When 5396, 6248 and 7739 are divided by the greatest number X, the remainder in each case is Y. Which of the following is true?
Answer & explanation
Correct answer: option 4
The greatest number which leaves same remainders on dividing a, b, c & d is HCF [(b-a), (c-b), (d-c)]
Now, a, b & C HCF [(b-a), (c-b)]
= (6248 - 5396), (7739 - 6248)
= 852, 1491
↓ ↓
↓
HCF = 213
Now, X = 213
Y = \(\frac{5396}{213}\) = (71⇒ remainder)
Now, check option (4) , X = 3Y
213 = 3 × 71
213 = 213
Hence, X = 3Y