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Domnu wrote:Btw, I don't think the answer is C... the answer should be A.
If sqrt(x) is an integer, then x has to be an integer. So, x = 12, 13, 14, 15, 16 only. But 16 is the only perfect square, and sqrt(16) = 4 (not -4). So, the answer is A.
If you know what imaginary numbers are, this is where they come in. But if you're not sure what this is, then never mind.
I am with you here. I think there is some really bad, misleading information going on in this thread. Look at √x, for any x. On the GMAT, x will definitely be positive. But the result, √x, will be either the positive or the negative square root. It is absolutely incorrect to say that √9 only equals 3 on the GMAT. (-3) × (-3)=9, even on the GMAT. The answer to the original question, as you write, is C.Domnu wrote: Sqrt(-16) is an imaginary number... -4 squared is positive 16. Where is the imaginary concept in the problem?
Despite what everybody says about "GMAT Land" and assuming that only a positive root exists - I Call BS.
I agree with C, but above statement is wrong. Can anyone confirm?It is absolutely incorrect to say that √9 only equals 3 on the GMAT
Ian Stewart wrote:The square root symbol is defined as a function: it only produces one answer. By definition, the square root symbol gives the *non-negative* square root of whatever's underneath the root. So if you see the square root symbol over the number 9, the answer is most certainly 3, and most certainly *not* -3. This is true in GMAT mathematics, and true in every other branch of mathematics - there are no special mathematical rules or definitions specific to the GMAT (except, perhaps, that we ignore complex numbers on the GMAT).
All of that said, 9 does have two square roots: 3 and -3. It's just that when you see the square root symbol over the number 9, we ignore the negative answer, because of how the symbol is defined.
I hadn't even looked at the original question - I was only replying to your and jakesing's posts above - but yes, it's certainly A.cameronwu wrote: You're suggesting the answer is (A), correct?
You can't solve the equation y^2 = 9 as you're doing. You're assuming that √y^2 is equal to y, and it is not necessarily equal to y:jakesing wrote:Ok So I get that that is the convention, but can someone explain to me how the following isn't a contradiction?
In the example given a few posts above, it says if y^2=9, y= +/-3. But if y=√9, then y=3. Maybe it's just me, but I'm pretty certain those two statements are equal. The way you solve the first one is by taking the square root of both sides, resulting in y=√9. I'm really perplexed right now.
Why couldn't sqrt(x) = 3 and still fit the rule? 3 is an integer between 2 and 5 as well.sanjana wrote:Why isnt the answer D?
1 is sufficient as pointed out.
For statement2,it says 2<sqrtx<5
The question says sqrt(x) is an integer
Cant we say from this that sqrt x = 4,hence X=16 and
2<4<5?
Please clarify.
sqrt(x) could also be 3, in which case x is 9. So Statement 2 is not sufficient.sanjana wrote:Why isnt the answer D?
1 is sufficient as pointed out.
For statement2,it says 2<sqrtx<5
The question says sqrt(x) is an integer
Cant we say from this that sqrt x = 4,hence X=16 and
2<4<5?
Please clarify.
Lemme get thisStuart Kovinsky wrote:
You ask a great question, because it's essential to understand the difference, especially in data sufficiency.
Let's make up a DS question to illustrate the difference:
Q: What's the value of x?
(1) x = √9
(2) x^2 = 9
Step 1 of the Kaplan Method for DS: focus on the question stem.
We're asked for the value of x; not much to think about here. We need 1 and only 1 value for a statement to be sufficient and, as of right now, we have no restrictions on x at all.
Step 2 of the Kaplan Method for DS: consider each statement by itself, in conjunction with the stem.
(1) we know that the "√" sign means "postive root of". 9 only has one positive root: 3. Therefore, x must be 3... sufficient.
(2) we know that if x^2 = 9, x could be +/- 3... 2 possible values, therefore insufficient.
As an algebraic aside, here's the "official" way to solve this equation:
x^2 = 9
x^2 - 9 = 0
(x + 3)(x - 3) = 0
x = -3 or +3
(1) is sufficient and (2) is insufficient: no need to combine, select (A).
Stuart Kovinsky wrote:Why couldn't sqrt(x) = 3 and still fit the rule? 3 is an integer between 2 and 5 as well.sanjana wrote:Why isnt the answer D?
1 is sufficient as pointed out.
For statement2,it says 2<sqrtx<5
The question says sqrt(x) is an integer
Cant we say from this that sqrt x = 4,hence X=16 and
2<4<5?
Please clarify.
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