Question 18547
To make it a little clearer, give them variables.
Jessica=JE
John=JO
Karen=KA
Before making them into equations, give yourself some examples.
For example:
If John had 5 books, Jessica would have 20 books.
If Jessica had 20 books, Karen had 4 books.

Now set up a mathematical equation
{{{4*JO=JE}}}
{{{5*KA=JE}}}
Back to your question.
If Karen had 40 books, what is the least number of books Jessica could have?
Plug 40 in for KA
{{{5*40=JE}}}
{{{200=JE}}}
So, your answer would be (e)200.

SECOND QUESTION
Same method, give variables to the people
Judy=J
Adam=A
Set up a mathematical equation
NOW: {{{J=2A}}}
6 YEARS AGO: {{{J=5A}}}
For this one I would try each answer:
(a)6 years ago, Judy was 4 years old. That means Adam isn't even born yet.
6 years later, Judy was 10 years old, Adam is 6 years old. DOESN'T WORK
(b)6 years ago, Judy was 10 years old. That makes Adam 2 years old.
6 years later, Judy was 16 years old and Adam is 8 years old. WORKS, BUT MUST CONSIDER ALL CHOICES
(c)6 years ago, Judy was 14 years old. That makes Adam 2.8 years old. DOESN'T WORK*
(d)6 years ago, Judy was 18 years old. That makes Adam 3.6 years old. DOESN'T WORK*
(e)6 years ago, Judy was 28 years old.  That makes Adam 5.6 years old. DOESN'T WORK*

Now we can see that (b) is the only one that works. 
Problems above with the * doens't mean that you can't have a decimal for an age. You can, I just wanted to save your time and did the work in my head.
Hope this helps!