In how many rearrangements of the word SCINTILLATING will no two 'I' come together?Explanation:Let us consider the following arrangement without the three I’s._S_C_N_T_L_L_A_T_N_G_No two I’s would come together if the I’s are placed in the blanks. So, the question boils down to first finding out the number of ways in which three blanks can be chosen out of 11 blanks. This can … [Read more...] about GRE Hard Math – Permutation Combination

# GRE Arithmetic Theory & Practice Questions

## GRE Practice: Chess Board Probability

What is the probability that two squares(smallest dimension) selected randomly from a chess board have only one common corner?Explanation:From the diagram you see that considering the top two rows, there are 14 ways of choosing two squares with just one common corner.Like wise rows (2, 3), (3, 4)…….(7, 8) can be considered. Therefore, number of ways = 14 x 7 = … [Read more...] about GRE Practice: Chess Board Probability

## Permutation Combination – chess board

How many squares are there on a chess board?P.S. No, the answer is not 64Explanation:Of course, as you might think, aren’t there only 8 x 8 = 64 squares on a chess board? Well, no. All these 64 squares are squares of 1 block. However, one can notice that there are squares of 4 blocks too i.e., 7 x 7 = 49. Likewise, until the largest square which is the chess board … [Read more...] about Permutation Combination – chess board

## Quantitative Comparison – Number Properties

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

## Number Properties LCM HCF

If the HCF of two natural numbers whose sum is 216 is 12, how many such pairs exist?Answer: 3 pairsExplanation: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