Rachel discarded exactly 45 percent of pens fhat she owned. which of the following could be the total number of pens that she has left? plz explain a)22 b)24 c)26 d)28

It is nasty and teachers are not above giving this kind of thing on a test. I call this hiding in the corner, because whoever posed the question is trying to be clever. All you can do is try each one of the answers to see which one does not give a fractional answer. I don't think there is any other way to do this. The hint is in the word possible. And Mathmate is right. This is a piece of trickery and skulduggery. Rachel still has 55% of her pens left. So

55/100 * x = 24
0.55 x = 24
x = 46.6 which cannot be the answer. 

55/100 x = 26 This does not look promising
0.55 x = 26
x = 26/0.55
x = 47.3 Not the answer.

28 is done the same way. The division gives 50.9. It's close but not right.

A<<<< answer.

The total number of pens left will be exactlly 1 - 0.45 = 0.55 of some integer. That is, the number remaining must be evenly divisible by .55 = 55/100 = 11/20. In order for that to be true, it must be a multiple of 11.

The correct choice is
  A) 22 . . . . . . . . the only choice that is a multiple of 11


Rachel originally had 22/(11/20) = 40 pens. She discarded 0.45*40 = 18 of them, so had 22 remaining.

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