y=(1/2)-(1/3)+ (1/6)-(1/10)+(1/12)-(1/14)+(1/16)

Hi amsm25:

This is how i solved it the fastest.

Take all the plus terms and put them together and do the same with the minus terms.
Then we have Sum = 1/2 + 1/6 + 1/12 + 1/16 - (1/3 + 1/10 +1/14).
=(1/2+1/6+1/12) + 1/16 - (1/3+1/10+1/14)
= (6+2+1)/12 + 1/16 - (140 + 42 + 30)/420 (In this step i have taken the product of the denominators as the base denominator for evaluation).
= 9/12 + 1/16 - 212/420
= 3/4 + 1/16 - 0.5 (Note that half of 420 is 210, therefore 212/420 ~=0.5)
= 0.75 +0.06 - 0.5 (3/4 is 0.75 and 1/16 ~=0.06)
= 0.81 - 0.5
= 0.31

If you're good with decimal approximations, it might be fastest to convert from the start:

.5 - .33 + .17 - .1 + .08 - .07 + .06

.5 + .17 + .08 + .06 - .33 - .1 - .07

.81 - .33 - .1 - .07

.81 - .5 = .31

It's possible you could end up with something between .31 and .35, in which case you'd have to go back and check to see if you rounded up or down more.

Bill@VeritasPrep wrote:If you're good with decimal approximations, it might be fastest to convert from the start:

.5 - .33 + .17 - .1 + .08 - .07 + .06

.5 + .17 + .08 + .06 - .33 - .1 - .07

.81 - .33 - .1 - .07

.81 - .5 = .31

It's possible you could end up with something between .31 and .35, in which case you'd have to go back and check to see if you rounded up or down more.

@Bill, IMO, this is the best method for this problem

y=(1/2)-(1/3)+ (1/6)-(1/10)+(1/12)-(1/14)+(1/16)
Which of the following is best approx of Y?
1).1
2).31
3).35
4).4
5).6

the first one 0.5 - 0.33 = 0.18 ==> answer has to be greater than 0.18 .... so either 31 or 35

amsm25 wrote:y=(1/2)-(1/3)+ (1/6)-(1/10)+(1/12)-(1/14)+(1/16)
Which of the following is best approx of Y?
1).1
2).31
3).35
4).4
5).6

Another approach:
The sum of the first 3 terms = 1/2 - 1/3 + 1/6 = 3/6 - 2/6 + 1/6 = 1/3.

After the first 3 terms, since -1/10 represents a greater change than +1/12, and -1/14 represents a greater change than +1/16, the correct answer must be a bit less than 1/3.

The correct answer is B.

GMATGuruNY wrote: Another approach:
The sum of the first 3 terms = 1/2 - 1/3 + 1/6 = 3/6 - 2/6 + 1/6 = 1/3.

After the first 3 terms, since -1/10 represents a greater change than +1/12, and -1/14 represents a greater change than +1/16, the correct answer must be a bit less than 1/3.

The correct answer is B.

@Mitch, it's a good idea