NIMCET 2022 — Reasoning PYQ
NIMCET | Reasoning | 2022The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5, respectively is
Choose the correct answer:
- A.
127
(Correct Answer) - B.
123
- C.
235
- D.
305
127
Explanation
1. Subtract the remainders from the given numbers:
For 1657, the remainder is 6:
1657−6=1651
For 2037, the remainder is 5:
2037−5=2032
2. Find the HCF of 1651 and 2032: We can use the Long Division Method to find the HCF:
Divide 2032 by 1651:
2032=1651×1+381
Now, divide 1651 by the remainder 381:
1651=381×4+127
Finally, divide 381 by the new remainder 127:
381=127×3+0
3. Identify the HCF: Since the last divisor that gives a remainder of 0 is 127, the HCF is 127.
Conclusion
The greatest number that divides 1657 and 2037 while leaving remainders 6 and 5 is 127.
Correct Option: (A) 127
Explanation
1. Subtract the remainders from the given numbers:
For 1657, the remainder is 6:
1657−6=1651
For 2037, the remainder is 5:
2037−5=2032
2. Find the HCF of 1651 and 2032: We can use the Long Division Method to find the HCF:
Divide 2032 by 1651:
2032=1651×1+381
Now, divide 1651 by the remainder 381:
1651=381×4+127
Finally, divide 381 by the new remainder 127:
381=127×3+0
3. Identify the HCF: Since the last divisor that gives a remainder of 0 is 127, the HCF is 127.
Conclusion
The greatest number that divides 1657 and 2037 while leaving remainders 6 and 5 is 127.
Correct Option: (A) 127