ISEE Lower Level – Example Problems and Solutions

Here are a couple examples of problems you might see on the Lower Level ISEE along with their solutions.


(A) miniature
(B) poor
(C) tough
(D) ambitious

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

If a student knows the definition of impoverished, then the problem is fairly simple. Impoverished means poor, which is answer choice (B). However, if the student does not know the definition, then the problem becomes much more difficult. We can see that the word impoverished contains “pover,” which looks a lot like the word “poverty.” Lo and behold — both words stem 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 even pauper, possibly) can help in figuring out the meaning of the word “impoverished.” “Im-” is a prefix that means the same thing as “in-“, which means “in.” Therefore, “impoverished” can be thought of as “in the state of poverty.”


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

This question is a rephrased division problem and can be translated into, “what is the remainder when Emily divides $7 into $100?” How do we know this? The keyword 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 what number we multiply $7.00 by in order to get to $100.00. In other words,

$7.00 times what number of books equals $100.00?
7x = 100 (x is a variable representing the number of books)

In order to solve this algebra 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 left after she buys the books.

Source by Andrew Thatcher

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