Logical Questions And Answers

21⟩ You are standing next to a well, and you have two jugs. One jug has a content of 3 liters and the other one has a content of 5 liters. How can you get just 4 liters of water using only these two jugs?

► Fill 3 liter jug n store it in a bucket.

► Again Fill 3 liter jug n store dat water in 5 liter jug.

► Again Fill 3 liter jug n store dat water till 5 liter jug gets full.

► u will get 1 liter water in dat 3 liter jug cuz u filled 5 liter jug by 3 liter jug twice i.e 3x2.

► store the remaining 1 liter into the bucket where v stored 3 liter. u will get 4 liter water now i.e 3+1

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22⟩ On a nice summer day two tourists visit the Dutch city of Gouda. During their tour through the center they spot a cosy terrace. They decide to have a drink and, as an appetizer, a portion of hot "bitterballs" (bitterballs are a Dutch delicacy, similar to croquettes). The waiter tells them that the bitterballs can be served in portions of 6, 9, or 20. What is the largest number of bitterballs that cannot be ordered in these portions?

Every natural number is member of one of the following six series:

0, 6, 12, 18, ...

1, 7, 13, 19, ...

2, 8, 14, 20, ...

3, 9, 15, 21, ...

4, 10, 16, 22, ...

5, 11, 17, 23, ...

If for a number in one of these series holds that it can be made using the numbers 6, 9, and 20, then this also holds for all subsequent numbers in the series (by adding a multiple of 6). To find out what the largest number is that cannot be made using the numbers 6, 9, and 20, we therefore only need to know, for every series, what the smallest number is that can be made in that way. In the series 0, 6, 12, 18, . the smallest number that can be made is 0 so there is no number that cannot be made.In the series 1, 7, 13, 19, ... the smallest number that can be made is 49 (20+20+9) so 43 is the largest number that cannot be made.

In the series 2, 8, 14, 20, ... the smallest number that can be made is 20 so 14 is the largest number that cannot be made.In the series 3, 9, 15, 21, ... the smallest number that can be made is 9 so 3 is the largest number that cannot be made.In the series 4, 10, 16, 22, . the smallest number that can be made is 40 (20+20) so 34 is the largest number that cannot be made.In the series 5, 11, 17, 23, ... the smallest number that can be made is 29 (20+9) so 23 is the largest number that cannot be made.Therefore, 43 is the largest number that cannot be made using the numbers 6, 9, and 20

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23⟩ Barbara has boxes in three sizes large, standard, and small. She puts 11 large boxes on a table. She leaves some of these boxes empty, and in all the other boxes she puts 8 standard boxes. She leaves some of these standard boxes empty, and in all the other standard boxes she puts 8 (empty) small boxes. Now, 102 of all the boxes on the table are empty. How many boxes has Barbara used in total?

By putting 8 boxes in a box, the total number of empty boxes increases by 8 - 1 = 7. If we call x the number of times that 8 boxes have been put in a box, we know that 11 + 7x = 102. It follows that x=13. In total, 11 + 13 ?8 = 115 boxes have been used. .

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24⟩ The letters A, B, C, D, E, F and G, not necessarily in that order, stand for seven consecutive integers from 1 to 10 D is 3 less than A B is the middle term F is as much less than B as C is greater than D G is greater than F 1. The fifth integer is (a) A (b) C (c) D (d) E (e) F 2. A is as much greater than F as which integer is less than G (a) A (b) B (c) C (d) D (e) E 3. If A = 7, the sum of E and G is (a) 8 (b) 10 (c) 12 (d) 14 (e) 16

the list goes:

E F D B C A G

hence,ans

1.b

2.d

2.b

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25⟩ There are 7 letters A,B,C,D,E,F,G All are assigned some numbers from 1,2 to 7. B is in the middle if arranged as per the numbers. A is greater than G same as F is less than C. G comes earlier than E. 1) Which is the fourth letter ? ( B / D / F/ E) 2) what is the difference between A and F? ( 3 /4/ 5/ 6) 3 Choose 4 consecutive letters? ( ABCD / BDFE / AEFB / NONE OF THESE )

1 2 3 4 5 6 7

F D C B G E A

B is the middle one means ,B=4.

