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Aaron G.
Yale Grad (SAT 1600), Six Years of Experience, SAT/ACT/GRE/Subject Tutoring
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SAT
TutorMe
Question:

What is the ones digit of 347^105? a) 1 b) 3 c) 5 d) 7 e) 9

Aaron G.
Answer:

The correct answer is (d), or 7. When you get a problem like this -- where the number is so big your calculator can't display it properly -- you'll need to find a pattern to how the number changes when you take different powers of it. For example, 47^1 = 47, which has a ones digit of 7. 47^2 = 2209, which has a ones digit of 9. 347^3 has a ones digit of 3. 347^4 has a ones digit of 1, and 47^5 has a ones digit of 7. If you take the next few powers, you'll see the pattern repeat itself. This means that every fourth power of 47 has a ones digit of 1. So 47^104 has a ones digit of 1. That means that 47^105 must have a ones digit of 7 -- the next digit in the pattern we found before. If you didn't have enough time to work out the answer, you could still make a good guess by getting rid of (c) before you guessed. Remember -- the only numbers with a ones digit of 5 are multiples of 5, and since 47 isn't a multiple of 5, none of its powers will be either.

GRE
TutorMe
Question:

If 65 percent of the people who check out a certain library book are Spanish majors, what is the ratio of the number of Spanish majors who check out the book to non-Spanish majors who check out the book? a) 6 to 3 b) 13 to 5 c) 13 to 7 d) 26 to 10 e) 65 to 35

Aaron G.
Answer:

The answer is (c), or 13 to 7. An easy way to answer questions like this is to assume that a certain number of people checked out the book, and see how many were Spanish majors. For example, we could assume that 100 people checked it out -- 100 is an easy number to use with percentages. That would mean 65 Spanish majors checked it out, and 100-65 = 35 non-Spanish majors checked it out. So you know that, if 65 Spanish majors were to check out the book, 35 non-Spanish majors would check it out. The ratio of 65 to 35 simplifies to a ratio of 13 to 7. (You'll get the same ratio for any number you start with, not just 100, since ratios are consistent for any starting value.)

ACT
TutorMe
Question:

If triangle ABC has one side (A) of length 8, and one side (B) of length 10, which of the following could NOT be the length of side C? a) 4 b) 8 c) 10 d) 18

Aaron G.
Answer:

The answer is (d), or 18. Any two sides of a triangle must be longer, combined, than the third side of that triangle. (Try to draw a triangle where this isn't true, and you'll quickly see why!) Since side C can't be as long as sides A and B combined, it must be less than 8+10, or less than 18.

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