If ~x = |14x|, which of the following must be true?

Question

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

Showmeyaa · Accepted Answer

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)!

PolarisTestPrep · Answer

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)

rocky620 · Answer

Bunuel   chetan2u 
Can/Should we assume  ~  equal to 14?

chetan2u · Answer

rocky620 , yes you are correct.
 But ~ is 14 when x is positive and ~ is -14 when x is negative.

~x = |14x|=14*|x|, that is 14 times the absolute value of x.

I. ~2 = ~(-2)
 ~2=14*|2| and ~(-2)=14*|-2|=14*|2|....Yes

II. ~3 + ~4 = ~7
~3=14*|3|=14*3 and ~3=14*|4|=14*4
~7=14*|7|=14*7
 ~3 + ~4 = 14*3+14*4=14*7= ~7....Yes

III. The minimum possible value of ~x is zero
~x = |14x|=14*|x|, and the minimum value of an absolute is 0, hence, 0 is the least value of ~x.
Yes

E

Crytiocanalyst · Answer

1)~2 = |14 * 2| = 28
~(-2) = |14* -2| = 28

2)~3 = |14 * 3| = 42
~4 = |14 * 4| = 56 , 
Sum = 98
~7 = |14 * 7| = 98 
3)Any any modulus least value is at zero

Therefore IMO E

rak08 · Answer

For 2nd one you can also apply the property

mod A + mod B = Mod (A+B) ??

Am i wrong in this?

as both 3&4 are positive numbers so above applies

If ~x = |14x|, which of the following must be true?

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GMAT Problem Solving (PS) Questions

If ~x = |14x|, which of the following must be true?

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