naveenhv wrote:On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by thin tick marks, and also into sevenths, as indicated by small tick marks.
What is the least possible distance between any two of the tick marks?

a) 1/70

b) 1/35

c) 2/35

d) 1/12

e) 1/7

now the distance would be minimum when we have; minimum numerator and maximum denominator;
now the maximum value of denominator would be 35 because number line from 0 to 1 is divided in segments of fifths and sevenths and denominator can be maximum only if we consider different segments because if we consider the nos. from same segment then denominator would be either 5 or 7; now the minimum value of numerator would be 1; when we subtract 15 from 14; to understand this part; lets consider the following algebraic relation;
distance between any two points can be given as;
|a/5-b/7|; here a varies from 1 to 4 and b varies from 1 to 6;
now |7a-5b|/35 would be minimum if a=2 and b=3; hence our answer should be 1/35; B