integers

[parulmahajan89]

if a equals sum of even integers from 2-20 inclusive and b is sum of odd integers from 1-19,inclusive. What is value of a-b?

1) 1
2) 10
3) 19
4) 20
5) 21

[theCodeToGMAT]

To find: a - b

a = 2 + 4 + 6 ... + 20

Sum of First Even numbers = (n)(n+1) = (10)(11) = 110

b = 1 + 3 + ... 19

Sum of first Odd Numbers = (n)^2 = (10)^2 = 100

Difference = 110 - 100 = 10

[spoiler]{B}[/spoiler]

[[email protected]]

Hi parulmahajan89,

Sequence questions are often based on a pattern. If you can spot the pattern, then you can avoid a lot of heavy calculations and deduce the correct answer in a much faster way.

Here, if we compare the first term of A and the first term of B, we have...

2-1 = 1

Next, let's compare the second term of A and second term of B...

4-3 = 1

This pattern will continue all the way up to the 10th term of A and tenth term of B...

20-19 = 1

We have 10 of these identical results: 10(1) = 10

Final Answers: B

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

[Brent@GMATPrepNow]

if a equals sum of even integers from 2-20 inclusive and b is sum of odd integers from 1-19 inclusive. What is value of a-b?

1) 1
2) 10
3) 19
4) 20
5) 21

First notice that the two sums include of all 20 integers from 1 to 20 inclusive.
HALF of those integers are in sum a, and HALF are in sum b.
So, each sum (sum a and sum b) consists of 10 integers.

Notice:
sum a = 2 + 4 + 6 + ... + 18 + 20
sum b = 1 + 3 + 5 + ... + 17 + 19

So, (sum a) - (sum b) = (2 + 4 + 6 + ... + 18 + 20) - (1 + 3 + 5 + ... + 17 + 19)
= (2 - 1) + (4 - 3) + (6 - 5) + ... + (18 - 17) + (20 - 19) [perform the subtraction in PARTS]
= 1 + 1 + 1 + ... + 1 + 1
How many 1's are there? There are 10 of them.

So, we get a final sum of 10
Answer: B

Cheers,
Brent

[GMATGuruNY]

if a equals sum of even integers from 2-20 inclusive and b is sum of odd integers from 1-19,inclusive. What is value of a-b?

1) 1
2) 10
3) 19
4) 20
5) 21

Alternate approach:

For any set of evenly spaced integers:
average = median = (biggest + smallest)/2.
sum = (number)(average).

a = the sum of the EVEN integers between 1 and 20, inclusive:
number of integers = 10.
average = median = (biggest + smallest)/2 = (20+2)/2 = 11.
sum = (number)(average) = 10*11 = 110.

b = the sum of the ODD integers between 1 and 20, inclusive:
number of integers = 10.
average = median = (biggest + smallest)/2 = (19+1)/2 = 10.
sum = (number)(average) = 10*10 = 100.

Thus:
a-b = 110-100 = 10.

The correct answer is B.