quantitative comparison (qc) is a huge part of the gre math, roughly half. often, when prepping, you may forget this and spend much more time on problem solving. quantitative comparison is a unique beast—while the math concepts are the exact same as those covered in problem solving, qc can be very tricky. in fact, the test writers work very hard to make these questions seem very straightforward. yet, there is usually a trap, or a twist, waiting to ensnare the unsuspecting test taker.
the format will always be the same: comparing two quantities (column a vs. column b), with the same 4 answer choices that evaluate the relationship between the 2 quantities. however, the quantities for column a and b can be anything from expressions with variables to references to a quantity in a geometric shape.
| column a | column b |
|---|---|
| the number of positive multiples of 49 less than 2000 | the number of positive multiples of 50 less than or equal to 2000 |
a. the quantity in column a is greater
b. the quantity in column b is greater
c. the two quantities are equal
d. the relationship cannot be determined from the information given
the approach
first off, we must understand what a multiple is. a multiple is any number that results when multiplying an integer, x, by 1, 2, 3, 4…
if x is equal to 5, then the multiples of 5 would be:
5 x 1 = 5
5 x 2 = 10
5 x 3 = 15
5 x 4 = 20
5 x 5 = 25
5 x 6 = 30…
from the table above, we can see that any multiple of 5 is divisible by 5. for instance, 1000/5 = 200. therefore, 1000 is a multiple of 5.
the question above asks us how many multiples of 49 are less than 2000. we can divide 2000 by 49 to see how many multiples of 49 are less than 500. doing so may take awhile. a faster way is to note that 49 is very close to 50. quick math allows us to determine that 50 x 40 is 2000. therefore, 49 x 40 equals 40 less than 2000, or 1960. if we were to multiply 49 x 41, we are adding 1960 + 49, which takes us to 2009. this is greater than 2000. therefore, we know that there are only 40 multiples of 49 less than 2000.
what about column b? well, we’ve already figured out that 40 x 50 equals 2000. but, here is the tricky part. whereas column a stipulated that the number has to be less than 2000, column b says the number has to be less than or equal to 2000. therefore, there are 40 multiples of 50 that are less than or equal to 2000.
answer (c).
first instincts:
there is a good chance that your first instinct was a. clearly, 49 is lower than 50, so it has to have more multiples. usually, when the answer to a quantitative comparison question appears obvious at first glance, there is some twist to the problem. in this case, the twist was the wording in column b: less than or equal to 2000. so, be wary of a qc question that seems too easy. look for a twist or a trap.
more quantitative comparison tips and strategies:
- dealing with variables
- striving for equality
- logic over algebra
- comparing in parts
- estimation with a twist
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