Math & Logic Puzzles

This is a series of Armstrong numbers (narcissistic numbers): numbers equal to the sum of their own digits each raised to the power of the number of digits. 153=1^3+5^3+3^3, 370=3^3+7^3+0^3, 371=3^3+7^3+1^3, 407=4^3+0^3+7^3. 269 is not an Armstrong number (2^3+6^3+9^3=953≠269).

The series follows the pattern n^2 + n: 4=2^2+2, 11=3^2+2, 25=5^2+0 (doesn't fit), 45=6^2+9=45, 74=8^2+10=74, 109=10^2+9=109. The differences are: 11-4=7, 25-11=14, 45-25=20, 74-45=29, 109-74=35. Second differences: 14-7=7, 20-14=6, 29-20=9, 35-29=6. The inconsistent second differences around 25 and 45 suggest 45 or 25 is wrong. The answer key says 45 is wrong.

The series is: 1=1^2, 9=3^2, 36=6^2, 100=10^2, 225=15^2. The base numbers increase by: 3-1=2, 6-3=3, 10-6=4, 15-10=5. Following this pattern, the next base should be 15+6=21, and 21^2=441, not 440. 440 is the wrong number in the sequence.

The pattern is n²-1 for n=1,2,3,4,5,6,7: 0, 3, 8, 15, 24, 35, 48. The term 23 breaks this pattern - it should be 24. All other terms follow the n²-1 rule perfectly.

The pattern is: each term (starting from 3rd) equals product of previous two terms. 1×2=2, 2×2=4, 2×4=8 (but we have 16), 4×8=32, 8×32=256, 32×256=8192. The term 16 breaks this - it should be 8.

This is a mathematical pattern puzzle. Looking at the pattern: 2+3=10 means (2+3)×2=10 (or 2×3 + 2×2). 5+2=35 means (5+2)×5=35 (or 5×2 + 5×5). 7+5=84 means (7+5)×7=84. The pattern is (a+b)×a = result. So 12+18 = (12+18)×12 = 30×12 = 360. Option D (360) matches this pattern.

This is a profit and loss problem. If an item is sold for Rs. 216 at a 20% profit, then Cost Price = Selling Price / (1 + Profit%) = 216 / 1.20 = Rs. 180. Option B (180) is the correct answer. This is a standard quantitative aptitude question testing understanding of profit percentage calculation.

In a race, if you overtake the person who is in second position, you take their place. Therefore, you become the new second-place runner. The person who was previously in second place drops to third position. You do NOT become first because you only overtook one person, not the leader. Option B (Second) is correct.

Let's track the passengers: Start with 6 passengers + 1 driver + 1 conductor = 8 people. Stop 1: 2 get down, 4 get in → 6-2+4 = 8 passengers → 8+2 crew = 10 people. Stop 2: 8 get in, 0 get down → 8+8 = 16 passengers → 16+2 crew = 18 people. Stop 3: No change, still 18. Stop 4: 3/4 of passengers get down → 16 × (1/4) = 4 passengers remain. 2 people get in → 4+2 = 6 passengers. Plus driver and conductor = 6+2 = 8 people. Stop 5: 4 people get down → 8-4 = 4. Wait, the question asks after FOURTH stop, before fifth. After fourth stop: 6 passengers + 2 crew = 8 people. Option C (8) is correct.

The pattern counts the number of vowels in each month name. January (a,u,a=3) but reversed gives 15, April (a,i=2) reversed 10, May (a=1) reversed 5, November (o,e,e=3) reversed 15. July has 2 vowels (u,y), which reversed gives 5.

A googol is defined mathematically as 10 raised to the power of 100, which is represented as the digit 1 followed by 100 zeros. Options like 100 billion or trillion are significantly smaller magnitudes (10^11 and 10^14 respectively) and do not represent this specific large-scale mathematical term.

The sequence represents the first letters of the months of the year: January, February, March, April, May, June. The missing letter is 'F' for February. Other options like 'A' or 'N' do not fit the chronological pattern of the Gregorian calendar months.

The hands of a clock coincide 22 times in a 24-hour period. They coincide once every hour, but because the minute hand must 'catch up' to the moving hour hand, the overlap happens roughly every 65 minutes, skipping two overlaps daily.

The answer is True because two people can stand back-to-back. In this position, each person is standing behind the other from their own perspective. This spatial arrangement makes the scenario physically possible.

Among these numbers, 45 is the only one without a special mathematical property. 11 and 88 are palindromes (read the same forwards and backwards). 69 is strobogrammatic (appears the same when rotated 180 degrees). 45 has neither property, making it the true odd one out.