G comes earlier than E & A>G=F<C means A-G=C-F. so.the order can be arranged as shown above.

1.B=4.

2.A-F=7-1=6.

3.None Of These

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26⟩ Let D be the set of all points in the real plane such that |x| + |y| <= 1, where |x| (respectively |y|) denotes the absolute value of x (respectively y). Prove that amongst every 5 points in D, there exist two points whose distance from one another is at most 1.

Yes,D is a square with ends at (0,1),(1,0),(-1,0),(0,-1), and also we could draw a round which will go through these four points. Its equation is x^2+y^2=1. we could see the square is totally contained within the round. Also we will notice that any points in the round will have distance less than 1 from each other. So in conclusion, every points in D have distance at most 1 from each other .

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27⟩ You are given 8 identical balls .... but one of them is slightly heavier than the rest.... given a old scale (not electronic one) and only two trials to weigh ... can u spot the odd one out?

Take six balls 3 on each side and weigh. the weighter ball is not there then put the other two in scale and u can find. or else take the balls from the weighter side of the scale and take two from them and put in the scale. if that two are equal the the ball in your hand is the weightest one.

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28⟩ Seventy five years ago pharmacists weighed medicine on balances like the ones you have been using. The mass pieces were very expensive, so a pharmacist would buy as few mass pieces as possible. If a pharmacist had 1-g, 3-g, and 9-g mass pieces, he or she could weight out any number of grams from 1 g to 13 g. Show how could measure all of the masses from 1 g to 13 g using only the three mass pieces given?

Ya,he can measure..

Initially 2 gm will be calculated by taking 3 gm and removing 1 gm using 1 gm mass..Then similarly,

2=3gm-1gm

4=3gm+1gm

5=9gm-(3gm+1gm)

6=9gm-3gm

7=(9gm+1gm)-3gm

8=9gm-1gm

10=9gm+1gm

11=(9gm+3gm)-1gm

12=9gm+3gm

13=9gm+3gm+1gm

Thus he can measure from 1-13 gms

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29⟩ A cyclist drove one kilometer, with the wind in his back, in three minutes and drove the same way back, against the wind in four minutes. If we assume that the cyclist always puts constant force on the pedals, how much time would it take him to drive one kilometer without wind?

The cyclist drives one kilometer in three minutes with the wind in his back, so in four minutes he drives 1 1/3 kilometer. Against the wind, he drives 1 kilometer in four minutes. If the wind helps the cyclist during four minutes and hinders the cyclist during another four minutes, then - in these eight minutes - the cyclist drives 2 1/3 kilometers. Without wind, he would also drive 2 1/3 kilometers in eight minutes and his average speed would then be 17.5 kilometers per hour. So it will take him 3 3/7 minutes to drive one kilometer..

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30⟩ Postman Pat delivers the mail in the small village Tenhouses. This village, as you already suspected, has only one street with exactly ten houses, numbered from 1 up to and including 10. In a certain week, Pat did not deliver any mail at two houses in the village; at the other houses he delivered mail three times each. Each working day he delivered mail at exactly four houses. The sums of the house numbers where he delivered mail were on Monday 18 on Tuesday 12 on Wednesday 23 on Thursday 19 on Friday 32 op Saturday 25 on Sunday he never works Which two houses did not get any mail that week?

If postman Pat would have delivered mail three times at each house, then the total sum of the house numbers per day would be (1+2+3+4+5+6+7+8+9+10)?=165. Now that sum is 18+12+23+19+32+25=129. The difference is 165-129=36; divided by 3 this is 12. The sum of the house numbers where no mail was delivered is therefore 12. The following combination are possible

2+10

3+9

4+8

5+7

Each day at four houses the mail was delivered. On Tuesday the sum was 12. 12 can only be made from four house numbers in 2 ways:

1+2+3+6

1+2+4+5

The same holds for Friday with the sum of 32:

5+8+9+10

6+7+9+10

From this we can conclude that the house numbers 1, 2, 9 and 10 for sure have received mail, which means that the combination 2+10 and 3+9 are not possible. Also the combination 5+7 is not possible, because mail was delivered either at house 5 or at house 7. Thus the only remaining solution is: houses 4 and 8.

