Are the hare and tortoise together covering the distance at a speed equal to the sum of their individual speeds?.

Solution:

The hare and the tortoise are together covering the distance at 13 miles per hour (i.e., on adding their speeds). So, they will cover the distance of 52 miles in 4 hours. Thus, in 4 hours, they will meet and the hare will have traveled 40 miles.

Alternative Solution through Equations:

Note that : Distance = Speed × Time

Let t be the time before the hare and the tortoise meet.In t hours, the hare will travel 10 t miles.In t hours, the tortoise will travel 3 t miles.

Now,10 t + 3 t = 52 So, t = 52 ⁄ 13 = 4 hours.

Thus, distance traveled by hare before meeting = 10 × 4 = 40 miles.

Fraction of life spent by Man Wrinkle as an old man = 1 − (1/4 + 1/8 +1/2) = ...

Solution:

Fraction of life as a boy = 1/4Fraction of life as a youth = 1/8Fraction of life as an active man = 1/2Fraction of life as boy, youth and active man = 1/4 + 1/8 + 1/2 = (2 + 1 + 4)/8 = 7/8Fraction of life as an old man = 1 − 7/8 = 1/8Thus, one-eighth of Man Wrinkle's life (as an old man) is 9 years.So, Man Wrinkle's Age = 72 years.

It may be noted that: Life as boy = 72/4 = 18 years. Life as youth = 72/8 = 9 years.Life as active man = 72/2 = 36 years.Life as old man = 72/8 = 9 years.

The problem may also be solved by setting up the following equation: a/4 + a/8 + a/2 + 9 = a where a denotes Man Wrinkle's age in years. The equation may be solved as shown below.7a/8 + 9 = a 9 = a − 7a/8 = a/8a/8 = 9 or a = 72.

Therefore, life spent as active man = 72/2 = 36 years.

Hint:

If you pick 2 gloves blindly, can they be of different colors?If you pick 3 gloves blindly, can they be of different colors?

Solution:

To find a pair, Mr. Brown must pick at least 2 gloves. But, if he picks 2 gloves blindly, then they may be of different colors. If he picks 3 gloves blindly, then there are only 2 possibilities: all 3 gloves are of the same color, or 2 gloves are of the same color and 1 is of a different color. Both these possibilities guarantee Mr. Brown a pair of gloves of the same color. Thus, Mr. Brown should minimally pick 3 gloves to be certain to find a pair of gloves of the same color.

Food for thought:

Would the problem change significantly if the word "gloves" was replaced by "shoes" in the problem statement? Does it matter that there are "left" and "right" shoes?

Suppose the problem statement was modified to read: What is the minimum number of gloves Mr. Brown will have to pick to be certain to find a pair of black gloves (rather than simply gloves of the same color)? Is the minimum number still 3? 

Calculate the number of wheels assuming 2 wheels for each cycle.Then, determine the number of extra wheels.

Solution:

Assuming 2 wheels for each cycle, 19 cycles will have 38 wheels. But, there are 48 − 38 = 10 extra wheels.

As bicycles have 2 wheels and tricycles have 3 wheels, there is 1 extra wheel per tricycle in the park. Thus, the 10 extra wheels belong to 10 tricycles.

Suppose 7 monkeys take 7 minutes to eat 7 bananas. 

1. How many minutes would it take 2 monkeys to eat 2 bananas?

 

2. How many monkeys would it take to eat 56 bananas in 56 minutes?

How many minutes does it take one monkey to eat one banana?

Solution:

1. It would take 7 minutes for 2 monkeys to eat 2 bananas; and

2. it would take 7 monkeys 56 minutes to eat 56 bananas.

Food for thought:

What assumptions are made in arriving at the solution?

Does one assume that 7 monkeys take 1 minute to eat 1 banana and that all bananas are consumed at the same pace?

Or does one assume that 1 monkey takes 7 minutes to eat 1 banana and that all monkeys eat at the same pace?

A pillar 9 feet tall casts a shadow 3 feet long on the ground. If the pillar was 21 feet tall, how many feet in length would the shadow be ?

