A number lying between 1000 and 2000 is such that on division by 2,3,4,5,6,7 and 8 leaves remainders 1,2,3,4,5

Answer 1

There is one answer between 1000 and 2000, and it is 1679. Here's how I did it:

I wrote a program that iterates i from 1000 to 2000. For each value of i, the program iterates j from 2 to 8. If mod(i,j) doesn't equal (j-1), the program sets a failure flag. If any value of i passes all the tests, the failure flag isn't set, and it prints out the number.

This works because the modulus function mod(i,j) gives you the remainder you'd get dividing i by j.

The numbers that pass this test are all of the form (840*n - 1), where n = 1, 2, 3...

839, 1679, 2519, 3359, et cetera.

Answer 2

It is not 1679 from previous answers

1679/7 = (239 * 7) + 6 this remainder is not in {1,2,3,4,5}
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1019,1079, 1103, 1109, 1139, 1187, 1199, 1259, 1271, 1313, 1319, 1439, 1499, 1523, 1529, 1559, 1607, 1619, 1679, 1691, 1733, 1739, 1859, 1919, 1943, 1949, 1979

When divided by 2,3,4,5,6,7 and 8 leaves remainders 1,2,3,4,5 .

If there is a typo in the question such that the question should be A number lying between 1000 and 2000 is such that on division by 2,3,4,5,6,7 and 8 leaves remainders 1,2,3,4,5,6,7 has only one solution: 1679

Peter

Answer 3

find the LCD of 2,3,4,5,6,7,8
which will be 840
since it is not between 1000 and 2000
*2
which will be 1680
subtract 1
1679