Number theory is rich in problems of an especially —– sort: they are tantalizingly simple to state but —– difficult to solve.
Tip! Know your vocabulary
Sentence completion is a piece of cake if you know your vocabulary. If you don’t, it’s a nightmare. So study that vocabulary! Here are definitions of the tricker words in the problem:
tantalizing – having or exhibiting something that provokes or arouses expectation, interest, or desire, especially that which remains unattainable
cryptic – puzzling
spurious – counterfeit
abstruse – incomprehensible, archaic
ostensibly – apparently
vexing – upsetting, annoying
Tip! Look for key words and dividers!
Remember, there is only going to be one correct answer to a sentence completion problem. The key words and dividers (words such as and/or/but/although or punctuation such as colons, semicolons, and certain commas) will give you the proof you need to support your answer.
In this case, we have a colon, which acts as an equal sign that neatly divides the problem in half. Let’s visualize this problem mathematically:
Number theory is rich in problems of an especially ____ sort = tantalizingly simple to state but ____ difficult to solve
This question involves two blanks, which makes it trickier than average.
Tip! When you’re dealing with two-blank sentences, tackle them one blank at a time. Start with the easier blank and then move on to the harder blank.
In this case, let’s start with the second blank. Once we have figured out the second half of the equal sign (what number theory problems are equal to), it will be a lot easier to know what goes on the other side. We are left with this statement:
tantalizingly simple to state but ______ difficult to solve
Look for the key words and dividers in this sentence. After we bold our key words and italicize our dividers, our sentence looks like this:
tantalizingly simple to state but ______difficult to solve
Since “but” is our divider, we know we are looking for something that is the opposite of “tantalizingly.”
Tip! Before looking at your answer choices, predict the blank in your own words. Then, compare the word you’ve selected to your answer choices.
What is the opposite of tantalizingly? If something is tantalizing, it is intriguing, arousing expectation, interest or desire. In the case of the phrase “tantalizingly simple,” it means that the problems appear intriguingly–even deceptively–simple to solve. Something tantalizing is known for being intriguingly good and desirable. What, then, would be the opposite of something tantalizing? Something that is known for being uninteresting, bad, and undesirable.
Let’s take a look at the second part of each of our answer choices and eliminate anything that does not meet these criteria.
Tip! All it takes is one wrong word to make an entire answer wrong!
We can quickly eliminate choices (B), (C), and (D). Neither “equally,” “ostensibly,” nor “rarely” approximate the qualities of uninteresting, bad, or undesirable. Now we’ve narrowed our choices down to (A) or (E).
To be absolutely certain of the right answer, let’s look at the definitions of deceptively and notoriously to see which better fits the opposite of tantalizingly.
deceptively – perpetually misleading
notoriously – widely and unfavorably known
Now that we have the two definitions, the better fit should be obvious. Although “deceptively” does fit the negative connotations necessary for the opposite of tantalizingly, it does not fit nearly as well as “notoriously.” Something notorious is widely and unfavorably known, while something tantalizing is known for being intriguingly good and desirable. Based on the second blank, choice (E) looks like our best bet.
Just to be 100% certain, let’s make sure that the first part of choice (E) fits with the sentence.
Tip! With two-blank sentences, make sure both answer choices make sense.
Let’s look at the first half of our sentence. Now that we have filled in the second half of the equation, the first half should be much easier. Our mathematical equation now looks like this:
Number theory is rich in problems of an especially ____ sort = tantalizingly simple to state but notoriously difficult to solve.
Tip! Think about whether the blank should express a positive or a negative idea.
In this case, is the first blank expressing a positive or a negative idea? Put yourself in the shoes of someone solving this problem. If you were trying to tackle a problem that was tantalizingly simple to state but notoriously difficult to solve, how would you feel? Probably pretty upset, frustrated and unhappy that, of all the people in the world, you were selected to solve this tricky problem.
Does vexingly, our word from choice (E) fit this meaning? Yes. Vexed means upset or annoyed, exactly the way you would feel if confronted with such a problem. Now that we have ensured that both parts of the answer fit in the blank, we can confidently select choice (E) as our final answer.
Want more practice? Click here for a sample Critical Reading problem and solution!