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# Is x+y < 1 (1) x < 8/9 (2) y < 1/8

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Intern
Joined: 06 Jan 2012
Posts: 28
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Is x+y < 1 (1) x < 8/9 (2) y < 1/8 [#permalink]

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23 Mar 2012, 13:39
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Question Stats:

61% (00:38) correct 39% (00:32) wrong based on 379 sessions

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Is x+y < 1

(1) x < 8/9
(2) y < 1/8
[Reveal] Spoiler: OA

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Joined: 02 Sep 2009
Posts: 44644
Re: Is x+y < 1 [#permalink]

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23 Mar 2012, 13:44
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dddmba2012 wrote:
Is x+y < 1
1. x < 8/9
2. y < 1/8

Is x+y<1

(1) $$x<\frac{8}{9}=\frac{64}{72}$$. Not sufficient by itself.

(2) $$y<\frac{1}{8}=\frac{9}{72}$$. Not sufficient by itself.

(1)+(2) $$x+y<\frac{64}{72}+\frac{9}{72}=\frac{73}{72}$$, so $$x+y<\frac{73}{72}$$ --> $$x+y$$ may or may not be less than 1 ($$x+y$$ could be less than 1 as well as more than 1, in the range $$(1,\frac{73}{72})$$). Not sufficient.

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Re: Is x+y < 1 (1) x < 8/9 (2) y < 1/8 [#permalink]

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24 Sep 2013, 07:05
Dear Bunuel,
Although i understand the solution after reading it,can you please help me in understanding the line of thinking.I never thought of multiplying the bases by a common factor.What concept's understanding would prompt me to ?

Thank you
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Joined: 02 Sep 2009
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Re: Is x+y < 1 (1) x < 8/9 (2) y < 1/8 [#permalink]

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24 Sep 2013, 07:32
fido wrote:
Dear Bunuel,
Although i understand the solution after reading it,can you please help me in understanding the line of thinking.I never thought of multiplying the bases by a common factor.What concept's understanding would prompt me to ?

Thank you

We need to compare some fractions. Easiest ways is to find the least common denominator and proceed.
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Is x+y < 1 (1) x < 8/9 (2) y < 1/8 [#permalink]

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24 Sep 2013, 10:19
Is x+y < 1?
a) x < 8/9
b) y < 1/8

The answer to this question is E. By adding the inequalities, we find that x + y < 8/9 + 1/8 = 73/72, but it remains possible that x+y is somewhere between 1 and 73/72. It may be easier to see this using decimals, rather than fractions. Recall that 8/9 = 0.8888...., and that 1/8 = 0.125. Using both statements, we might have that x = 0.88, and that y = 0.121, so x+y can be equal to 1.01, and therefore can be greater than 1.
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Re: Is x+y < 1 (1) x < 8/9 (2) y < 1/8 [#permalink]

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25 Jan 2017, 09:59
dddmba2012 wrote:
Is x+y < 1

(1) x < 8/9
(2) y < 1/8

Each statement alone doesn't convey anything.
If you combine the statements, then you get x+y < 73/72. x and y can have any value which is less than 8/9 and 1/8. Eg: x:8/9.001 y: 1/8.01
Hence E.
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Re: Is x+y < 1 (1) x < 8/9 (2) y < 1/8 [#permalink]

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05 Mar 2017, 08:21
Again, failed to think 73/72 may be taken as 1 or more than 1 as well !!
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Is x+y < 1 (1) x < 8/9 (2) y < 1/8 [#permalink]

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25 Jun 2017, 11:45
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$$x+y < 1$$

(1) $$x < \frac{8}{9}$$

As we don't know the value of y, this equation is not sufficient =====> (1) NOT SUFFICIENT

(2) $$y < \frac{1}{8}$$

As we don't know the value of x, this equation is not sufficient =====> (2) NOT SUFFICIENT

Combining (1) & (2)

Lets solve x first

$$x < \frac{8}{9}$$

$$x < 8 * 0.11$$

$$x < 0.88$$

Lets solve for y

$$y < \frac{1}{8}$$

$$x < 0.125$$

Adding $$x + y = 0.88 + 0.125$$

We get $$x+y = 1.005$$

As the value of $$x + y$$ can take the highest value as $$1.004$$ans any value lower than that which is $$< 1$$

We can say that x can be > 1 or x can be < 1

Hence, =====> Both (1) & (2) NOT SUFFICIENT

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Re: Is x+y < 1 (1) x < 8/9 (2) y < 1/8 [#permalink]

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20 Dec 2017, 17:19
Hi All,

When dealing with fractions in GMAT Quant questions, it's sometimes helpful to convert from fraction-to-decimal (doing so might make the requisite math faster or easier).

We're asked if (X+Y) is less than 1. This is a YES/NO question.

1) X < 8/9

This FACT tells us that X is LESS than .88888...., but we don't know anything about Y.
Fact 1 is INSUFFICIENT

2) Y < 1/8

This FACT tells us that Y is LESS than .125, but we don't know anything about X.
Fact 2 is INSUFFICIENT

Combined, we know that (X+Y) must be LESS than .8888.... + .125 = 1.01388888....

IF... the sum = 1, then the answer to the question is NO.
IF... the sum = 0, then the answer to the question is YES.

Combined, INSUFFICIENT

[Reveal] Spoiler:
E

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Re: Is x+y < 1 (1) x < 8/9 (2) y < 1/8   [#permalink] 20 Dec 2017, 17:19
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