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by MartyMurray » Wed Aug 03, 2016 9:56 pm
Arsenal wrote:If x = 2t and y = t/3, what is the value of x - y?

1. t² - 3 = 6

2. t³ = -27
Statement 1:

t² - 3 = 6

t² - 9 = 0

(t + 3)(t - 3) = 0

t = 3 or -3

Plug into x - y

3: 6 - 1 = 5

-3: -6 - (-1) = -5

Two different answers.

Insufficient.

Statement 2:

If t³ = -27, then t can only equal -3.

From the work for Statement 1 we know the value for x - y when t = -3.

Sufficient.

The correct answer is B.
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by Arsenal » Wed Aug 03, 2016 10:25 pm
Thanks Marty.

I posted this question to check if we need to consider 3 and -3 both values of t.

I have a doubt. Suppose X^2 = 25, then x=5 and -5.
In case of GMAT i read somewhere we take only positive roots.

Thanks in advance!
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by GMATGuruNY » Wed Aug 03, 2016 11:24 pm
Arsenal wrote:I have a doubt. Suppose X^2 = 25, then x=5 and -5.
In case of GMAT i read somewhere we take only positive roots.
The square root symbol -- √ -- means THE POSITIVE ROOT ONLY:
√25 = 5.
But x²=25 does not include this symbol.
Thus, x²=25 implies that x=±5.
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by MartyMurray » Thu Aug 04, 2016 4:24 am
Arsenal wrote:I have a doubt. Suppose X^2 = 25, then x=5 and -5.
In case of GMAT i read somewhere we take only positive roots.
x² = 25 can be rewritten as x² - 25 = 0.

x² - 25 = (x + 5)(x - 5)

Consider the above statement logically.

If x = -5, then (x + 5) = 0, making (x + 5)(x - 5) = 0.

So -5 clearly works one of the values of x.

The only reason √x is always positive is that, as Mitch said, √x is by definition the positive option only.
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by Matt@VeritasPrep » Fri Aug 05, 2016 2:48 pm
Arsenal wrote:Thanks Marty.

I posted this question to check if we need to consider 3 and -3 both values of t.

I have a doubt. Suppose X^2 = 25, then x=5 and -5.
In case of GMAT i read somewhere we take only positive roots.

Thanks in advance!
For historical/genealogical reasons, we only consider the positive root when we use the square root sign. So √25 has ONLY one solution, 5, but x*x = 25 has two solutions, 5 and -5.

It all comes down to whether you're using the √ sign or not.
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