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

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:

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

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!):

- The units digit of
*x*is 3 (the remainder when divided by 10 is always the same as the units digit). *p*is the product of 3 consecutive integers. Factor out*n*first:*n*(*n*^{2}– 1). Then, factor the difference of squares:*n*(*n*+ 1)(*n*– 1). A number × one greater × one smaller = the product of 3 consecutives.*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).*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.*q*must be prime. If*q*were a non-prime integer, it would have at least one factor between 1 and itself.*n*is odd. 2*k*must be even (regardless of what*k*is), so adding 1 to an even will give us an odd.*b*must be positive. The even exponents hide the sign of*a*and*c*, but*a*^{2}and*c*^{4}must be positive, so*b*^{3}– and therefore*b*– must be positive.*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.- 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 2
^{5}will be a factor of 96, but 2^{6}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!

Hi Céilidh Erickson,

I have given gre twice, the first time I got a score of 304(158 M and 146 V) and I got admit into Washington State University and University of Texas Arlington, I was motivated to give it again since I thought there was a scope of improvement in both math and verbal and I was looking to get funded because I cannot afford the entire fee.

However the second time I was working and studying which gave me barely three to four hours(two in the morning and two in the evening) a day for a period of three months, In my mocks I got a score of 308 on an average and even delayed it by a month to score better. but disappointingly I scored a 302 (157 M and 145 V). I was extremely devastated since I put in a lot of efforts along with work to improve my chances. I cant understand where I went so wrong. I am a native speaker of English but face a lot of trouble in the verbal section especially in the reading.

I even considered giving it again a third time but my counselor and instructor tell me it is not worth it. I want to give it again but i am afraid that I might lose out on another year if I do not succeed. I really want to know where I am going wrong and whether giving it a third time is advisable.

@Irene from my approach, I don’t have any solution in equation manner rather than that, personally I have solved this question with narrative way.

If there are two or more equations about multiple of some number is other number,

Equation :

(1) 4 times GRE equal multiple of 44 and

(2) 3 times GRE equal multiple of 45,

I have to find the solution which is the combination of factor that satisfy both of two equations.

From equation (1) the GRE score have factor of 11 and from (2) GRE score have factor of 15.

So GRE score must have “the greatest common factor” from this two number.

How do we find that? By searching least prime factor from two number which are 11, 3, and 5. Finally the greatest common factor is the product of those prime numbers.

I hope my narrative explaination helps you.

Irene – you’re on the right track. The way to translate “4 times my score is a multiple of 44” into algebra would be 4S = 44n (where n is some integer). Then divide by 4 and you get S = 11n.

You could translate the next statement to 3S = 45m (where m is an integer, but a different integer from n), and then to S = 15m.

We *could* then set 11n = 15m… I’m just not sure how that would help. The question is really “what do we know about S?” Setting these two expressions equal to each other (while mathematically valid) doesn’t really clarify anything about S. The revelations about S came from the step before. If S = 11n, then S must be a multiple of 11; if S = 15m, it must be a multiple of 3 and 5.

There are an infinite number of multiples of 3, 5, and 11. Algebraically, it might look like S = (3)(5)(11)p, or S = 165p (where p is some integer). We need the added constraint that GRE scores must be between 130-170. The only multiple of 165 in that range is 165. So the algebra can’t get us all the way there – we need GRE concepts as well.

With Number Properties, try not to turn everything into an algebraic equation/expression. It’s often easier to think conceptually: “what is this really telling me? What do I already know?”

Did that help?

I get confused with the terms “multiple of”. Is there an algebraic way to write out equations for “4 times my score is a multiple of 44 – translation: the score is a multiple of 11” ?

Would this be, if S is score, 4xS=44 (integer), then S= 11(integer). At this point it looks like you do the same for the second equation to get S= 15(integer). Here, would you set both equations equal since both equal score? If you do, where do you go from there?

If different from above, for “A multiple of 11, 3, and 5? It must be a 165.” is there an equation?

I feel I’ve made a mess of things but I’m not sure where