The lengths of the shadows are to one another as the heights of the pillars.

Solution:

The lengths of the shadows are to one another as the heights of the pillars. Thus,

Length of the shadow for a pillar 21 feet tall = (21 / 9) × 3 = 7 feet.

Food for thought:

What other factor(s) does the length of a shadow depend on? Does the time of the day or the position of the sun determine the length of the shadow?

Your teacher has a total of 49 chalks. When a chalk reduces to 1/7 of its original size, it gets too small for her to hold for writing and hence she keeps it aside. But your teacher hates wasting things and so, when she realizes that she has enough of these small pieces to join and make another chalk of the same size, she joins them and uses the new chalkstick. If she uses one chalk each day, how many days would the 49 chalks last?

The chalks that are made by joining pieces together will again leave behind pieces!

 57

Hint       

Solution:

Your teacher uses one chalk each day. Hence the total number of days she uses 49 chalks is 49. Each chalk leaves a fraction of 1/7 its size... so 49 such fractions remain. Since 7 such fractions are joined to give a new chalk, your teacher combines all the fractions to get 7 chalks which can again be used for 7 days. Hence, she has managed to use 49 chalks for (49 + 7) days!

But, what about the leftovers of the chalks used over the last 7 days?? They can be joined to form yet another chalk... which means another day! So, your teacher uses the 49 chalks for a total of 57

days.

Food for thought:

Does the teacher actually use one chalk each day or 6/7 each day? Is there any ambiguity (or lack of clarity) in the problem statement? Interpreting the question posed is an important first step in problem-solving. Re-reading the problem statement often helps!

A snail creeps 5 ft up a wall during the daytime. After all the labor it does throughout the day, it stops to rest a while... but falls asleep!! The next morning it wakes up and discovers that it has slipped down 2 ft while sleeping.

If this happens every day, how many days will the snail take to reach the top of a wall 44 ft in height?

On the "last" day, the snail will reach the top and there will not be any question of slipping down.

Solution:

On the first day, the snail climbs up 5 ft and slips down 2 ft while sleeping. So, next morning, it is 3 ft from where it started. The snail thus travels 3 ft upwards every day. Therefore, in 13 days, it has traveled a distance of 39 ft from the bottom.

Here lies the catch to the problem! On the last day, the snail travels 5 ft upwards and hence reaches the top of the wall in a total of 14 days.

Alternative Solution through Equation:

Let x be the number of days the snail takes to reach the top of the wall 44 ft in height.

On the last day, the snail will reach the top by traveling 5 ft upwards and there will not be any question of slipping down. The number of remaining days excluding the last day are (x − 1). Since the snail climbs up 5 ft and slips down 2 ft while sleeping, it travels 3 ft upwards

on each of these remaining days. Thus,

Distance traveled on last day + Distance traveled on remaining days = Wall height; or 5 + 3 (x − 1) = 44

On solving the above equation, we get

3 (x − 1) = 44 − 5 = 39; orx = (39 / 3) + 1 = 14.

Last vacation, my cousin came over to stay at my home. We made the most of her stay at my place... and I even earned a few chocolates.

Everyday, we would play a game of chess. Whoever lost the game owed a chocolate to the other. After the last game we played (that was the day she was to leave), we counted the number of games each of us had won and lost. Wow! I had won more than her. So, she handed me 6 chocolates... though she herself was the winner in 13 games.

How many days did my cousin spend at my place?

The number of chocolates I got equals the number of games I won MORE than my cousin did.Solution:

My cousin won 13 games. Since I got 6 chocolates, I must have won 6 games more than my cousin did. So, I won a total of 19 games. Thus, the total number of games that we played was 32. Since we played a game each day, that was the number of days my cousin stayed at my house! 

A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked, "How many gold coins do we have?"

After pausing a moment, he replied, "Well! If I divide the coins into two unequal numbers, then 31 times the difference between the two numbers equals the difference between the squares of the two numbers."

