If a equals the sum of the even integers from 2 to 200, inclusive, and

Question

If a equals the sum of the even integers from 2 to 200, inclusive, and b equals the sum of the odd integers from 1 to 199, inclusive, what is the value of a - b?

A. 10
B. 100
C. 190
D. 200
E. 210

Marcab · Accepted Answer

Number of even integers from 2 to 200, inclusive is  (200-2)/2 + 1  or  198/2 + 1  or  100 .
Mean of evenly spaced set that includes all the even numbers from 2 to 200 inclusive is  (200+2)/2  or  101 .
Therefore a=  101*100

Number of odd integers from 1 to 199, inclusive is  (199-1)/2 + 1  or  198/2 +1  or  100 .
Mean of evenly spaced set that includes all the odd numbers from 1 to 199, inclusive is  (199+1)/2  or  100 .
Therefore b= 100*100

hence a-b= (100 * (101-100))  or  100 
+1B

Bunuel · Answer

Similar questions to practice: if-x-is-equal-to-the-sum-of-the-integers-from-30-to-127276.html (MGMAT) if-m-equals-the-sum-of-the-even-integers-from-2-to-128426.html if-x-is-equal-to-the-sum-of-the-even-integers-from-40-to-97544.html Hope it helps.

thorinoakenshield · Answer

PROBLEM:
If a equals the sum of the even integers from 2 to 200, inclusive, and b equals the sum of the odd integers from 1 to 199, inclusive, what is the value of a - b?

A. 10
B. 100
C. 190
D. 200
E. 210

SOLUTION:

Use following formulae for such problems:

Sum of evenly spaced integers = (# of integers)*(mean of integers)

# of integers =   + 1
Mean of integers = (last + first)/2

In above problem:

# of integers =   + 1= 100 and  + 1 = 100
Mean of integers = (200 + 2) = 101 and (199 + 1)/2 = 100

Sum of integers = (101*100) = 10100 and (100*100) = 10000

Thus their difference (a - b) = 100

ANSWER:B

EMPOWERgmatRichC · Answer

Hi All,

When a GMAT Quant question asks you to deal with a big group of numbers, there's almost always a built-in pattern that can help you to avoid a lengthy "math approach."

Here, we're given two groups:

Group A = the sum of all the EVEN integers from 2 to 200, inclusive
Group B = the sum of all the ODD integers from 1 to 199, inclusive

We're asked for the value of A - B

Calculating any of these individual totals would take some work, but notice how the two groups follow a pattern:

(The first term in A) - (The first term in B) = 2 - 1 = 1

(The second term in A) - (The second term in B) = 4 - 3 = 1

This pattern will continue as you compare each successive term in each group

Since we're dealing with just the even numbers in Group A, 200/2 = 100 total terms.
This means that we'll have 100 differences of "1"
The Total difference will be 100(1) = 100

Final Answer:  B

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

Temurkhon · Answer

A: 2,4,6,8,10,12,14

B: 1,3,5,7, 9, 11,13

see that every number in A is exactly 1 more than such number in B.

difference is exactly the number of term in A and B and it is 100

B

mvictor · Answer

if we have 100 even and 100 odd then the difference between the sum of even ones and odds one will be 100.
logically thinking, each even number will be 1 more than preceded odd number. since we have 100 even numbers, then the difference is 100.

stonecold · Answer

Here is my solution to this one =>
a= 100/1  = 50*202
b= 100/2 =50*200

Hence a-b= 50  = 50*2 = 100

Hence B

If a equals the sum of the even integers from 2 to 200, inclusive, and

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If a equals the sum of the even integers from 2 to 200, inclusive, and

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards