Data Sufficiency

If x^2 + 5y = 49, is y an integer

1. 1 < x < 4
2. x^2 is an integer

vip wrote:

Stmt(1): x=2, y=9
x=4, y=33/5 so INSUF

Stmt(2) Same, plug in the same numbers so insuf

Combing the two still doesn't make difference

E

vip, can you please explain why both statements together do not suffice

This is what I think

x^2 is an integer and 1<x<4 so x^2 will be either 4 or 9. And in both cases y will be integer.

Hi Kajcha,
if we combine both then

x^2 is an integer and 1<x<4 so x^2 will be either 4 or 9 an integer
so we can be certain x is an integer.

now if x =3 then x^2 =9 now 49-9 = 40 so y can be 8

now suppose x is 2 then x ^ 2 =4, now y can be 9 as 5*9 =45

so 4 + 45 =49

but now think of y as 8.000000005

now if we multiply 3 ^ 2 + 5 * 8.000000005

will give us 49.000000..

now in any convention in the world (incl GMAT) we would write this as 49

so INSUFF

the idea here is unless mentioned in a Q we cannot assume that a value is an integer.

so ans should be E, Is it correct ?

samir, I totally understand your point and the answer is indeed E. However, to me its look like you are contradicting yourself.

On one hand, I completely agree with you on this, you are saying we should not assume a value is integer unless it is mentioned in the question

on the other hand you are writing a value of 49.000000025 as 49. This is something very hard for me to digest. For this question if we don't assume 49.00000.. as 49 x^2 will not be integer and this contradicts the question.

Hi Kajcha,
I totally agree with you, but as I mentioned the decimal value is actually associated with "y" and not "x"

so we can write it like this for e.g. when x =3 as

3 ^ 2 + 5 * 8.000000005 = 49 .00....

here 3 ^ 2 will always be 9 so x in integer there is no doubt in that. but the 5X8.00... value will actually have the decimal associated with it leading to 49.00000.... so x does't contribute the decimal, neither is it required to be a decimal if we consider the eqaution vice versa, as you mentioned coz there are two operands here x^2 & 5y so if y is decimal & x^2 an integer still the result would be an decimal.

Kajcha here I would like to ask u a question, have u seen problems on the GMAT where the actual results come out like 3.897 but the answer choices have 4 for you to answer, I have come across such questions many times.

so basically if our actual ans is 3.897, this could have been for some reasons like for e.g one of the operands in the equation/formula that gave us this value would have decimal, but the ACTUAL answer choice is 4 so this does not mean that the value is now an integer. It will remain a decimal because it gave a solution 3.897 and 4, same logic applies here. i.e y is a decimal it gave a value of decimal value of 40.00000.. which was then added to the sqaure of integer x i.e 3 ^2 i.e 9, which ultimately gave us the ans 49.0000000...

So IMO such questions may have some vaidity associated with them, because the GMAT answer choices or value assignments in such eqautions are always rounded, otherwise the question itself will not be correct mathematically coz if one of the operands in a sum is an integer the other has to be an integer to give an integer answer.

Like u I have my own grievances with such problems which have an inherent contradiction in them, However I cope with it by assuming that none of the terms in a problem is an integer unless mentioned explicitly for every term in the question.

Hope this helps to resolve some of doubts.