DS: Is x + y < 1 ?

[Saurav]

Is X + Y < 1 ?

1. X < 8 / 9

2. Y < 1 / 8

[Guest]

Is the answer E

Statement 1 only talks about X so Insufficient
Statement 2 only talks about Y so Insufficient

Both taken together: X<8/9 ( 0.888~0.89)

Y < 1/8 ( 0.125)

Take the extreme case of example. Let X=0.88 and Y =0.124 ( both satisfy the condition but the sum is greater than 1 ) and take any lower value of x and y the sum is less than 1 . So E is the correct answer.

[Saurav]

I was thinking on the following lines.

if A > B and C > D then A + C > B + D.

hence conditions 1 and 1 together give us X + Y < 8/9 + 1/8 which is sufficient to answer the question. Hence Statement 1 and 2 together.

[scrooge]

1) does not suffice since y is not known
2) does no suffice since x is unknown

1) and 2) say x+y <73/72 => x=Y<1 or >1 hence does not suffice !!!
IMO E

[RonPurewal]

I was thinking on the following lines.

if A > B and C > D then A + C > B + D.

hence conditions 1 and 1 together give us X + Y < 8/9 + 1/8 which is sufficient to answer the question. Hence Statement 1 and 2 together.

you're right up to the point where you declare that the inequality x + y < 8/9 + 1/8 is sufficient to answer the question. no, it isn't.

big takeaway:
an INEQUALITY for a quantity DOES NOT GUARANTEE SUFFICIENCY in finding that quantity.[/b]
this stands in contrast to actually finding the quantity, i.e., with an equals sign, as in "x + y = 2/3". that sort of thing represents a single value for the quantity, so it's inevitable that it will yield either a "yes" or a "no" to whatever question is in the prompt.
by contrast, an inequality is NOT a single value; it represents an infinitude of values, unless there are other restrictions hemming those values in. because the inequality represents multiple values, it can still be insufficient.

analogy:
is laura at least 21 years old?
(1) laura is at least 18 years old.
it should be easy to see that statement (1) is sufficient, even though it gives you an inequality L > 18; laura could be, say, 19 years old ("no") or 50 years old ("yes").

same deal here:
8/9 + 1/8 = 73/72, which is greater than 1.
therefore, knowing that x + y < 73/72 is insufficient to address the issue of whether x + y < 1, because x + y could be, say, 1/2 ("yes") or any value between 1 and 73/72 ("no").

therefore, (e).

note that it's unnecessary to actually find values between 1 and 73/72. since 73/72 is greater than 1, it's good enough merely to realize that such intermediate values exist.

--

postscript:
you also can't swing all the way in the other direction. i.e., you can't assume that an inequality is always insufficient, either.
for instance, if i told you x + y < 71/72, then this is sufficient to determine that x + y < 1 (because 71/72 is less than 1). similarly, if you know that laura is over 25 years old, then you know that she is over 21 (because 25 is greater than 21).

so:
takeaway:
you have to WORK OUT INEQUALITIES to figure out whether they're sufficient. do not take shortcuts with inequalities as you would with equations.