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.
_________________

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.
_________________

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.
_________________

\(x+y < 1\)

(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
_________________

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:

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

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
_________________

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________