The wife looked puzzled. Can you help the merchant's wife by finding out how many gold coins they have?

(a + b) (a − b) = ...

The merchant has 31 gold coins. It is easy to check this... Let's divide the 31 coins into two unequal numbers, say, 25 and 6. Then,

31 (25 − 6) = (25 × 25) − (6 × 6).

Food for thought:

Note that the 31 coins can be divided into any two unequal numbers, a and b, not necessarily 25 and 6, so long as a + b = 31. Isn't that interesting?

The above problem is solved in a straightforward manner if one knows the following formula:

a2 − b2 = (a + b) (a − b) 

It was Diane's first day at school. The teacher suggested that it would be a good idea for each child to meet every other child in the class. The teacher said, "When you meet, please shake hands and introduce yourself by name."

If there were 10 children in the class, how many total handshakes were there?

Each child shakes hands with every OTHER child once and only once.

Solution:

The class has 10 children. The first child shakes hands with the other 9 children. The second child has already shaken hands with the first child, and so has to shake hands with only the other 8 children. In this manner, the second-last child has to shake hands with only one child, and the last child has already met all the children. Thus, the number of handshakes is

9 + 8 + ........ + 2 + 1 = 45.

If there were 10 children in the class, then there were 45 total

handshakes.

Food for thought:

It is obviously assumed that each child shakes hands with every other child once and only once.

More importantly, is there a quick way to add 9 + 8 + ........ + 2 + 1 ? Indeed, there is! It simply equals 9 × 10 / 2. Can you show why such a formula holds? 

"Dad, where had you been?" asked Herbert.

"I had been to the attic, my son," replied Dad. "And do you know what I saw there? There was a big web with 28 spiders and flies on it."

"How many spiders were there?" asked the little boy with curiosity.

"Well, there were a total of 186 legs on the web," answered Dad with a smile. "Now you can find out how many spiders were there by yourself. Can't you?"

Can you help the little boy find out how many spiders were on the web in the attic?

Hint:

Calculate the number of legs assuming 6 legs for each insect. Then, determine the number of extra legs.

Solution:

Assuming 6 legs for each insect, 28 insects will have 168 legs. But, there are 186 − 168 = 18 extra legs.

It is important to note that spiders have 8 legs and flies have 6 legs. So, there are 2 extra legs per spider on the web. Thus, the 18 extra legs belong to 9 spiders.

Alternative Solution through Equations:

Let s be the number of spiders and f be the number of flies. Then,

s + f = 28; and 8s + 6f = 186.

On solving the above two equations, we get

8s + 6 (28 − s) = 186; or 2s = 186 − (6 × 28). Thus, s = 9.

There is a number that is 9 times the sum of its digits. What is this number?Look for a 2-digit number.Solution:

The number is 81, simply because81 = 9 (8 + 1).

How does one find this number?

Let t be the digit in the tens place and u be the digit in the units place. Then, the number is 10 t + u, and the sum of its digits is t + u. The following equation can be readily written:

10 t + u = 9 t + 9 u or 1 t = 8 u.

Thus, t / u = 8 / 1. Since t and u are digits, t must be 8 and u must be 1.

Food for thought:

Is the assumption of a 2-digit number a valid one?

It was vacation time, and so I decided to visit my cousin's home. What a grand time we had! In the mornings, we both would go for a jog. The evenings were spent on the tennis court. Tiring as

these activities were, we could manage only one per day, i.e., either we went for a jog or played tennis each day. There were days when we felt lazy and stayed home all day long.

Now, there were 11 mornings when we did nothing, 13 evenings when we stayed at home, and a total of 8 days when we jogged or played tennis. For how many days did I stay at my cousin's place?

Hint:

A Venn diagram with two intersecting sets may help in visualization. The two sets could be "days we did nothing in the morning" and "days we stayed at home in the evening."

Solution:

Let

x denote the number of days we jogged in the morning and stayed at home in the evening;

y denote the number of days we played tennis in the evening and did nothing in the morning; and

z denote the number of days we neither jogged nor played tennis.

