Advanced gre math practice12/31/2023 The first 10 perfect squares go from 1 to 100. Remember that cross-multiplying is a perfectly legitimate move in GRE QCs, as long as all the concerned numbers are positive.Ĥ) Think about the numbers in K. We can express both denominators in that factored form, and multiply both quantities by 25. Any positive is greater than any negative.ģ) These numbers are probably a little bit bigger than what you would be likely to see on the GRE, but notice that even for this, we don’t need a calculator! Notice that both denominators are multiples of 25.Īnd, of course, 525 is just one more factor of 25, so Meanwhile, we are adding two positive things in Quantity B, so that must be positive. That has to be negative! Quantity A is negative. (something less than 1/2) minus (something greater than 1/2) It would be a nightmare to try to perform this exact calculation. It’s much easier to find common denominators if one denominator is a multiple of the other, so group the fractions together accordingly.Ģ) For this one, do NOT find common denominators. Notice that 6 is a multiple of 3 and 14 is a multiple of 7. Notice how the problem is framed in the solution, and notice what important observations were used to simplify it.ġ) This one isn’t too hard, but it can be simplified. You should understand factors, multiples, prime factorizations, and remainders.įor difficult problems, as some of these are, it’s very important to read the solutions carefully. You should know what is what isn’t a prime number, as well as everything it means to be a prime number. With integer properties, there are a number of important distinctions that could come into play. With fractions, think about simplifying comparisons: for example, bigger numerator makes the fraction bigger, but bigger denominator makes the fraction smaller. The real issue is finding the way to look at the problem, the way to interpret it or reframe it, so that the pertinent comparison becomes much easier to see. It may appear to demand a long tedious calculation, but don’t be fooled: that is not the real issue. As a general rule, a GRE QC question is designed for a quite straightforward comparison or simplification. Your job on the GRE QCs is to compare, not to calculate. Nowhere is this truer than it is on the Quantitative Comparisons. It is interested in the test taker’s ability to re-frame the question in a way that leads to significant simplification. The GRE doesn’t care about long calculations, but it does care about your ability to use logic and number sense to simplify calculations. In fact, if you find yourself getting sucked into a long detailed calculation anywhere on the GRE Quant section, you are probably doing something the hard way. It’s important to remember that the GRE is not particularly interested in your ability to perform long detailed calculations. Integer properties and fractions on the GRE QC When N is divided by 7, the quotient is Q 2 and the remainder is R 2, and Q 2 > 5Q 1.ĩ) The number N is any non-negative integer, and When N is divided by 35, the quotient is Q 1 and the remainder is R 1. 8) N is a large integer, not divisible by 7.
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