# EXPLAINED: How to nail 5 incredibly challenging SAT questions

Business Insider asked Shaan Patel, the founder of SAT prep company 2400 Expert, to identify some of the hardest SAT questions he has ever come across, and then provide the tips and tricks he advises to solve them.

Here’s what he came up with.

Question 1: If x5k = a and x2k2 = b, what is the value of x3 ?

(A) a/b

(B) ak/b

(C) a2k2/b

(D) a – b

(E) a2 – b2

For those of us who are algebraically challenged, this question can be tough. So I’ll show you how to solve this problem using no algebra at all! We’ll use a strategy called Plugging in Numbers or PIN.

To start, plug in a couple simple numbers for x and k. Let’s make x = 2 and k = 3.

x5k is now 25(3). So a = 96.

x2k2 is now 2232. So b = 36.

x3 is now 23 or 8.

Now, just plug in a = 96 and b = 36 into the answer choices, and see which one yields 8. Only answer choice B works (96*3/36 = 8)!

This strategy works well because it allows us to work with tangible numbers rather than abstract variables.

Question 2: What is the units (or ones) digit of 72515?

(A) 2

(B) 3

(C) 5

(D) 6

(E) 9

To solve this problem, let’s use a strategy called Simplify Impractical Problems. When faced with a problem that seems impossible to solve (even with a calculator), create a simpler version of the problem and try to find a pattern. Let’s start by simply listing out powers of 7.

71 = 7

72= 49

73= 343

74= 2,401

75= 16,807

76= 11,649

Do you notice anything about the units digits of the above numbers? They repeat the pattern 7, 9, 3, and 1. Therefore, every 4 numbers the pattern repeats. So how many times will the pattern repeat in 72515?

Well, 2515 divided by 4 gives us 628.75. This means that the pattern would repeat 628 times with 3 left over. Essentially, the units digit of 72515 will be the 3rd number in the pattern — or 3.

Question 3: Select the underlined word or phrase that needs to be changed to make the sentence correct.

At the press conference, the baseball player attributed his home runs, making sure to avoid  questions of athletic

A B C

enhancement drug usage, as hard work and training. No error

D E

This is one of the toughest types of grammar issues to spot on the SAT: idiom errors. An idiom is a phrase that commonly goes together in the English language. In this question, the idiomatically incorrect phrase is “attributed…as.” To correct this, the sentence should read “attributed…to”.

Question 4: Read choices (A) through (E), replacing the underlined part with each answer choice to determine which revision results in a sentence that is clear and precise and meets the requirements of standard written English.

The main purpose of the research experiment by Professor Balkin in the organic chemistry department is to discover more efficient energy sources and to develop cost-effective production methods

(A) The main purpose of the research experiment by Professor Balkin in the organic chemistry department is

(B) The main purposes of the research experiment by Professor Balkin in the organic chemistry department is

(C) The main purpose of the research experiment by Professor Balkin in the organic chemistry department is that they will be able

(D) The main purposes of the research experiment by Professor Balkin in the organic chemistry department are

(E) The main purpose of the research experiment by Professor Balkin in the organic chemistry department are

To solve this problem, it’s helpful to use the strategy Ignore Prepositional Phrases. Prepositional phrases typically do not contain errors and are often only there to distract you. So if we cross out the prepositional phrases “of the research experiment,” “by Professor Balkin,” and “in the organic chemistry department,” the simplified sentence would read:

“The main purpose is to discover more efficient energy sources and to develop cost-effective production methods”

By ignoring the prepositional phrases, it’s now more clear that there are actually two purposes: “to discover…” and “to develop…” To fix this singular-plural issue, we need an answer that states “purposes are.” Only answer choice D works!

Question 5: Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole.

Although he was ——- and even childish when he first began working on board the fishing vessel, the youth quickly gained experience and maturity as the months went by.

(A) Garrulous

(B) Precarious

(C) Precocious

(D) Disturbed

(E) Callow

For hard sentence completions, there isn’t much of a strategy — you have to know the definitions of the words. In this case, callow means inexperienced or immature, which works perfectly in the blank. Most companies give you a huge list of SAT vocabulary words to memorise, but don’t give you a strategy for to memorise them. At 2400 Expert, we teach our students to memorise vocabulary words using the 7-times method. This means to repeat the synonym of a particular vocabulary word 7 times. Do this for the 10-15 vocabulary you plan to memorise for that day. Quiz yourself at the end and repeat any words you forget 7 times again.

This is the memorization method I used in high school after my science teacher told of us a study found that people remember something after they see it 7 times. I’m not sure if this is true, but the 7-times method has worked thousands of our students (including me). Luckily, the New SAT coming out in March 2016 will not have obscure vocabulary!