Brain Teasers

Jai Ganesh · 2009-01-24 03:25:11

Answer to #210:-
Correct, JaneFairfax!

Jai Ganesh · 2009-01-24 04:00:46

#211. A four-digit number is formed using the four digits 1, 2, 3, and 4 without repeating any one of them. What is the sum of all such possible numbers?

JaneFairfax · 2009-01-24 04:23:24

Jai Ganesh · 2009-01-24 04:30:23

Answer to #211:

Perfectly right, JaneFairfax!

#212. How many multiples of 9 can be found which are less than 9999 and are perfect cubes?

JaneFairfax · 2009-01-24 08:43:22

Jai Ganesh · 2009-01-24 18:14:25

Answer to #212.

Correct, JaneFairfax!

#213. A country with monetary unit X has printed currency notes of denomination 2X, 5X, 10X, 20X, 25X, and 50X notes. What would be the minimum number of notes required to pay exactly 78X, 69X and 101X to three different persons?

#214. A car is being driven in a straight line at a uniform speed towards the base of a vertical tower. The top of the tower is observed from the care and in the process, it takes 10 minutes for the angle of elevation to change from 45° to 60°. After how long would the care reach the base of the tower?

#215. If both a and b belong to the set {1, 2, 3, 4}, then what is the number of equations of the form

having real roots?

#216. What is the value of x if

?

#217. What is the sum of all two-digit numbers which leave a remainder 3 when divided by 7?

#218. What is the sum of 'n' terms of the series

?

Jai Ganesh · 2009-01-25 03:25:34

#219. There are 12 towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such taht every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many telephone lines are required?

#220. A square tin sheet of side 12 inches is converted into a box with open top by the following steps. The sheet is p[laced horizontally; then, equal sized squares of side x inches are cut from the four corners of the sheet. Finally, the four resulting sides are bent vertically upwards in the shape of a box. If x is an integer, that value of x maximizes the volume of the box?

JaneFairfax · 2009-01-25 03:56:26

Muggleton · 2009-01-25 07:39:27

JaneFairfax wrote:

Muggleton · 2009-01-25 08:03:06

JaneFairfax · 2009-01-25 09:53:06

Jai Ganesh · 2009-01-25 18:39:20

Answers to #213, #214, #215, #216, #217, #218, #219, and #220:-
The performances have been......

Answers to #213, and #219 are correct, JaneFairfax!
Regarding #220, if you insist that I should use only Metric units in my questions, I shall do so. But in my opinion, one should be prepared to convert from Metric to any other system or otherwise, while answering a question. Please tell me, is the language spoken in every part of the world the same? Is the education system the same; and most importantly, is the monetary unit the same? Unit conversions, Translations and adaptation shouldn't be a cause of worry.
Answers to #215, #217, and #218 are correct, Muggleton!
Please check the answers #214, #216, and #220 again.

Jai Ganesh · 2009-01-25 19:39:32

#221. Let

be a square of side a. Another square is formed by joining the midpoints of the sides of . The same process is applied to to form yet another square , and so on. If
be the areas of the squares and be the perimeters of the squares , then what is the following ratio equal to?

#222. If ABCDEF is a regular Hexagon, what is the ratio of the area of the triangle ACE to that of the Hexagon ABCDEF?

#223. Consider two cloth-cutting processes. In the first case, n circular cloth pieces are cut from a square of side a in the following steps: the original square of side a is divided into n smaller squares, not necessarily of the same size; then a circle of maximum possible area is cut from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the side of square a and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes. What is the ratio of the total area of scrap cloth generated in the first process to that in the second process?

JaneFairfax · 2009-01-25 23:46:47

Last edited by JaneFairfax (2009-01-26 11:37:52)

Jai Ganesh · 2009-01-26 03:52:24

Answers to #220, #221, and #222:-
Answer to #222 is correct.

Answer to #220:- The side of the square tin sheet is 12 units. If 4 units are cut off from each side, the resulting box would have dimensions 4x4x4, that is, volume of 64 cu.units.
However, if 2 units are cut from each side, the resulting box would have dimensions 8x8x2, that is, 128 cu.units. Clearly, the latter produces a box of greater volume.
Muggleton had said x was 4 units.

