How many obtuse-angled triangles can you form with 10,24,x as the sides where x is an integer? Answer: 14 Explanation: For three numbers to form an obtuse-angled triangle the square of the largest number should be greater than the sum of the squares of the other two numbers. For three numbers to form a triangle the sum of any two numbers should be greater than the … [Read more...] about Geometry – Obtuse Angled Triangles
GRE Problem Solving
Number Properties – Divisibility Basics
If n is a natural number what is the remainder when (23*35*57*79)^n is divided by 2? Answer: 1 Explanation: 23, 35, 57, 79 are all odd numbers. The product of any number of odd numbers will also be an odd number and an odd number raised to any power will again be an odd number. When an odd number is divided by 2 the remainder is 1. If n is a natural number what is the … [Read more...] about Number Properties – Divisibility Basics
Geometry Circles – Angle in Same Segment
Q,R,S,T are four points on the circumference of a circle. QT is the perpendicular bisector of RS. PQ is a tangent drawn to the circle from an external point P. If angle(SQP) = 20, find angle(TRS). Answer: 70 degrees Explanation: Consider the diagram below. QT is the perpendicular bisector of a chord RS. Hence QT has to pass through the centre of the … [Read more...] about Geometry Circles – Angle in Same Segment
GRE Quant |Probability Maximum & Minimum
A medium difficulty GRE Quant Sample Question in Probability. Ms Li works at an office where the work timing is from 9:00 AM to 6:00 PM. 25% of a year she goes late to office and 35% of a year she leaves early from office. If P is the probability that she works at office the entire day then (a) 0.25 ≤ P ≤ 0.35(b) 0.25 ≤ P ≤ 0.65(c) 0.4 ≤ P ≤ 0.65(d) 0.35 ≤ P ≤ 0.4(e) 0.35 ≤ … [Read more...] about GRE Quant |Probability Maximum & Minimum
Cyclic Quadrilateral Circles
In a cyclic quadrilateral ABCD, the diagonals intersect at E. If AE = 4 and EC = 9, what is the minimum length of diagonal BD? Answer: 12 Explanation We know that when two chords of a circle intersect at a point, AE*EC = BE*ED Hence, BE*ED = 4*9 = 36. Given the product of two quantities their sum is minimum when the two quantities are equal. Hence … [Read more...] about Cyclic Quadrilateral Circles