One of twelve pool balls is a bit lighter or heavier (you donot know) than the others. At least how many times you have to use an odd balance-type pair of scales to identify this ball?
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Solution
Let us mark the balls using number from 1 to 12 and these special symbols.
X? means I know nothing about ball number X.
XL means that this ball is may be lighter than the others;
XH means that this ball is maybe heavier than the others.
X means this ball is 'normal'.
Step I At first, Lay on the left pan balls 1?2?3?4? and on the right pan balls 5?6?7?8? If there is equilibrium,then the wrong ball is among 9-12.
Step II Put 1, 2, 3 on the left and 9?10?11 on the right pan. If there is equilibrium, then the wrong ball is number 12 and comparing it with another ball it canfind out if it is heavier or lighter.
Step III If the left pan is heavier, 12 is normal and 9 L 10L 11 L, weigh 9L and 10L If they are the same weight,then ball 11 is lighter than all other balls. If they are not the same weight, then the lighter ball is the one up.
Step IV If the right pan is heavier, then 9H 10H and 11H and the procedure is similar to the former text.
Step V If the left pan is heavier,then 1 H 2H 3H4H 5L6L 7L 8L and 9. 10.11.12, Now lay on the left pan 1 H2H 3H 5L and on the right pan 4H 9.10.11. If there is equilibrium then the suspicious balls are 6 L 7L and 8L.
Step VI Identifying the wrong one is similar to the former case of 9L 10L 11 L. If the left pan is lighter,then the wrong ball can be 5L or 4H.Compare for instance 1 and 4H.Step VII If they weigh the same, then ball 5 is lighter than all the others, otherwise ball4 is heavier. If the left pan is heavier, then all balls are normal except for 1 H, 2H and 3H, identifying the wrong ball among 3 balls was described earlier.In all possible way at least 3 times we have to weigh to find out which one isodd one.
A solid, four inch cube of wood is coated with blue painton all sixsides. Then the cube is cut into smaller one-in chcubes. These new one-inch cubes will have either three blue sides, two blue sides, one blue side or no blue sides.How many two colored side will be threre ?
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Solution
There are 8 corners cubes which are of three sided coloured. Central 4 cube in all the six faces are 1 sided coloured cubes. Remaining visible border cubes are two side coloured cubes.
Hence. 8 cubes from front side + 8 cubes from backside + 4 from left side +4 cubes from right side = 24 cubes (all two side colored cubes are covered in these 24 cubes including top and bottom faces)
A person has the capability of thinking 100 lines of code in 5 minutes and can type 100 lines of code in 10 minutes. He takes a break for five minutes after every ten minutes. How many lines of codes will he complete typing after an hour?
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Solution
Starting from zero time (time= 0 min) the person thinks for first 5 min (time = 5 min) then types 50 lines of code in next 5 min (time =10 min). then take break for 5 min(time =15 min). then again types the remaining 50 lines (of 10 min typing) for next 5 min (time =20 min).The procedure goes in first 50 min. hew rites 100 lines.Then he thinks for 5 min (time = 25 min). Again takes break for 10 min (time = 40 min).
Now he has completed 200 lines of codes in 40 min.We have 20 min remaining. Then he takes break for 5 min (time = 45 min) thinks for 5 min (time = 50 min)and got time to type for next 5 min (time = 55 min) as last 5 min is for break time (time =60 min). Thus he can write maximum 250 lines.
Ram and Hari, started from A and B towards B and A at 6:00 and 7:00 am respectively. They meet each other at 9:00 am and continued towards their respective destinations. Ram reaching B turns back and catches up with Hari before Hari reaches A at 11:00 am. At what time will Hari reach A.
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Solution
Let speed of Ram is 'x' and that of Hari is 'y'.After 3 h Ram started from A(6 : 00 am) and after 2 h Hari started from B (7 : 00 am) both meet at 9 : 00 am so, during their meet distance travelled by Ram is 3x and by Hari is 2y.Again they meet at 11:00 am 2 h from 9:00 am. Duringth is 2 h, distance travelled by Ram is 2x and distance travelled by Hari is 2y.
As Ram has reached B and again turns back towards A and then they both meet at 11:00 am. The distance covered in terms of y is 2y (from Ist meeting to B)+ 2y(from B to I st meeting point) + 2y (from Ist meeting point to 2nd meeting point) = 6y
Thus 2x = 6y ⇒x =3y
Thus total distance between A and B is
3x + 2y = 11y
Hari has already covered 4y distance for covering remaining 7y distance, he needs 7h.
So the time is 11 :00 am + 7h =6 pm
Wendy, a student, is an avid backgammon player. All students play either chess or checkers, but some checkers players do not play chess because they do not understand chess strategy. Backgammon players never play checkers,because they do not find checkers challenging. Therefore,Wendy must understand chess strategy.Which of the following must be true for the conclusion drawn above to be logically correct?
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Solution
The argument’s premises boil down to the following:1. Wendy is a student who plays backgammon.2. All students play either chess or checkers, but no backgammon player plays checkers.Based on these premises we can conclude that Wendy plays chess. In order to also conclude that Wendy understands chess strategy, we must assume that all chess players understand chess strategy:
Premise:X is an A.
Assumption:All A’s are B’s.
Conclusion:X is a B.
Statement (a)provides the assumption needed to draw the conclusion.
If a, a +2 and a + 4 are prime numbers, then the number of possible solutions for a is
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Solution
a, a + 2, a + 4 are prime numbers.Put value of ‘a’ starting from 3, we will have 3, 5 and 7 as the only set of prime numbers satisfying the given relationships.
DIRECTIONS: A sentence is broken into 3 parts (a),(b) and (c). Read each sentence to find out any grammatical error in it. The error if any will be in the part of the sentence the letter of that part is the answer.
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Solution
If I do not economise
Which one of the following option is the closest in meaning to word Radiant?
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Solution
The meaning of the word Radiant (Adjective) as used in the passage is : showing great happiness, love or health; giving a bright light.
It is difficult to speak a language fluently unless ______regularly.
Choose the correct alternative.
My friend and I decided to watch a play,however______enjoyed it.