Then,

y + z = number of mornings we did nothing = 11 x + z = number of evenings we stayed at home = 13 x + y = number of days we jogged or played tennis = 8

Adding the above three equations and dividing both sides by 2 gives

x + y + z = 16

Since there are only three types of days, the total number of days

I stayed with my cousin is their sum, i.e., 16.

Food for thought:

Can you solve this puzzle using a Venn diagram with two intersecting sets? Could the two sets be "days we did nothing in the morning" and "days we stayed at home in the evening"? 

Bill takes the underground train to work and uses an escalator at the railway station. If Bill runs up 7 steps of the escalator, then it takes him 30.0 seconds to reach the top of the escalator. If he runs up 15 steps of the escalator, then it takes him only 18.0 seconds to reach the top.

How many seconds would it take Bill to reach the top if he did not run up any steps of the escalator at all?

Hint:

Calculate the speed of the escalator or the time of travel for each step. Then, determine the total steps in the escalator.

Solution:

If he runs up 7 steps, then he needs 30.0 seconds to reach the top. If he runs up 15 steps, then he needs 18.0 seconds to reach the top.

The 8 additional steps take 12.0 seconds. Therefore, each step takes 1.5 seconds.

Total steps in escalator = 7 + 30.0 / 1.5 = 27 or Total steps in escalator = 15 + 18.0 / 1.5 = 27.

If Bill did not run up any steps at all, he would reach the top of the escalator in 40.5 seconds (i.e., 27

steps × 1.5 seconds/step).

Alternative Solution through Equations:

Let the total number of steps in the escalator be x. The escalator moves at a constant speed given by

Speed of escalator = (x − 7)/30.0 = (x − 15)/18.0

The above equation may be solved as follows.

18.0 (x − 7) = 30.0 (x − 15); or x = (15 × 30.0 − 7 × 18.0) / (30.0 − 18.0) = 27.

Now, Speed of escalator = (27 − 7)/30.0 = (27 − 15)/18.0 = 1/1.5 steps/second. Time to reach top = Total Steps / Speed = 40.5 seconds.

Grandpa:

"My grandson is about as many days as my son is weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 160 years. Can you tell me my age in years?"

Hint:

Let g be the grandson's age in years. Then, is grandpa's age 12g in years? Is the son's age 7g in years?

Solution:

Grandpa:

"This problem is conveniently solved by writing down the necessary equations. Note that there are 12 months in a year, 52

weeks in a year, and 365 days in a year.

Let m be my age in years. If s is my son's age in years, then my son is 52s weeks old. If g is my grandson's age in years, then my grandson is 365g days old. Thus,

365g = 52s.

Since my grandson is 12g months old,

12g = m.

Since my grandson, my son and I together are 160 years,

g + s + m = 160.

The above system of 3 equations in 3 unknowns (g, s and m) can be solved as follows.

m / 12 + 365 m / (52 × 12) + m = 160 or

52 m + 365 m + 624 m = 624 × 160 or

m = 624 × 160 / 1041 = 96.

So, I am 96 years old."

Food for thought:

Why is the word "about" used in the Problem Statement in the sentence "My grandson is about as many days as my son is weeks"? Calculate the son's age and the grandson's age. Then, verify whether the first equation (i.e., 365g = 52s) is exactly satisfied.

An elegant solution is possible on realizing the significance of the word "about" in the Problem Statement.

Elegant Solution:

The first equation (365g = 52s) can be approximated by

7g = s.

As before, the other two equations are

12g = m

g + s + m = 160.

The above system of 3 equations in 3 unknowns (g, s and m) can be simply solved as follows.

g + 7g + 12g = 160 or 20g = 160.

m = 12g = 12 × 160 / 20 = 96.

So, Grandpa is 96 years old. .

When is four half of five?• When it Is a riman neumeral • F(IV)e

What can run but never walks, has a mouth but never talks, has a head but never weeps, and has a bed but never sleeps??

A river

How can you use the letters in NEW DOOR to make one word?

one word

What are ID ten T mistakes?

