What is the value of |x|?
(1) |x^2 + 16| - 5 = 27
(2) x^2 = 8x - 16
OA
D
How statement1 is sufficient.
In this we will have two cases and both will have different value?
case 1 = |x^2 + 16| - 5 = 27
case 2 = |x^2 + 16| - 5 = -27
Please explain.
Many thanks in advance .
Kavin
What is the value of |x|
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- fiza gupta
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1) |x^2 + 16| - 5 = 27
|x^2 + 16| = 32
x^2 + 16 = 32 (i) or x^2 + 16 = - 32 (ii)
(ii) will not hold true in this case
because x^2(always positive or 0) + 16(always positive) so sum of both will be always positive
x^2 + 16 = 32
x = +4 or -4 => |x| = 4
SUFFICIENT
2) x^2 = 8x - 16
x^2 - 8x + 16 =0
x = 4 => |x|=4
SUFFICIENT
SO D
|x^2 + 16| = 32
x^2 + 16 = 32 (i) or x^2 + 16 = - 32 (ii)
(ii) will not hold true in this case
because x^2(always positive or 0) + 16(always positive) so sum of both will be always positive
x^2 + 16 = 32
x = +4 or -4 => |x| = 4
SUFFICIENT
2) x^2 = 8x - 16
x^2 - 8x + 16 =0
x = 4 => |x|=4
SUFFICIENT
SO D
Fiza Gupta
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Hi Kavin,
You have to be careful about how you 'manipulate' equations that include an Absolute Value. In Fact 1, we're given...
| X^2 + 16 | - 5 = 27
| X^2 + 16 | = 32
On the GMAT, "X^2" can never be a negative number, so adding 16 to X^2 cannot end in a negative result either. Knowing that, this equation CANNOT result in -32, so you have to remove that option from consideration.
GMAT assassins aren't born, they're made,
Rich
You have to be careful about how you 'manipulate' equations that include an Absolute Value. In Fact 1, we're given...
| X^2 + 16 | - 5 = 27
| X^2 + 16 | = 32
On the GMAT, "X^2" can never be a negative number, so adding 16 to X^2 cannot end in a negative result either. Knowing that, this equation CANNOT result in -32, so you have to remove that option from consideration.
GMAT assassins aren't born, they're made,
Rich
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S1:
|x² + 16| = 32
So (x² + 16) = 32 or (x² + 16) = -32. The second case is impossible, since no square is negative, so our only possibility is the first one: (x² + 16) = 32, or x² = 16, or |x| = 4. SUFFICIENT!
S2:
x² - 8x + 16 = 0
(x - 4)² = 0
x = 4, so |x| = 4, SUFFICIENT!
|x² + 16| = 32
So (x² + 16) = 32 or (x² + 16) = -32. The second case is impossible, since no square is negative, so our only possibility is the first one: (x² + 16) = 32, or x² = 16, or |x| = 4. SUFFICIENT!
S2:
x² - 8x + 16 = 0
(x - 4)² = 0
x = 4, so |x| = 4, SUFFICIENT!
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Hi Kevin,Needgmat wrote:What is the value of |x|?
(1) |x^2 + 16| - 5 = 27
(2) x^2 = 8x - 16
OA
D
How statement1 is sufficient.
In this we will have two cases and both will have different value?
case 1 = |x^2 + 16| - 5 = 27
case 2 = |x^2 + 16| - 5 = -27
Please explain.
Many thanks in advance .
Kavin
Though you got the solution for the question. I see that you have written incorrect expressions for case 1 and case 2.
When you consider two cases: one on either side, you must get rid of the modulus. So the correct way of writing would be:
First take non-modulus numbers on the RHS,
Thus, |x^2 + 16| = 27 + 5
=> |x^2 + 16| = 32
Case 1 = x^2 + 16 = 32
Case 2 = x^2 + 16 = -32
Hope this helps!
-Jay
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We need to determine the value of |x|.Needgmat wrote:What is the value of |x|?
(1) |x^2 + 16| - 5 = 27
(2) x^2 = 8x - 16
Statement One Alone:
|x^2 + 16| - 5 = 27
Notice that x^2 + 16 is always positive since x^2 is always nonnegative. Therefore, |x^2 + 16| = x^2 + 16, and hence solving the equation |x^2 + 16| - 5 = 27 is equivalent to solving x^2 + 16 - 5 = 27.
x^2 + 16 - 5 = 27
x^2 + 11 = 27
x^2 = 16
Taking the square root of both sides, we get x = -4 or 4, and thus the absolute value of -4 or 4 = 4.
Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
x^2 = 8x - 16
We can simplify the given equation and determine x.
x^2 = 8x - 16
x^2 - 8x + 16 = 0
(x - 4)(x - 4) = 0
x = 4
Since x = 4, |x| = 4. Statement two alone is also sufficient to answer the question.
Answer: D
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