If a + b=ab and a, b are natural numbers then how many pairs of (a, b) are there? Answer: 1 pair – (2, 2) Explanation a + b = ab ab – a – b = 0 ab – a – b + 1 = 1 (a – 1)(b – 1) = 1 Now, for this to be true, given that a and b are natural numbers a – 1 = b – 1 = 1. i.e., 1 x 1 = 1 Therefore, a = 2 and b = 2. … [Read more...] about Numerical entry – Number Properties
GRE Quant Practice Questions
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
Rates – Time, Speed and Race
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
Numeric Entry – Probability, Number Properties
A four-digit number is to be formed with the digits {0, 1, 2, 3, 4, 5} without repetition. What is the probability that this number will leave a remainder 2 when divided by 9? Answer: 0.14 Explanation Required probability = (number of four digit numbers that leave a remainder 2 when divided by 9) / (total number of four digit numbers that can be formed) If a … [Read more...] about Numeric Entry – Probability, Number Properties
Quantitative Comparison – Coordinate Geometry
Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices:(A) Quantity A is greater.(B) Quantity B is greater.(C) The two quantities are equal.(D) The relationship cannot be determined from the information given.A circle with radius 5 and passing through the … [Read more...] about Quantitative Comparison – Coordinate Geometry