Idiot

What is full of holes but still holds water?

A sponge

How could all of your cousins have an aunt who is not your aunt?

Ur mom is their aunt

A light-tight wooden box has three switches on the outside that control three light bulbs on the inside. When the box is closed you can turn the switches on or off but when you open the box how can you tell which switch controls each bulb without touching the switches?

Turn one switch on for five mts then tur it off and turn on another switch b4 u open the box ,one bulb will b lit, one will be cool and another will be hot

On my way to the fair, I met 7 jugglers and a bear, every juggler had 6 cats, every cat had 5 rats, every rat had 4 houses, every house had 3 mouses, every mouse had 2 louses, every louse had a spouse. How many in all are going to the fair?

Just me coz all of then was the one whom ive just sawn

Imagine you are in a sinking rowboat surrounded by sharks. How would you survive?

Quitting ur imagine

Johnny's mother had four children. The first was April, the second was May, and the third was June. What was the name of her fourth child?

Jonnie

You are driving a bus. Four people get on, three people get off, then eight people get on and ten people get off, then 6 people get on and 2 more people get off. What color were the bus driver's eyes?

There was an airplane crash, every single person died, but two people survived. How is this possible?

The peacock is a bird that does not lay eggs. How do they get baby peacocks?

• The Mississippi River is the dividing line between Tennessee and Arkansas. If an airplane crashed exactly in the middle of the Mississippi River there, where would the survivors be buried?

• We don’t burry survivers

• A man and his son were in an automobile accident. The man died on the way to the hospital, but the boy was rushed into surgery. The emergency room surgeon said "I can't operate, that's my son!" How is this possible?

• Cos that was her mother

• Why is the letter T like an island?

• Coz its in middle of water

How do you make seven even?

Take s awey s

How many seconds are in a year?12

A butcher is six foot tall, wears size 14 shoes, and has a 50 inch waist. What does he weigh?meat

Forewards it is heavy, backwards it is not. What is it?ton

The Begining of eternityThe end of spaceThe begining of every end The end of every place What am I?????? letter e

+

Answer: Option D

Explanation:

The boy in the photograph is the only son of the son of Suresh's mother i.e., the son of Suresh. Hence, Suresh is the father of boy.

If A is the brother of B; B is the sister of C; and C is the father of D, how D is related to A?

A. Brother B. Sister

C. Nephew D. Cannot be determined

Answer & Explanation

Answer: Option D

Explanation:

If D is Male, the answer is Nephew.

If D is Female, the answer is Niece.

As the sex of D is not known, hence, the relation between D and A cannot be determined.

Note: Niece - A daughter of one's brother or sister, or of one's brother-in-law or sister-in-law. Nephew - A son of one's brother or sister, or of one's brother-in-law or sister-in-law.

As you move diagonally down, numbers follow the sequence of Prime Numbers.

You have been imprisoned in a castle and your prison guards decide to tempt you with freedom, but at a big risk. They show you 2 doors, each with a guard standing in front, one door leads to the hanging gallows and the other leads directly out the castle and into freedom. You are told that one guard is a liar, and will always lie and the other guard will speak only the truth.You have no idea which guard is which, or what door is what.Your prison guards laugh and inform you that you may only ask One question.Impossible you think at first, but then you have a moment of inspiration. What question do you ask?

You ask any guard "Which door would the other guard say I should open?" and then choose the opposite!Hypothesing and imagining that Door A leads to freedom and Door B to death. If you ask the Truth Guard (unknowingly of course) he would say, truthfully, that the other guard would say you should open door B.If you ask the Lying Guard (unknowingly of course) he would lie, and say that the other guard would show you door B.

So you must always choose the opposite of what either guard tells you.

Using only basic arithmetic operations (+ - x /) can you get 98 using only 7 sevens? Each 7 may only be used once and you must use all 7 sevens.

7 7 7 7 7 7 7

 

(7x7x(7+7)/7)+7-7

Q: Choose the correct sentence: The yolk of an egg IS white. The yolk of an egg ARE white?