Find the greatest number which is such that when 697, 909 and 1227 are divided by it, the remainders are all the same?
Correct answer: D. 106
- A. 53
- B. 112
- C. 108
- D. 106
Explanation
If the remainders are equal, the greatest divisor must divide the differences between the numbers. The differences are 909 - 697 = 212 and 1227 - 909 = 318, and gcd(212, 318) = 106, so the required number is 106. The likely mistake is option b, 112, which does not divide both differences.
Last updated
About Ratio and Proportion
Ratios compare quantities in the same units, while proportions state that two ratios are equal. Problems cover simplification, division in a given ratio, direct and inverse variation, scale, and missing terms, with attention to the difference between a ratio and a fraction representing part of a whole.
Practise Arithmetic
1,060 free Arithmetic MCQs from Mathematics, each with the correct answer and an explanation. Unlimited attempts, no account needed.
Exams that ask Mathematics questions like this
Mathematics is on 67 papers prepared for on TestUstad, and all of them draw the same bank, so this question is worth knowing for every one of them.