What is the value of x?

[la2ny]

Hi,

This is a 500-600 level DS problem from CAT. It's kinda a stupid question, but I don't see why answer C "Both statements TOGETHER are sufficient" couldn't be the right answer. The correct answer is "E". Couldn't we just solve for y in statement 1 and substitute it in statement 2, which will give us value for x? Also follows the rule of 2 equations, 2 variables -- we must be able to solve for x. Let me know why the answer is E. Thanks.

What is the value of x?

(1) x + 2y = 4

(2) 5x + y + 15 = 3x - 3y + 23

[chicagophil]

I think the issue is that when you simplify (2) you get a multiple of (1), so you don't actually have two independent equations to solve for two variables...

(2) 5x + y + 15 = 3x - 3y + 23
=
2x + 4y = 8

which is 2 times equation (1)

if you rearrange (1) to get x = 4 - 2y, and plug into (2) you get:

2(4 - 2y) + 4y = 8
8 -4y + 4y = 8
8 = 8

which doesn't get you anywhere.

[la2ny]

Thanks for the reply. As I was doing this problem, I didn't bother to do all the math as you have shown. I simply recognized that there were 2 variables, 2 equations, so I thought that should show sufficiency. Anyway, I hope someone from MGMAT can weigh in and provide their explanation to this one as well. Seems like such a simple problem and I want to know their reasons for why it's answer E.

[tim]

This is a very common trap the GMAT sets for you. There IS no general rule that says 2 equations is enough to solve for 2 variables. You have to be careful and carry out the calculations to be sure..

[velchal_rao]

If you simply the STATEMENT 2 alone you get x + 2y - 4 =0
which is the same as STATEMENT 1 ...so the answer is E

Because both are the same equations , they are not two equations and two variables

i used to make this mistake ...the quadratic equations can be disguised so simplify

[RonPurewal]

If you simply the STATEMENT 2 alone you get x + 2y - 4 =0
which is the same as STATEMENT 1 ...so the answer is E

Because both are the same equations , they are not two equations and two variables

i used to make this mistake ...the quadratic equations can be disguised so simplify

There are no quadratic equations in this problem.

In any case -- the most important principle here is that you should NEVER trust "rules of thumb" on data sufficiency.
If a "rule" works 99% of the time, and has exceptions 1% of the time, it's pretty much certain that DS problems are going to test that 1%. That's the whole reason why DS is on the exam in the first place.

[velchal_rao]

thank you

sorry for using quadratic ...i
just meant two equations two variables

[RonPurewal]

No problem.

The point here is that you should EXPECT "rules of thumb" to give wrong answers on DS.

In other words, if you have a "rule" that has exceptions -- like the "two equations, two unknowns" rule discussed here -- then you should go into DS problems expecting that the answer derived from trusting those rules is going to be WRONG.

This is, after all, one of the main reasons why DS exists in the first place: to test your understanding of when things work and when they don't.