Si agrupo mis lápices de 2 en dos me sobra 1; si lo hago de 3 en 3, también me sobra 1 y si lo hago de 5 en 5 ocurre los mismo.¿Cuántos lápices tengo si son más de 30 y menos de 40?

31 pencils

Step-by-step explanation:

What we must do is reduce the range of responses, the first thing is to limit the numbers to the interval between 30 and 40.

If it is two by two and there is one left, it means that all the pairs are eliminated.

If it is five in five and there is one left over, the ones ending in 5 are also eliminated.

If it is three by three and there is one left over, the 33 and 39 are eliminated.

Taking this into account, the possibilities are reduced to two numbers only, 31 and 37.

37 is discarded because when it is grouped from five to five, there are 2 left over.

So the answer is 31, you have 31 pencils.

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: