GMAT PREP QUESTION

Question

Is X + Y < 1 ?

1. X < 8 / 9

2. Y < 1 / 8

I picked C, but the answer is E

If you give both numbers a common denominator, you get

1) X< 64/72
2) Y< 9/72

Obviously, each statement alone is insufficient. But I'm confused why together they don't work. Since X must be less than 64/72, the largest it can be is 63/72. And since Y is less than 9/72, the largest it can be is 8/72. Together, their maximum values add up to 71/72, which is less than 1. Why can't you definitively say that X + Y < 1?

jayjk78 · Answer

8/9 = 0.8888 lets round it (remember 1/9 = 0.111) 1/8= 0.125 without rounding it to two decimals there is still scope for it to equal to 1 or below. hence both statement are not suff.

logitech · Answer

Stockmoose16 wrote:Is X + Y < 1 ?

1. X < 8 / 9

2. Y < 1 / 8

I picked C, but the answer is E

If you give both numbers a common denominator, you get

1) X< 64/72
2) Y< 9/72

Obviously, each statement alone is insufficient. But I'm confused why together they don't work. Since X must be less than 64/72, the largest it can be is 63/72. And since Y is less than 9/72, the largest it can be is 8/72. Together, their maximum values add up to 71/72, which is less than 1. Why can't you definitively say that X + Y < 1?

BE VERY CAREFUL!

x<1
y<2

means, x+y<3

Think them together!

so

X < 8 / 9
Y < 1 / 8

X+Y < 73/72

Hence, E

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

cramya · Answer

Stockmoose,
I think since the inequalities face the same direction u can add like u said before in one of ur posts

x+y < 73/72 like Logitech said and we dont know if its between 1.0 and 1.01 which would make it > 1 ot rit could be <1 we dont know

INSUFF since we cant come to a definite yes or no

hence E

scoobydooby · Answer

But I'm confused why together they don't work. Since X must be less than 64/72, the largest it can be is 63/72. And since Y is less than 9/72, the largest it can be is 8/72. Together, their maximum values add up to 71/72, which is less than 1. Why can't you definitively say that X + Y < 1?[/quote]

x could well be 63.5/72 and y could be 8.5/72, and if you add you can get 72/72=1 so x+y not neccessary less than 1

lilu · Answer

I'd like to pull this thread up and see if any of the experts can comment on this problem.

I have the same confusion as scoobydooby has because I think that the problem states that values need to be LESS than 8/9 and 1/8 and if we take the closest values (but less) to these, we get a value less than 1.....
Shouldn't C be the answer?

Ian Stewart · Answer

lilu wrote:I'd like to pull this thread up and see if any of the experts can comment on this problem.

I have the same confusion as scoobydooby has because I think that the problem states that values need to be LESS than 8/9 and 1/8 and if we take the closest values (but less) to these, we get a value less than 1.....
Shouldn't C be the answer?

No, the answer is E. Using both statements, we know that

X < 8 / 9
Y < 1 / 8

It's perfectly fine to add inequalities as long as they face the same way, so we have

X < 64/72
Y < 9/72
X+Y < 73/72

That's all we can conclude from the information given, and X+Y can certainly be somewhere between 1 and 73/72. There's no reason why X can't be just slightly less than 64/72 here - X could be 63.9/72 = 639/720, for example. Y could also be just slightly less than 9/72; Y could be 8.9/72 = 89/720. Then X+Y = 639/720 + 89/720 = 728/720, which is greater than 1.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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