The GRE’s not a math test – it’s a foreign language test!

by Céilidh Erickson Sep 16, 2015

Imagine that you asked a friend of yours what she got on the Quant section of the GRE. Instead of answering you directly, she said “let’s just say that 4 times my score is a multiple of 44, and 3 times my score is a multiple of 45.”

Could you tell what score she got? If not… you may need to work on your GRE translation skills! Most people expect math on the GRE to be like math in high school, when memorizing formulas and applying them correctly – rigorous memorization and meticulous application – was all you needed to get an A. That’s not nearly enough on the GRE, though!

Because the math content of GRE is relatively simple (middle school and basic high school math), the only way to make the test challenging is to make the structure complex. Test writers encode simple concepts in complicated language. Instead of saying “n is odd,” for example, they’ll say “the remainder when n is divided by 2 is 1.” That way, we have to do the extra work of translating: if a number has a remainder when divided by 2, it can’t be even. It must be odd!

To move through the test quickly and efficiently without getting stuck, you’ll need to quickly decode complex GRE language to find the simple underlying concept.

See if you can translate these coded messages:

1. the remainder when x is divided by 10 is 3.
2. p = n³ – n, where n is an integer
3. integer y has an odd number of distinct factors
4. |b| = –b
5. the positive integer q does not have a factor r such that 1<r<q
6. n = 2k + 1, where k is a positive integer
7. a²b³c⁴ > 0
8. x and y are integers, and y^x < 0
9. what is the greatest integer n for which 2ⁿ is a factor of 96?

When you come across this kind of coded language, ask yourself, “what is the underlying concept here? What are the clues?” Then, create flashcards – coded message on the front, translation and explanation on the back.

Then, push yourself further: try to think of different iterations of the same idea (e.g. a/b > 0, or pqr < 0) and make flashcards for those. Here are the translated versions of the codes above (but make sure you try to translate them yourself before you look at these answers!):

1. The units digit of x is 3 (the remainder when divided by 10 is always the same as the units digit).
2. pis the product of 3 consecutive integers. Factor out n first: n(n² – 1). Then, factor the difference of squares: n(n + 1)(n – 1). A number × one greater × one smaller = the product of 3 consecutives.
3. y is a perfect square (like 9, whose factors are 1, 3, & 9). Any non-square integer will have an even number of distinct factors (e.g. 5: 1 & 5, or 18: 1, 2, 3, 6, 9, & 18).
4. b must be negative or 0. If the absolute value of b (the distance from 0) is equal to –b, then –b cannot be negative; it must be positive or 0. If –b = 0, then b = 0 as well. If –b is positive, then b itself must be negative.
5. q must be prime. If q were a non-prime integer, it would have at least one factor between 1 and itself.
6. n is odd. 2k must be even (regardless of what k is), so adding 1 to an even will give us an odd.
7. b must be positive. The even exponents hide the sign of a and c, but a² and c⁴ must be positive, so b³ – and therefore b – must be positive.
8. y must be negative, because only a negative base would yield a negative term. And x must be odd, because an even exponent would make the term positive.
9. How many factors of 2 are there in 96? If we break 96 down, we get a prime factorization of 2×2×2×2×2×3, so 2⁵ will be a factor of 96, but 2⁶ won’t.

A lot of the coded language on the GRE comes from Number Properties concepts (perhaps because “even & odds” and “positives & negatives” seem elementary until we disguise them). You probably already know the basic rules: even + odd = odd, even × odd = even, etc. Don’t just make flashcards for the basic rules – look for the coded language, and be ready to translate.

By the way, that student that I mentioned at the beginning…were you able to figure out her score?

4 times my score is a multiple of 44 – translation: the score is a multiple of 11.

3 times my score is a multiple of 45 – translation: the score is a multiple of 15, and therefore 5 and 3.

A multiple of 11, 3, and 5? It must be a 165.

A score like that takes serious translation skills!