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Earn 100
A boy took a seven-digit number ending in , and raised it to an even power greater than . He then took the number , and raised it to a power which leaves the remainder when divided by . If he now multiplies both the numbers, what will be the unit's digit of the number he so obtains?
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Important Questions on Number Systems
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Two friends were discussing their marks in an examination. While doing so, they realised that both the numbers had the same prime factors, although Raveesh got a score which had two more factors than Harish. If their marks are represented by one of the options as given below, which of the following options would correctly represent the number of marks they got?
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A number is such that when divided by , , , or , it leaves the remainder , , , or , respectively. Which is the largest number below that satisfies this property?
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A number, when divided by , , and , leaves a remainder of . Find the least number (after ) that satisfies this requirement.
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A number, when divided by , , and , leaves a remainder of . Find the second-lowest number (not counting ) that satisfies this requirement.
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A number, when divided by , , and , leaves a remainder of . Find the highest two-digit number that satisfies this requirement.
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A number, when divided by , , and , leaves a remainder of . Find the highest three-digit number that satisfies this requirement.
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A frog is sitting on vertex of a square . It starts jumping to the immediately adjacent vertex on either side in a random fashion and stops when it reaches point . In how many ways can it reach point if it makes exactly jumps?
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Three bells ring at intervals of seconds, seconds, and seconds, respectively. If they ring together for the first time at a.m. in the morning, after what interval of time will they together ring again for the first time?
