If n is the sum of the integers from -203 to 200, inclusive,

Vincen wrote:If n is the sum of the integers from -203 to 200, inclusive, then n =

A. -606
B. -456
C. -233
D. -3
E. 0

OA is A.

Can I use the Gauss Formula to solve this exercise?

Hi Vincen,

The GMAT is not the test of your mathematical ability; it rather tests your quantitative ability that also involves your mathematical ability. If you sense that a problem involves laboured math, you must change your approach.

This question is far easier than you think. You must look for the pattern of numbers.

It is given that n is the sum of the integers from -203 to 200, inclusive.

So, n = –203 –202 –201 –200 –199 –198 –197 ... 0 ... 197+ 198 + 200

We see that the sum of –200 –199 –198 –197 ... 0 ... 197+ 198 + 200 would be 0. Each positive number has its equivalent negative number.

Thus, n = –203 –202 –201 + 0 = –606.

The correct answer: A

Hope this helps!

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-Jay
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Hi Vincen,

Whenever a GMAT question appears to involve adding or multiplying a large group of numbers together, there is almost certain to be a 'shortcut' in terms of how to get to the solution. In this case, adding up all of the numbers in order cannot possibly be what we're supposed to do here (it would take far too long).

Since we're summing all of the integers from -203 to +200, inclusive, you should notice that ALL of the positive terms get 'cancelled out' by a negative term (for example, +1 and -1 cancel out). The only terms that are not cancelled out are -203, -202 and -201. The sum of those terms is -606.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Vincen wrote: ↑

Fri Sep 08, 2017 3:22 pm

If n is the sum of the integers from -203 to 200, inclusive, then n =

A. -606
B. -456
C. -233
D. -3
E. 0

OA is A.

Can I use the Gauss Formula to solve this exercise?

Solution:

Since sum = average x quantity:

sum = (-203 + 200)/2 x [200 - (-203) + 1]

sum = -3/2 x 404 = -606

Alternate Solution:

First, note that the sum of the integers from -200 to 200, inclusive, is equal to zero because every negative integer has its positive counterpart so, for example, -200 + 200 = 0, and -199 + 199 = 0, etc.

Thus, the only unpaired negative integers are -203, -202, and -201, which sum to -606.

Answer: A

Vincen wrote: ↑

Fri Sep 08, 2017 3:22 pm

If n is the sum of the integers from -203 to 200, inclusive, then n =

A. -606
B. -456
C. -233
D. -3
E. 0

n = (-203) + (-202) + (-201) + (-200) + (-199) + (-198) + . . . . . .+ (-3) + (-2) + (-1) + 0 + 1 + 2 + 3 + . . . . . + 198 + 199 + 200

Notice that, for each RED negative number, we have a BLUE negative number such that the two values add to ZERO (for example, (-33) + 33 = 0)

This leaves us with: n = (-203) + (-202) + (-201) + 0 + 0 + 0 + 0 .......+ 0 + 0
= -606

Answer: A