N.B.: there are various possibilities for the actual post delivery of the whole week.

For example: Monday houses 1, 3, 5 and 9

Tuesday houses 1, 2, 3 and 6

Wednesday houses 1, 5, 7 and 10

Thursday houses 2, 3, 5 and 9

Friday houses 6, 7, 9 and 10

Saturday houses 2, 6, 7 and 10 .

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31⟩ There is a whole number n for which the following holds if you put a 4 at the end of n, and multiply the number you get in that way by 4, the result is equal to the number you get if you put a 4 in front of n. In other words, we are looking for the number you can put on the dots in the following equation 4... = 4 ?...4 Which number must be put on the dots to get a correct equation?

n4*4=4n.

1) if n is single digit number then we get n will be fraction.

2)similarly tru for n as 2,3,4 digit numbers we won't get.

3) let n=abcde

then

abcde4*4=4abcde

which by solving we get 13*abcde=133328

so abcde=10256.

thus 102564*4=410256

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32⟩ The gentlemen Dutch, English, Painter, and Writer are all teachers at the same secondary school. Each teacher teaches two different subjects. Furthermore Three teachers teach Dutch language There is only one math teacher There are two teachers for chemistry Two teachers, Simon and mister English, teach history Peter does not teach Dutch language Steven is chemistry teacher Mister Dutch doesn't teach any course that is thought by Karl or mister Painter. What is the full name of each teacher and which two subjects does each one teach?

Since Peter as only one doesn't teach Dutch language, and mister Dutch doesn't teach any course that is taught by Karl or mister Painter, it follows that Peter and mister Dutch are the same person and that he is at least math teacher. Simon and mister English both teach history, and are also among the three Dutch teachers. Peter Dutch therefore has to teach next to math, also chemistry. Because Steven is also chemistry teacher, he cannot be mister English or mister Painter, so he must be mister Writer. Since Karl and mister Painter are two different persons, just like Simon and mister English, the names of the other two teachers are Karl English and Simon Painter. Summarized:Peter Dutch, math and chemistrySteven Writer, Dutch and chemistrySimon Painter, Dutch and historyKarl English, Dutch and history..

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33⟩ Two friends, Alex and Bob, go to a bookshop, together with their sons Peter and Tim. All four of them buy some books; each book costs a whole amount in shillings. When they leave the bookshop, they notice that both fathers have spent 21 shillings more than their respective sons. Moreover, each of them paid per book the same amount of shillings as books that he bought. The difference between the number of books of Alex and Peter is five. Who is the father of Tim?

For each father-son couple holds: the father bought x books of x shillings, the son bought y books of y shillings. The difference between their expenses is 21 shillings, thus x2 - y2 = 21. Since x and y are whole numbers (each book costs a whole amount of shillings), there are two possible solutions: (x=5, y=2) or (x=11, y=10). Because the difference between Alex and Peter is 5 books, this means that father Alex bought 5 books and son Peter 10. This means that the other son, Tim, bought 2 books, and that his father is Alex. .

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34⟩ A number is called a palindrome when it is equal to the number you get when all its digits Postman Pat delivers the mail in the small village Tenhouses. This village, as you already suspected, has only one street with exactly ten houses, numbered from 1 up to and including 10. In a certain week, Pat did not deliver any mail at two houses in the village; at the other houses he delivered mail three times each. Each working day he delivered mail at exactly four houses. The sums of the house numbers where he delivered mail were on Monday 18 on Tuesday 12 on Wednesday 23 on Thursday 19 on Friday 32 op Saturday 25 on Sunday he never works Which two houses didn't get any mail that week?

