Raman ranks sixteenth from the top and forty-ninth from the bottom in a class. How many students are there in the class ?
Answer: A
Correct answer: 64
Raman is counted from both ends, so the class holds \[ 16 + 49 - 1 = \mathbf{64} \] students, the 1 being subtracted because Raman himself is counted twice.
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How many such digits are there in the number 7346285 which are as far away from the beginning of the number, as they will be when arranged in ascending order within the number?
Answer: C
Correct answer: Two
Arranged in ascending order the digits of 7346285 run 2, 3, 4, 5, 6, 7, 8. Comparing position by position, only 3 (second in both) and 4 (third in both) keep their places - so the answer is two.
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What is the 13th letter of the English Alphabet?
Answer: A
There are 26 English Alphabets. They are:
A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z.
Therefore, from the left end the 13th letter is M and is Consonent. And from the right end the 13th letter is N and is Consonent.
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A bus for Delhi leaves every thirty minutes from a bus stand. An enquiry clerk told a passenger that the bus had already left ten minutes ago and the next bus will leave at 9.35 a.m. At what time did the enquiry clerk give this information to the passenger?
Answer: D
Correct answer: 9.15 a.m.
Buses leave every thirty minutes, so the one before the 9.35 bus left at 9.05. That bus had gone ten minutes earlier, which puts the conversation at \[ 9.05 + 10\text{ min} = \mathbf{9.15\ a.m.} \]
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Six friends A, B, C, D, E and F joined an institute in the year 1993 but on different days. Only E has joined after C and D. C joined immediately before A and immediately after B. F is not the first or the last person to join. D will not be in any corner.
Who is the first person joining the Institute?
Answer: D
Correct answer: B
E alone joined after C and D, so E was last. B, C and A joined in that order without a break, and neither D nor F could take a corner place, which leaves only one arrangement: B, C, A, then D and F, then E. So B joined first.
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How many combinations of two-digit numners having 8 can be made from the following numbers?
8, 5, 2, 1, 7, 6
Answer: D
Correct answer: 11
With 8 as the first digit there are five numbers - 85, 82, 81, 87, 86 - and with 8 as the second digit another five: 58, 28, 18, 78, 68. Adding 88 itself gives \[ 5 + 5 + 1 = \mathbf{11} \]
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If the following series is written in the reverse order, which number will be fourth to the right of the seventh number from the left?
7, 3, 9, 7, 0, 3, 8, 4, 6, 2, 1, 0, 5, 11, 13
Answer: D
Correct answer: 0
Reversed, the series reads 13, 11, 5, 0, 1, 2, 6, 4, 8, 3, 0, 7, 9, 3, 7. The seventh number from the left is 6, and counting four places to its right lands on the eleventh, 0.
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Count each 1 in the following sequence of numbers that is immediately followed by 2, if 2 is not immediately followed by 3. How many such l’s are there?
1 2 1 3 4 5 1 2 3 5 2 1 2 6 1 4 5 1 1 2 4 1 2 3 2 1 7 5 2 1 2 5
Answer: B
Correct answer: 4
Counting the 1s that are followed by a 2 which is not itself followed by a 3 gives 4. The pair 1 2 3 is excluded each time it occurs, because there the 2 is followed by a 3.
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The weights of 4 boxes are 20, 30, 50 and 70 kilograms. Which of the following cannot be the total weight, in kilograms, of any combination of these boxes and in a combination a box can be used only once?
Answer: B
Correct answer: 160
The possible totals are the four weights singly (20, 30, 50, 70), in pairs (50, 70, 80, 90, 100, 120), in threes (100, 120, 140, 150) and all together (170). 160 appears nowhere among them, so it cannot be made.
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Pearl Towers is taller than Sky Towers but shorter than Unity Towers. Unity Towers and Cyber Towers are of same height. Pearl Towers is shorter than Indus Towers. Amongst the buildings, who is the second shortest?
Answer: A
Correct answer: Pearl Tower
The comparisons give \( \text{Sky} < \text{Pearl} < \text{Unity} = \text{Cyber} \) and \( \text{Pearl} < \text{Indus} \). Sky is therefore the shortest and Pearl the next shortest, the other three all standing above it.
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