21. The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?
Answer:
Explanation:There will be 20 3s in between 1 to 100
Similarly, 20 3s in between 200 to 300 but (100+20) in between 300 to 400 (because at unit place 19 3s and 10's place 1 and 100 3s at 100's place ) and 20 3s in between 400 to 500
20 3s in between 500 to 600
20 3s in between 600 to 700
20 3s in between 700 to 800
20 3s in between 800 to 900
20 3s in between 900 to 1000
So total number of 3s will be 180+19+1+100 = 300 This count is in decimal but in question base value is 8 so we need to convert (300)8 = 192
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22. If Valentine's day of 2005 was celebrated on a Monday. What day is Feb 14th, 2010?
Answer:
Explanation:In leap year 2 odd days Ordinary year 1 odd days.
From 2005 to 2010, there is one leap year and 4 ordinary year. So totally 6 odd days.
So answer is Sunday.
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23. One day Rapunzel meets Dwarf and Byte in the Forest of forgetfulness. She knows that Dwarf lies on Mondays, Tuesdays and Wednesdays, and tells the truth on the other days of the week. Byte, on the other hand, lies on Thursdays, Fridays and Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Rapunzel - Dwarf: Yesterday was one of those days when I lie. Byte: Yesterday was one of those days when I lie too. What day is it?
Answer:
Explanation:Answer is Thursday
As the condition says that the dwarf lie on Monday, Tuesday & Wednesday so they will speak truth that they lied on Thursday also on the other side the bytes speak lie on Thursday and will tell that they spoke lie on Wednesday. So the day has to be Thursday as no other option satisfies the condition also.
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24. If a three digit number 'abc' has 3 factors, how many factors does the 6-digit number 'abcabc' have?
Answer:
Explanation:abc' has exactly 3 factors, so 'abc' should be square of a prime number. (This is an important inference, please remember this).
Any number of the form paqbrc will have (a + 1) (b + 1) (c + 1) factors, where p, q, r are prime. So, if a number has 3 factors, its prime factorization has to be p2.
'abcabc' = 'abc' * 1001 or abc * 7 * 11 * 13 (again, this is a critical idea to remember)
Now, 'abc' has to be square of a prime number. It can be either 121 or 169 (square of either 11 or 13) or it can be the square of some other prime number.
When abc = 121 or 169, then 'abcabc' is of the form p3q1r1 1, which should have 4 * 2 * 2 = 16 factors. When 'abc' = square of any other prime number (say 172 which is 289), then 'abcabc' is of the form
p1q1r1s2 , which should have 2 * 2 * 2 * 3 = 24 factors So, 'abcabc' will have either 16 factors or 24 factors.
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25. Alice and Bob play the following coins-on-a-stack game. 20 coins are stacked one above the other. One of them is a special (gold) coin and the rest are ordinary coins. The goal is to bring the gold coin to the top by repeatedly moving the topmost coin to another position in the stack. Alice starts and the players take turns. A turn consists of moving the coin on the top to a position i below the top coin (0 ≤ i ≤ 20). We will call this an i-move (thus a 0-move implies doing nothing). The proviso is that an i-move cannot be repeated; for example once a player makes a 2-move, on subsequent turns neither player can make a 2-move. If the gold coin happens to be on top when it's a player's turn then the player wins the game. Initially, the gold coinis the third coin from the top. Then
Answer:
Explanation:In order to win, Alice's first move should be a 1- move.Because there are two possibilities after 1- move by Alice:-
1. When bob takes 0-move, then the coin config is same. But now Alice can neither take 1-move nor 0- move, so she has to take 2 or greater move (let it be 2 moves).Now we have only one coin above the gold coin. Bob can neither take 1-move nor 0-move nor 2- moves. So she has to take 3 or greater move. At the move greater than 2-move brings gold coin on top that makes Alice win.
2. Now bob takes 2-move after Alice's first move. Now there is only one coin above the gold coin. So Alice takes 0-move.Now we have only one coin above the gold coin. Bob can neither take 1-move nor 0-move nor 2-move. So she has to take 3 or greater move.
But the move greater then 2-move brings gold coin on top that makes Alice win.
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26. When 40! Is expressed in base 8 form, what is the last non-zero digit in the base 8 expansion?
Answer:
Explanation:We need to find the largest power of 8 that divides 40!.
We need to find the largest power of 2 that divides 40! This is given by (40/2) and then successive division by 2. = 20 + 10 + 5 + 2 + 1 = 38
So, 238 divide 40! Or, (23)12 × 22 divides 40! (23)12 divides the number or the base 8
representation ends with 12 zeroes. Now, the base 8
representation of this number will be some (abcd…n)8
× (1000000000000)8. Now, (abcd…n)8 does not end in 0 and is a multiple of 22. The last digit has to be 4.
The last non-zero digit is 4.
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27. The IT giant Tirnop has recently crossed a head count of 150000 and earning of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries and also write code at the same rate Suppose 16 such programmers take 16 minutes to write 16 lines of code in total. How many lines of code can be written by 96 programmers in 96 minutes? The IT giant Tirnop has recently crossed a head count of 150000 and earning of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries and also write code at the same rate Suppose 16 such programmers take 16 minutes to write 16 lines of code in total. How many lines of code can be written by 96 programmers in 96 minutes?
Answer:
Explanation:(16 men)*(16 min)/ (16 lines) = (96 men) (96 min)/x (lines)
Hence x=576
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28. Cadbury manufactures a chocolate box which contains "x" number of chocolates. There are three houses A, B, C in the neighbourhood of Cadbury. Since it was a new variety of chocolate the marketing managers of Cadbury decided to free chocolates to the children in the neighbouring houses A,B,C. In house A there are 3 children and in B there are 5 children and in C there are 7 children. After distributing the chocolates he was left with one chocolate in each case.
Answer:
Explanation:From the question, it is clear that the particular number should leave the remainder 1 while dividing it by 3,5 and 7.
211/3=Q+1
211/5=Q+1
211/7=Q+1
Hence 211 will be the answer
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29. Events A, B, C are mutually exclusive events such that: The set of possible values of x are in the interval
30. Fill dirt or fill soil is usually the sub-soil removed from an excavation site and is used to level a place or create artificial mounds. If the average density of sub- soil removed from a site is 3gm/cu cm and it weight 400 kg. How many hemispherical pits each of volume 240 cubic cm, can this sub-soil fill?
Answer:
Explanation:3 gm per cm cube and there are hemispheric pits of capacity 240 cm cube
So each hemisphere can contain 3*240=720 cm cube soil.
So total of 400 kg i.e. 400*1000=400000 gms will be held in 400000/720=555.55 so approximately 555.
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