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15 Jul 2021, 03:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
68% (01:25) correct
32%
(01:32)
wrong
based on 634
sessions
History
Date
Time
Result
Not Attempted Yet
If ~x = |14x|, which of the following must be true?
I. ~2 = ~(-2)
II. ~3 + ~4 = ~7
III. The minimum possible value of ~x is zero
A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
I. ~2 = ~(-2)
II. ~3 + ~4 = ~7
III. The minimum possible value of ~x is zero
A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
15 Jul 2021, 14:47
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Bunuel
If ~x = |14x|, which of the following must be true?
I. ~2 = ~(-2)
II. ~3 + ~4 = ~7
III. The minimum possible value of ~x is zero
A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
I. ~2 = ~(-2)
II. ~3 + ~4 = ~7
III. The minimum possible value of ~x is zero
A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
1)~2 = |14 * 2| = 28
~(-2) = |14* -2| = 28 - Valid
2)~3 = |14 * 3| = 42
~4 = |14 * 4| = 56 , Sum = 98
~7 = |14 * 7| = 98 - Valid
3)Yes, when x = 0, it is minimum!
IMO, (E)!
15 Jul 2021, 20:46
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Hello!
So what the squiggle does to a number is multiply it by 14 and then take the absolute value of the result
Absolute value must be 0 or positive, so III. is automatically true. This rules out A and B
As for I., does the absolute value of 2(14) = the absolute value of -2(14)?
|28| = |-28|?
Yes, absolute value measures the distance from 0 on the number line. Both 28 and -28 are 28 units away from 0 on the number line
In other words, the absolute value of either one is 28 and their absolute values are equal
I. is true, so the answer must either be D or E
Let's look at II.
You are taking 3 + 4 = 7, which is true, and multiplying each number by 14. You are then taking the absolute value of each number but since they are positive this has no effect.
Essentially you end up with:
14(3 + 4) = 14(7)
Doing the same thing to both sides of an equation keeps the equation valid. II. is true
I, II, and III are true
The answer is (E)
So what the squiggle does to a number is multiply it by 14 and then take the absolute value of the result
Absolute value must be 0 or positive, so III. is automatically true. This rules out A and B
As for I., does the absolute value of 2(14) = the absolute value of -2(14)?
|28| = |-28|?
Yes, absolute value measures the distance from 0 on the number line. Both 28 and -28 are 28 units away from 0 on the number line
In other words, the absolute value of either one is 28 and their absolute values are equal
I. is true, so the answer must either be D or E
Let's look at II.
You are taking 3 + 4 = 7, which is true, and multiplying each number by 14. You are then taking the absolute value of each number but since they are positive this has no effect.
Essentially you end up with:
14(3 + 4) = 14(7)
Doing the same thing to both sides of an equation keeps the equation valid. II. is true
I, II, and III are true
The answer is (E)
