In a 2000 m race, Gates gives Steve a headstart of 200 m and beats him by 30 sec. When Gates gives Steve a headstart of 3 mins he gets beaten by 1000 m. How long would Gates and Steve take to run the race individually? Answer: Gates – 4 mins and Steve – 5 mins. Explanation Let the speeds of Gates and Steve be ‘g’ and ‘s’ respectively. In the first case, since … [Read more...] about Rates – Time, Speed and Race
GRE Problem Solving
Sequences Series – nth term
Find the 50th term of the following series: 1 + 3 + 7 + 13 + 21 + ............ Answer: 2451 Explanation t2 – t1= 2 (2*1) t3 – t2= 4 (2*2) t4 – t3 = 6 (2*3) ……………………….. ………………………… ……………………….. t50 – t49= 98 (2*49) Adding all the equations, we get t50 – t1= 2 + 4 + 6 + ………. + 98 t50 – t1= 2450 t50 – 1 = 2450 Therefore, t50 = 2451 … [Read more...] about Sequences Series – nth term
Geometric Sequence – Triangles
One side of an equilateral triangle is 2 cms. The mid-points of its sides are joined to form another triangle whose mid-points are joined to form still another triangle. This process continues indefinitely. (i) Find the sum of the perimeters of all the triangles. (a) Cannot be determined (b) 4 (c) 12 (d) 8 (e) 10 Bonus Question (ii) Find the sum of the areas … [Read more...] about Geometric Sequence – Triangles
Inequalities and Absolute Values
The solution set for the inequality |x+2| < |4x+1| (a) -3/5 < x < 1/3 (b) -1/3 < x < 3/5 (c) 0 < x < 1/3 (d) -1/3 < x < 1/3 (e) None of these Correct Answer: (E) Explanation Since the expressions on both sides of the inequality are under modulus, you can square on both sides without disturbing the inequality. (x+2)2 < … [Read more...] about Inequalities and Absolute Values