Is x + y

Question

Is  x + y < 1  ?

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

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

Bunuel · Answer

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.

Answer: E.

fido · Answer

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

Bunuel · Answer

We need to compare some fractions. Easiest ways is to find the least common denominator and proceed.

IanStewart · Answer

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.

ydmuley · Answer

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 Hence, E is the Answer

EMPOWERgmatRichC · Answer

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

Final Answer:  E

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

dcummins · Answer

You can see that the statements are independently insufficient

Combined
Test x = 7/9 and y =2/9 
7/9+ 2/9 = 1 - --> NO

There are plenty of Yes answers to realise that even combined the statements are insufficient

nivivacious · Answer

Individually, its easy to see they're not sufficient.
Combining LCM being 72; we can see x+y<73/72 -> (1)
Question asks if x+y<1
But from (1) we can get either 
a) 72/72 which is 1 or 
b) 72.5/72 which is greater than 1 or 
c) 71/72 which is lesser than 1
We are unable to get a confirmed answer. 
Hence E

bumpbot · Answer

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

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