If postman Pat would have delivered mail three times at each house, then the total sum of the house numbers per day would be (1+2+3+4+5+6+7+8+9+10)?=165. Now that sum is 18+12+23+19+32+25=129. The difference is 165-129=36; divided by 3 this is 12. The sum of the house numbers where no mail was delivered is therefore 12. The following combination are possible: 2+10

3+9

4+8

5+7

Each day at four houses the mail was delivered. On Tuesday the sum was 12. 12 can only be made from four house numbers in 2 ways:

1+2+3+6

1+2+4+5

The same holds for Friday with the sum of 32

5+8+9+10

6+7+9+10

From this we can conclude that the house numbers 1, 2, 9 and 10 for sure have received mail, which means that the combination 2+10 and 3+9 are not possible. Also the combination 5+7 is not possible, because mail was delivered either at house 5 or at house 7. Thus the only remaining solution is: houses 4 and 8.

N.B.: there are various possibilities for the actual post delivery of the whole week. For example: Monday houses 1, 3, 5 and 9

Tuesday houses 1, 2, 3 and 6

Wednesday houses 1, 5, 7 and 10

Thursday houses 2, 3, 5 and 9

Friday houses 6, 7, 9 and 10

Saturday houses 2, 6, 7 and 10

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35⟩ Joyce has bought ten trees for her garden. She wants to plant these trees in five rows, with four trees in each row. The Question How must Joyce plant the trees?

The answer to this riddle is to arrange the trees in the shape of a 'star' as illustrated below.

DRAW A STAR TO GET THE ANSWER.

T

T T T T

T T

T

T T

Conventional 'Star drawing' has five lines. These five lines represent the five rows. At each node in the diagram where two 'lines of star' meet a tree can be planted. Thus each of the five rows has four trees.

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36⟩ You walk upwards on an escalator, with a speed of 1 step per second. After 50 steps you are at the end. You turn around and run downwards with a speed of 5 steps per second. After 125 steps you are back at the beginning of the escalator. How many steps do you need if the escalator stands still?

Let v be the speed of the escalator, in steps per second. Let L be the number of steps that you need to take when the escalator stands still. Upwards (along with the escalator), you walk 1 step per second. You need 50 steps, so that takes 50 seconds. This gives: L - 50 ?v = 50. Downwards (against the direction of the escalator), you walk 5 steps per second. You need 125 steps, so that takes 25 seconds. This gives: L + 25 ?v = 125. From the two equations follows: L = 100, v = 1. When the escalator stands still, you need 100 steps..

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37⟩ Tom has three boxes with fruits in his barn one box with apples, one box with pears, and one box with both apples and pears. The boxes have labels that describe the contents, but none of these labels is on the right box. How can Tom, by taking only one piece of fruit from one box, determine what each of the boxes contains?

Tom takes a piece of fruit from the box with the labels 'Apples and Pears'. If it is an apple, then the label 'Apples' belong to this box. The box that said 'Apples', then of course shouldn't be labeled 'Apples and Pears', because that would mean that the box with 'Pears' would have been labeled correctly, and this is contradictory to the fact that none of the labels was correct. On the box with the label 'Appels' should be the label 'Pears'. If Tom would have taken a pear, the reasoning would have been in a similar way. .

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38⟩ Richard is a strange liar. He lies on six days of the week, but on the seventh day he always tells the truth. He made the following statements on three successive days Day 1 "I lie on Monday and Tuesday." Day 2 "Today, it's Thursday, Saturday, or Sunday." Day 3 "I lie on Wednesday and Friday." On which day does Richard tell the truth?

We know that Richard tells the truth on only a single day of the week. If the statement on day 1 is untrue, this means that he tells the truth on Monday or Tuesday. If the statement on day 3 is untrue, this means that he tells the truth on Wednesday or Friday. Since Richard tells the truth on only one day, these statements cannot both be untrue. So, exactly one of these statements must be true, and the statement on day 2 must be untrue. Assume that the statement on day 1 is true. Then the statement on day 3 must be untrue, from which follows that Richard tells the truth on Wednesday or Friday. So, day 1 is a Wednesday or a Friday. Therefore, day 2 is a Thursday or a Saturday. However, this would imply that the statement on day 2 is true, which is impossible. From this we can conclude that the statement on day 1 must be untrue. This means that Richard told the truth on day 3 and that this day is a Monday or a Tuesday. So day 2 is a Sunday or a Monday. Because the statement on day 2 must be untrue, we can conclude that day 2 is a Monday. So day 3 is a Tuesday. Therefore, the day on which Richard tells the truth is Tuesday. .

