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

[amsm25]

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

AO- 2).31

[eagleeye]

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

[Bill@VeritasPrep]

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.

[mathbyvemuri]

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

[Aanderson]

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

[GMATGuruNY]

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.

[mathbyvemuri]

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