are six eggs in the basket. Six people each take one of the eggs. How can it be that one egg is left in the basket?

Answer: The last person took the basket with the last egg still inside.

24. Four friends in the sixth grade were sharing a pizza. They decided that the oldest friend would get the extra piece. Randy is two months older than Greg, who is three months younger than Ned. Kent is one month older than Greg. Who should get the extra piece of pizza?

A. Randy

B. Greg

C. Ned

D. Kent

Answer: Option C

Explanation:

If Randy is two months older than Greg, then Ned is three months older than Greg and one month older than Randy. Kent is younger than both Randy and Ned. Ned is the oldest.

25. A man lives in the penthouse of an apartment building. Every morning he takes the elevator down to the lobby and leaves the building. Upon his return, however, he can only travel halfway up in the lift and has to walk the rest of the way - unless it's raining. What is the explanation for this?

Answer: The man is a dwarf. He can't reach the upper elevator buttons, but he can ask people to push them for him. He can also push them with his umbrella.

26. Children are in pursuit of a dog whose leash has broken. James is directly behind the dog. Ruby is behind James. Rachel is behind Ruby. Max is ahead of the dog walking down the street in the opposite direction. As the children and dog pass, Max turns around and joins the pursuit. He runs in behind Ruby. James runs faster and is alongside the dog on the left. Ruby runs faster and is alongside the dog on the right. Which child is directly behind the dog?

A. James

B. Ruby

C. Rachel

D. Max

Answer: Option D

Explanation:

After all the switches were made,Max is directly behind the dog, James is alongside the dog on the left, Ruby is alongside the dog on the right, and Rachel is behind Max.

27. Why is it better to have round manhole covers than square ones?

Answer: Round covers cannot be dropped or fall down a manhole, unlike square ones.

28. All the trees in the park are flowering trees.Some of the trees in the park are dogwoods.All dogwoods in the park are flowering trees.If the first two statements are true, the third statement is

A. true

B. false

C. uncertain

Answer: Option A

Explanation:

All of the trees in the park are flowering trees, So all dogwoods in the park are flowering trees.

29. A man walks into a bar and asks for a drink of water. The bartender thinks for a minute, pulls out a gun and points it at him. The man says, "Thank you," and walks out.

Answer: The man has hiccups; the bartender scares them away by pulling a gun.

A Colombian man accidentally shot his nephew to death while trying to cure his hiccups by pointing a revolver at him to scare him, police in the Caribbean port city of Barranquilla said on Tuesday, the 24th of January 2006.

After shooting 21-year-old university student David Galvan in the neck, his uncle, Rafael Vargas, 35, was so distraught he turned the gun on himself and committed suicide, police said.

The incident took place on Sunday night while the two were having drinks with neighbors.

Galvan started to hiccup and Vargas, who works as a security guard, said he would use the home remedy for hiccups of scaring him. He pulled out his gun, pointed it at Galvan and it accidentally went off, witnesses told local television.

"They were drinking but they were aware of what was going on," one witness said.

30. Mara runs faster than Gail.Lily runs faster than Mara.Gail runs faster than Lily.If the first two statements are true, the third statement is

A. true

B. false

C. uncertain

Answer: Option B

Explanation:

We know from the first two statements that Lily runs fastest. Therefore, the third statement must be false.

3030 Logical Logical

ProblemsProblems

Submitted by: Submitted by:

Vallelyn B. SamonteVallelyn B. Samonte

Submitted to:Submitted to:

Mr. Victor L. FeliciaMr. Victor L. Felicia