If x-2t and y=t/3, what is the value of x - y?
1. t^2 - 3 = 6
2. t^3=-27
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Square root
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MartyMurray
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Statement 1:Arsenal wrote:If x = 2t and y = t/3, what is the value of x - y?
1. t² - 3 = 6
2. t³ = -27
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.
Marty Murray
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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!
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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GMATGuruNY
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The square root symbol -- √ -- means THE POSITIVE ROOT ONLY: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.
√25 = 5.
But x²=25 does not include this symbol.
Thus, x²=25 implies that x=±5.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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As a tutor, I don't simply teach you how I would approach problems.
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MartyMurray
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x² = 25 can be rewritten as x² - 25 = 0.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 = (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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Matt@VeritasPrep
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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.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!
It all comes down to whether you're using the √ sign or not.
