N is the smallest number that has 7 factors.Quantity A: Number of factors that sqrt(N) has.Quantity B: Number of factors that N-2 has.Explanation:A number with 7 factors will be of the form a6.N is given to be the smallest such number. Hence N = 26.Quantity A:Sqrt(N) = 23and this has 4 factors.Quantity B:N – 2 = 26 – 2 = 64 – 2 = 62 = 2 * 31 and this has 4 factors.Therefore, … [Read more...] about Quantitative Comparison – Number Properties

# GRE Arithmetic Theory & Practice Questions

## Number Properties LCM HCF

If the HCF of two natural numbers whose sum is 216 is 12, how many such pairs exist? Answer: 3 pairs Explanation: Let the two number be 12a and 12b where a and b are relatively prime. Then 12a + 12b = 216 a + b = 18 Now, this boils down to finding out all possible ways of writing 18 as a sum of two natural numbers co-prime to each … [Read more...] about Number Properties LCM HCF

## Permutation Rearrangement

8 directors, the vice chairman and the chairman are to be seated around a circular table. If the chairman should sit between a director and the vice chairman, in how many ways can they be seated? Answer: 8! * 2 Explanation: Let us consider the vice chairman and the chairman together as one entity. Hence, 8 directors + this entity can be arranged circularly in (9-1)! ways. … [Read more...] about Permutation Rearrangement

## Number Properties – Factorial & Remainders

If p = 1! + (2x2!) + (3x3!) + (4x4!)...... + (10x10!), what is the remainder when p+2 is divided by 11!? Answer: 1 Explanation: p = 1! + (2x2!) + (3x3!) + (4x4!)...... + (10x10!) p = (1x1!) + (2x2!) + (3x3!) + (4x4!)...... + (10x10!) But, (1x1!) = 2! – 1! (2x2!) = 3! – 2! (3x3!) = 4! – 3! And so on. Hence, p = 2! – 1! + 3! – 2! + 4! – 3! + 5! – 4! + 6! – 5! + 7! – 6! … [Read more...] about Number Properties – Factorial & Remainders

## Statistics – Mean, Median, Range

The maximum mark in an examination is 100 and the minimum is 0. The average mark of seven students such that no two of them have scored the same marks is 88. If the median score is 92 and all the marks are integers, what is the maximum possible difference between the largest and the smallest mark obtained by these seven students? Answer: 54 Explanation: Average mark of … [Read more...] about Statistics – Mean, Median, Range