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39⟩ Its always 1 to 6, its always 15 to 20, its always 5, but its never 21, unless its flying. What is this?

The answer is:

a dice. An explanation: "It's always 1 to 6": the numbers on the faces of the dice, "it's always 15 to 20": the sum of the exposed faces when the dice comes to rest after being thrown, "it's always 5": the number of exposed faces when the dice is at rest, "but it's never 21": the sum of the exposed faces is never 21 when the dice is at rest, "unless it's flying": the sum of all exposed faces when the dice is flying is 21 (1 + 2 + 3 + 4 + 5 + 6)..

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40⟩ A man has a wolf, a goat, and a cabbage. He must cross a river with the two animals and the cabbage. There is a small rowing-boat, in which he can take only one thing with him at a time. If, however, the wolf and the goat are left alone, the wolf will eat the goat. If the goat and the cabbage are left alone, the goat will eat the cabbage. How can the man get across the river with the two animals and the cabbage?

There are two solutions: First, the man takes the goat across, leaving the wolf with the cabbage. Then he goes back. Next, he takes the wolf across. Then the man goes back, taking the goat with him. After this, he takes the cabbage across. Then he goes back again, leaving the wolf with the cabbage. Finally, he takes the goat across. First, the man takes the goat across, leaving the wolf with the cabbage. Then he goes back. Next, he takes the cabbage across. Then the man goes back, taking the goat with him. After this, he takes the wolf across. Then he goes back again, leaving the wolf with the cabbage. Finally, he takes the goat across. .

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54 Logical Questions And Answers

21⟩ You are standing next to a well, and you have two jugs. One jug has a content of 3 liters and the other one has a content of 5 liters. How can you get just 4 liters of water using only these two jugs?

26⟩ Let D be the set of all points in the real plane such that |x| + |y| <= 1, where |x| (respectively |y|) denotes the absolute value of x (respectively y). Prove that amongst every 5 points in D, there exist two points whose distance from one another is at most 1.

27⟩ You are given 8 identical balls .... but one of them is slightly heavier than the rest.... given a old scale (not electronic one) and only two trials to weigh ... can u spot the odd one out?

29⟩ A cyclist drove one kilometer, with the wind in his back, in three minutes and drove the same way back, against the wind in four minutes. If we assume that the cyclist always puts constant force on the pedals, how much time would it take him to drive one kilometer without wind?

35⟩ Joyce has bought ten trees for her garden. She wants to plant these trees in five rows, with four trees in each row. The Question How must Joyce plant the trees?

39⟩ Its always 1 to 6, its always 15 to 20, its always 5, but its never 21, unless its flying. What is this?

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Logical

Home Basic Common Logical

54 Logical Questions And Answers

21⟩ You are standing next to a well, and you have two jugs. One jug has a content of 3 liters and the other one has a content of 5 liters. How can you get just 4 liters of water using only these two jugs?

26⟩ Let D be the set of all points in the real plane such that |x| + |y| <= 1, where |x| (respectively |y|) denotes the absolute value of x (respectively y). Prove that amongst every 5 points in D, there exist two points whose distance from one another is at most 1.

27⟩ You are given 8 identical balls .... but one of them is slightly heavier than the rest.... given a old scale (not electronic one) and only two trials to weigh ... can u spot the odd one out?

29⟩ A cyclist drove one kilometer, with the wind in his back, in three minutes and drove the same way back, against the wind in four minutes. If we assume that the cyclist always puts constant force on the pedals, how much time would it take him to drive one kilometer without wind?

35⟩ Joyce has bought ten trees for her garden. She wants to plant these trees in five rows, with four trees in each row. The Question How must Joyce plant the trees?

39⟩ Its always 1 to 6, its always 15 to 20, its always 5, but its never 21, unless its flying. What is this?

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