Regarding #221, Please do try again, JaneFairfax.

Jai Ganesh · 2009-01-26 04:01:09

#224. Two identical circles intersect such that their centers, and the points at which they intersect, form a square of side 1 cm. What is the area of the portion that is common to the two circles in square centimeters?

#225. What is the remainder obtained when x is divided by 70, where

?

#226. If

,
then which of the following is true?
(1)
(2)
(3)
(4)

JaneFairfax · 2009-01-26 12:43:26

I think I know what I did wrong for #221. I joined up the midpoints incorrectly. I joined up the midpoints of opposite sides instead of midpoints of adjacent sides.

A diagram would have been helpful for problems for this sort.

Jai Ganesh · 2009-01-26 17:04:17

I tend to post puzzles which require the highest degree of application of mind in 'Brain Teasers. I agree, a diagram would have been helpful. However, I wish to add, such questions are not always accompanied by diagrams.
I hope my reply regarding #220 has been clear enough.
That leaves #223, #224, #225, and #226 to be answered.......

Jai Ganesh · 2009-01-27 03:41:07

#227. What is the distance in centimeters between two parallel chords of length 32 centimeters and 24 centimeters in a circle of radius 20 centimeters?

JaneFairfax · 2009-01-27 03:55:03

#227. Are the chords on the same side of the centre, or on opposite sides of the centre? If on the same side,

If on opposite sides,

Jai Ganesh · 2009-01-27 04:16:32

Answer to #227:-
Thats correct, JaneFairfax! Both the possibilites have to be considered while solving the problem, and the two solutions ought to be given. That was exactly what was expected!

#228. In a chess competition involving boys and girls of a school, every player had to play every other player once. It was found that in 45 games, both the players were girls and in 190 games, both the players were boys. How many games were played in which one player was a boy and his opponent was a girl?

JaneFairfax · 2009-01-27 06:04:24

Jai Ganesh · 2009-01-27 17:07:44

Answer to #228:-
Correct, JaneFairfax!

#229. A piece of paper is in the shape of a right angled triangle and is cut along a line that is parallel to the hypotenuse; leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 square meters, what would the area of the smaller traingle be?

#230. Let a, b, c, d, and e be integers such that

.
Which of the following pairs contains a number that is not an integer?
(1)
(2)
(3)
(4)

#231. Two straight Roads R1 and R2 diverge from a point A at an angle of 120°. Adam starts walking from point A along R1 at a uniform speed of 3 km/hour. Wayne starts walking, starting at the same time as Adam, along R2 at a speed of 2 km/hour. They continue walking for 4 hours along their respective roads and reach points B and C on R1 and R2 respectively. There is a straight line path connecting B and C. Then Adam returns to point A walking along the line segments BC and CA. Wayne also returns to A after walking along line segments CB and BA. Their speeds remain unchanged. After Adam reaches A, how much more time would Wayne take to reach A?

JaneFairfax · 2009-01-28 01:39:20

Jai Ganesh · 2009-01-28 02:20:12

Answer to #231:-
Correct, JaneFairfax!

#232. A chemical plant has four Tanks, A, B, C, and D, each containing 1000 liters of a chemical. The chemicals are being pumped from one tank to the other as follows:-
From A to B @ 20 liters/minute.
From C to A @ 90 liters/minute.
From A to D @ 10 liters/minute.
From C to D @ 50 liters/minute.
From B to C @ 100 liters/minute.
From D to B @ 110 liters/minute.

Which tank gets empty first and how much times (in minutes) does it take to get empty after the pumping starts?

#233. A park has two identical circular tracks touching each other, and a rectangula track enclosing the two circles. Two athletes, A and B start running simultaneously from the point where one of the circular tracks touches the smaller side of the rectangular track. A runs along the rectangular track, while B runs along the two circular tracks which resembles the shape '8'. Approximately, how much faster than A does B have to run, so that they take the same time to return to their starting point?

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