Select the correct answerIn a class of students, if 1 is absent rest of people can be divided into 6 equal parts and if 2 are absent rest of them are divided into 7 equal parts, how many students are present in the class ?Options19285737

The problem can be solved by using the concept of Least Common Multiple (LCM).

Step 1: We know that the total number of students in the class is a number which when decreased by 1 can be divided by 6 and when decreased by 2 can be divided by 7.

Step 2: We need to find the LCM of 6 and 7, which is 42.

Step 3: The numbers which satisfy the above conditions are of the form 42k+1 and 42k+2.

Step 4: We start checking from k=1. For k=1, the numbers are 43 and 44. But 44 is not divisible by 7.

Step 5: For k=2, the numbers are 85 and 86. But 86 is not divisible by 7.

Step 6: For k=3, the numbers are 127 and 128. But 128 is not divisible by 7.

Step 7: For k=4, the numbers are 169 and 170. But 170 is not divisible by 7.

Step 8: For k=5, the numbers are 211 and 212. But 212 is not divisible by 7.

Step 9: For k=6, the numbers are 253 and 254. But 254 is not divisible by 7.

Step 10: For k=7, the numbers are 295 and 296. But 296 is not divisible by 7.

Step 11: For k=8, the numbers are 337 and 338. But 338 is not divisible by 7.

Step 12: For k=9, the numbers are 379 and 380. But 380 is not divisible by 7.

Step 13: For k=10, the numbers are 421 and 422. But 422 is not divisible by 7.

Step 14: For k=11, the numbers are 463 and 464. But 464 is not divisible by 7.

Step 15: For k=12, the numbers are 505 and 506. But 506 is not divisible by 7.

Step 16: For k=13, the numbers are 547 and 548. But 548 is not divisible by 7.

Step 17: For k=14, the numbers are 589 and 590. But 590 is not divisible by 7.

Step 18: For k=15, the numbers are 631 and 632. But 632 is not divisible by 7.

Step 19: For k=16, the numbers are 673 and 674. But 674 is not divisible by 7.

Step 20: For k=17, the numbers are 715 and 716. But 716 is not divisible by 7.

Step 21: For k=18, the numbers are 757 and 758. But 758 is not divisible by 7.

Step 22: For k=19, the numbers are 799 and 800. But 800 is not divisible by 7.

Step 23: For k=20, the numbers are 841 and 842. But 842 is not divisible by 7.

Step 24: For k=21, the numbers are 883 and 884. But 884 is not divisible by 7.

Step 25: For k=22, the numbers are 925 and 926. But 926 is not divisible by 7.

Step 26: For k=23, the numbers are 967 and 968. But 968 is not divisible by 7.

Step 27: For k=24, the numbers are 1009 and 1010. But 1010 is not divisible by 7.

Step 28: For k=25, the numbers are 1051 and 1052. But 1052 is not divisible by 7.

Step 29: For k=26, the numbers are 1093 and 1094. But 1094 is not divisible by 7.

Step 30: For k=27, the numbers are 1135 and 1136. But 1136 is not divisible by 7.

Step 31: For k=28, the numbers are 1177 and 1178. But 1178 is not divisible by 7.

Step 32: For k=29, the numbers are 1219 and 1220. But 1220 is not divisible by 7.

Step 33: For k=30, the numbers are 1261 and 1262. But 1262 is not divisible by 7.

Step 34: For k=31, the numbers are 1303 and 1304. But 1304 is not divisible by 7.

Step 35: For k=32, the numbers are 1345 and 1346. But 1346 is not divisible by 7.

Step 36: For k=33, the numbers are 1387 and 1388. But 1388 is not divisible by 7.

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