Let Tn = 1n + 2n + 3n + 4n. Find the number of values of n among first 100 positive integers such that Tn is divisible by 5.
- 48
- 50
- 67
- 75
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Quant Question Of The Day: 135
Quant Question Of The Day: 134
Author: TG.Raman
If x2+ y2 = 14x – 6y – 58, then what is the maximum value of 3x + 2y ? x2
+ y2 = 14x – 6y – 58 Or (x-7)2
+ (y+3)2 = 0 Since
(x-7)2 and (y+3)2 is always positive so the only value of
x and y that satisfy the above
equation is x = 7 and y =-3 So, the maximum value of 3x+ 2y = 15
1. -12
2. 15
3. 10
4. 6
5. None of these
See our previous ‘Questions of the Day’:
https://tathagat.mba/quant-question-of-the-day-134/
https://tathagat.mba/quant-question-of-the-day-133/
There are 3 persons- A, B and C. On some day, A lent pens to B and C as many as they had. After a month B gave as many pens to A and C as many as they have. After a month C did the same thing. At the end of this transaction each one of them had 16. Find the pens each originally had?
One way to solve it is by making 3 equations and solve them simultaneously. But there is rather easier way tosolve it using back tracking.
It’s given that at the end, each had 16 pens (16, 16, 16) i.e. after C gave pens to A & B as many as they had. It means that after getting pens from C their pens got doubled. So before C gave them pens, they had 8 pens each and C had 32 pens i.e. (8, 8, 32).
Similarly, before B gave pens to A & C, they had 4 & 16 pens respectively and B had 42 pens i.e. (4, 28, 16)
Again, before A gave pens to B & C, they had 14 & 8 pens respectively and A had 39 pens i.e. (26,14, 8)
Hence, initially A had 26 pens, B had 14 pens and C had 8 pens.
See our previous ‘Puzzles of the Day’:
https://tathagat.mba/puzzle-of-the-day-60/
https://tathagat.mba/puzzle-of-the-day-59/
Two books, four pens and five files cost Rs. 50. Three books, six pens and seven files cost Rs. 70. Find the cost of each file. Letx,y, z be the cost of each book, pen and file respectively.
Then we have,
2x + 4y + 5z = 50 ….. (1)
3x + 6y + 7z = 70 …. (2)
Here, the coefficients of x and y in equation (1) are in the ratio 1 : 2 whichis the same as that of the ratio in equation (2) . As the ratio of thesecoefficients are same we can find thevalue of variable z.
if we multiply (1) by 3 and (2) by 2 and subtract one from the other variablesx and y are eliminated and we get the value of z as 10.
Hence, The cost of each file is Rs . 10.
See our previous ‘Questions of the Day’:
https://tathagat.mba/quant-question-of-the-day-133/
https://tathagat.mba/quant-question-of-the-day-132/
There are 511 oranges and 9 empty boxes. An orange vendor asks his son to place all the 511 oranges in all the 9 boxes in such a manner that if he asks for any number of oranges from 1 to 511, his son should be able to pick them in terms of boxes. How did the son place all the oranges among the 9 boxes, given that any number of oranges can be put in one box? 1, 2, 4, 8, 16, 32, 64, 128, 256
The orange vendor can ask for only 1 orange, so one box must contain 1 orange.
He can ask for 2 oranges, so one box must contain 2 oranges.
He can ask for 3 oranges, in that case box one and box two will add up to 3.
He can ask for 4 oranges, so one box i.e. third box must contain 4 oranges.
Now using box number one, two and three containing 1, 2 and 4 oranges respectively, his son can give upto 7 oranges.Hence, forth box must contain 8 oranges.
Similarly, using first four boxes containing 1, 2, 4 and 8 oranges, his son can give upto 15 oranges. Hence fifth box must contain 16 oranges.
You must have noticed one thing till now that each box till now contains power of 2 oranges. Hence the answer is 1,2, 4, 8, 16, 32, 64, 128, 256. This is true for any number of oranges, here in our case only upto 511.
See our previous ‘Puzzles of the Day’:
https://tathagat.mba/puzzle-of-the-day-58/
https://tathagat.mba/puzzle-of-the-day-57/
A man is looking at a picture, in his mother’s, only brother’s, nephew’s house. Someone walks by this man and asks, “Who are you looking at?” The man answered, “I am looking at my son’s only sister’s, maternal grandfather’s daughter’s, husband’s, son’s father’s picture. Also, neither my wife nor I has brothers or sisters.” Whose house is the man in and who is he looking at? The man is in his own house and looking
at his own picture. Man’s mother’s only brother’s nephew is
the man himself as man do not have any brothers or sisters. Thus, he is in his
house. Man’s son’s only sister = his daughter daughter’s maternal grandfather =
Wife’s father maternal grandfather’s daughter = His
wife (as his wife do not have any brothers or sisters) Wife’s husband’s son’s father is
himself.
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https://tathagat.mba/puzzle-of-the-day-57/
https://tathagat.mba/puzzle-of-the-day-56/
A tank is connected with 7 pipes in total, some of which are inlet pipes and the others are outlet pipes. Each inlet pipe can fill the empty tank in 4 hours while each outlet pipe can empty the full tank in 5 hours. If all the pipes are opened together, it takes 2.5 hours for the empty tank to be filled. Find the number of inlet pipes. The data is tabulated below [ 5m – 4 ( 7-m)] (2.5) = 20
1. 3
2. 4
3. 5
4. 2
Inlet Outlet All Number m 7-m 7 Rate 5 4 5m – 4 ( 7-m) Time 4 5 2.5
5m – 28 + 4m = 8
m = 4.
See our previous ‘Questions of the Day’:
https://tathagat.mba/quant-question-of-the-day-132/
https://tathagat.mba/quant-question-of-the-day-131/
Since there is no conflict between what they said, it meant that either they both told a lie or both told the truth. In this case they both told a lie. The answer is the husband is older.
A lady and a gentleman are wife and husband. We do not know who is older.
Someone asked them: Who is older?
The wife said: I am older.
The husband said: I am younger.
At least one of them was lying. Who is older?
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https://tathagat.mba/puzzle-of-the-day-56/
https://tathagat.mba/puzzle-of-the-day-55/
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