Taking Advantage of The Question Stem:

by on December 30th, 2011

A key theme on the GMAT is that it rewards you for efficiently and effectively leveraging the assets that each question supplies.

Your job is to manipulate algebraic assets to solve for variables; to leverage geometric assets to fill in the blanks; to determine in Data Sufficiency which assets are sufficient and which are not. And, often, the most overlooked assets of all are waiting for you underneath the question itself.  The answer choices are part of the question.  Consider the question:

What is the sum of the first ten prime numbers?

(A)  129
(B)  130
(C)  138
(D)  142
(E)  156

Note that even though the numbers are relatively small, adding up a set of 10 numbers (after identifying them first) is still time-consuming and offers the potential for error.  To brute-force solve this you would need to correctly identify 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29.  Accidentally skip a prime or include a non-prime and your calculations will lead you astray. And even as you add those…there’s some potential for mistakes as you write down your work.  An easier method?

One of these answer choices is not like the others. 129 is the only odd possibility, and of the prime numbers you’ll find that one is even (2) and the other are necessarily odd.  And because Odd + Odd = Even, each pair of odd numbers will net an even sum.  But the ninth odd number, paired with 2, will net an odd sum. So you’ll have even + even + even + even + odd – and the result will be odd.  A is the only plausible answer.

Or you could use the answer choices in another way, just checking the units digit. 2 + 3 + 5 nets you 10, so a units digit of 0.  Then from the rest: 7 + 1 -> 8.  + 3  -> 1.  + 7 -> 8.  + 9 ->7.  + 3 -> 0.  And the only number left is a 9, so the correct answer must be 9.  Either way, you can save yourself plenty of time and margin-for-error by noting the differences between the answer choices and leveraging that information to streamline your work.  Before you begin calculating on a problem solving problem, make sure to check the answer choices first.  Sometimes they’re traps – but often they’re gifts.

2 comments

  • here 1 even prime+ 9 odd prime= 1 even prime+4 pairs of odd prime+1 odd prime=even+even+odd = odd

     as odd+odd=even

  • 1 even prime  + 1 odd prime + sum of (8 odd prime).
    = the first 2 expressions will give an odd number + the last expression gives you an even number( apply even+odd = odd and odd + odd = even)

    Therefore the 1st choice is correct.

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