 # ISEE Lower Level: Sample Problems and Solutions

Here are a couple of sample problems that you can see in the lower level ISEE along with their solutions.

VERBAL

IMPOVERISHED
(A) miniature
(B) poor
(C) hard
(D) ambitious

This synonym problem asks students to identify which answer choice means more exactly the same as the given word. This type of problem is primarily a vocabulary test.

If a student knows the definition of impoverished, then the problem is quite simple. Impoverished means poor, which is answer choice (B). However, if the student does not know the definition, the problem becomes much more difficult. We can see that the word impoverished contains “pover”, which looks a lot like the word “poverty”. Behold, both words come from the Latin word “pauper”, which means poor (the English word “pauper” means one who is poor). Knowing the definition of the word poverty (or possibly even destitute) can help you decipher the meaning of the word “impoverished.” “Im-” is a prefix that means the same as “in”, which means “in”. Therefore, “impoverished” can be considered as “in a state of poverty”.

MATH

Emily has \$ 100.00. Emily buys as many books as she can for \$ 7.00 each. How much money does Emily have left after buying the books?

This question is a reformulated division problem and can be translated into “what is the remainder when Emily divides \$ 7 by \$ 100?” How do we know this? The key word in this problem is “each”. We know that each book costs \$ 7.00, so if we buy three books, we multiply \$ 7.00 by three to find the total price; If we buy four books, we multiply \$ 7.00 by four to find the total price; etc. Emily has a limit of \$ 100.00, so we need to find the number that we multiply \$ 7.00 by to get to \$ 100.00. In other words,

\$ 7.00 multiplied by the number of books that equals \$ 100.00?
7x = 100 (x is a variable that represents the number of books)

To solve this algebraic equation, we divide both sides by 7 to isolate the variable, and we see that

x = 100/7

When 100 is divided by 7, the quotient is 14 and the remainder is 2. Therefore, Emily will spend \$ 98.00 (\$ 7.00 times 14) and have \$ 2.00 remaining after I buy the books.