Demons

Question 1

Finding the number of integers that a number is divisible by

Answer 1

Prime factorize the number, take each exponential power add one to it and then multiply these numbers we often confuse this process with the number of distinct factors so be careful!

Question 2

Cyclicity problem, exponents

Answer 2

Always check that exponent are positive integers by constrains else they could ruin a multiple of four i.e 4x0.5=2 i.e we would be looking for a remainder of 2 instead of 0.

Similarly for terminating decimals if we are given X/3^ax5 don’t conclude that because there is a 3 in the denominator the decimal will not terminate i.e the X in the numerator could always cancel 3 etc making it terminate or 3 could be raised to -1 i.e (a = -1)making it terminate.

Question 3

Leading zeros

Answer 3

don’t blindly assume because a perfect power of 10 falls in the range k-2 will cause ambiguity in Ds problems for example 97

Question 4

caution when using the LCM to compare the size of prime factors of numbers

Answer 4

Both numbers could contain the same prime factors i.e the smallest / largest could exist in both constituent numbers

Question 5

Data sufficiency on Overlapping sets

Answer 5

Remember that the essential square forms the grand total of a double set matrix i.e the sum of - Only A, Only B, Both A and B, neither A nor B.

All elements that don’t like A and B include Only A, Only B, and neither A nor B. i.e they might like one of the components individually hence only exclude only both A and B.