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# Is x+y < 1 1) x < 8/9 2) y < 1/8 Need a fast way to

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Retired Moderator
Joined: 18 Jul 2008
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Is x+y < 1 1) x < 8/9 2) y < 1/8 Need a fast way to [#permalink]

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01 Dec 2008, 19:50
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Is x+y < 1

1) x < 8/9

2) y < 1/8

Need a fast way to solve this.

Kudos [?]: 294 [0], given: 5

CEO
Joined: 17 Nov 2007
Posts: 3584

Kudos [?]: 4576 [1], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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02 Dec 2008, 05:27
1
KUDOS
Expert's post
10-sec method...

1. for negative x,y x+y is always less than 1
2. maximum value for x+y is (1/8+8/9). Is it larger than 1?
3. Think of following idea: 1/2<2/3<3/4<....7/8<8/9<9/10... Therefore, 1/8+8/9 > 1/8+7/8 ---> 1/8+8/9>1 ---> Answer is E.
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Kudos [?]: 4576 [1], given: 360

Retired Moderator
Joined: 18 Jul 2008
Posts: 962

Kudos [?]: 294 [0], given: 5

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02 Dec 2008, 11:34
Isn't C sufficient to solve this? Wouldn't the answer be always less than 1?

We can't use (8/9+1/8) to be the max because a) and b) specifically says that x is less than 8/9, and y is less than 1/8.

What I did was took the next highest number that satisfied X and Y

X = 7/8
Y = 1/9

Add them both and they are less than 1.

What's wrong with my method?

Kudos [?]: 294 [0], given: 5

SVP
Joined: 17 Jun 2008
Posts: 1535

Kudos [?]: 279 [0], given: 0

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02 Dec 2008, 12:29
You can add the two inequalities here (as the two inequalities have the same sign).

Hence, x + y < 8/9 + 1/8

Kudos [?]: 279 [0], given: 0

CEO
Joined: 17 Nov 2007
Posts: 3584

Kudos [?]: 4576 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

### Show Tags

02 Dec 2008, 12:36
Isn't C sufficient to solve this? Wouldn't the answer be always less than 1?

We can't use (8/9+1/8) to be the max because a) and b) specifically says that x is less than 8/9, and y is less than 1/8.

I agree that x+y cannot be equal to (8/9+1/8) but x+y could be equal to (8/9+1/8)-0.00000000000000001
In other words, x+y<(8/9+1/8)

What I did was took the next highest number that satisfied X and Y

X = 7/8
Y = 1/9

Add them both and they are less than 1.

What's wrong with my method?

You took too large step. You also could use a direct method without tricks: (8/9+1/8)=(64+9)/72=73/72>1. So, x+y could be 72.5/72>1
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Kudos [?]: 4576 [0], given: 360

Re: DS   [#permalink] 02 Dec 2008, 12:36
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