If |(7 - 3j)/2|

Question

If  |\frac{7 - 3j}{2}| \leq 4 , then which of the following must be true?

A.  j \leq -\frac{1}{3}

B.  j \leq \frac{3}{7}

C.  j \leq 5

D.  j \geq \frac{3}{7}

E.  j \geq 5

GMATinsight · Accepted Answer

ShreyasJavahar lxl < 3 means -3 < x < 3 Similarly l7 - 3j/2l ≤ 4 means -4 ≤ 7 - 3j/2 ≤ 4 Multiplying all sides with 2 -8 ≤ 7 - 3j ≤ 8 Multiplying -1 in inequality (which requires us to flip the inequation signs) 8 ≥ 3j - 7 ≥ -8 Adding 7 in all parts of inequation 8+7 ≥ 3j ≥ -8+7 15 ≥ 3j ≥ -1 Dividing inequation by 3 5 ≥ j ≥ (-1/3) Answer: Option C Hope this help!!!

Kinshook · Answer

Asked: If  |\frac{7 - 3j}{2}| \leq 4 , then which of the following must be true?

|\frac{7 - 3j}{2}| \leq 4 
 |7 - 3j| \leq 8 
|3j - 7| <=8
- 8 <= 3j - 7 <=8
-1 <= 3j <= 15
-1/3 <= j <= 5

IMO C

neo92 · Answer

How is the answer to this C when the solution set comes out as -1/3=<j<= 5? Doesn't solution C of j<=5 also extends for all values that are lesser than 5 ?

Bunuel · Answer

|\frac{7 - 3j}{2}| \leq 4  is equivalent to  -\frac{1}{3} \leq j \leq 5 .

So, if  -\frac{1}{3} \leq j \leq 5  then it must be true that j is less than or equal to 5. Or in another way, any possible j from the given range ( -\frac{1}{3} \leq j \leq 5 ) will for sure be less then or equal to 5. That's why the answer is C.

Check similar questions here:  Trickiest Inequality Questions Type: Confusing Ranges .

Hope it helps.

ShreyasJavahar · Answer

Hi Kinshook,
Could you please explain the logic behind flipping the values inside the modulus in the highlighted part?

amak9114 · Answer

You don't have to do it, I think he just did it so it looks cleaner. You'll end up flipping the signs when you divide by -3 anyway.

ScottTargetTestPrep · Answer

Multiplying both sides of the inequality by 2, we have:

|7 - 3j| ≤ 8

When we have a “less than or equal to” inequality, we can re-express it as a “between” statement, as shown below, and this allows us to drop the absolute value sign.

-8 ≤ 7 - 3j ≤ 8

-15 ≤ -3j ≤ 1

5 ≥ j ≥ -1/3

Answer: C

Hupadhayay · Answer

For me, Visualization helps in solving mod questions.
as I know |a| ≤ 4 means the solutions would lie between -4 to +4 (inclusive) on the number line as modulus means the distance from the origin to the solution on number line.
 
hence 7−3j => -8 to +8(inclusive)
−3j => -15 to 1 (inclusive)
-j => -5 to 1/3 (inclusive)
j => reverse the solutions on number line => -1/3 to 5 (inclusive)

GMATGuruNY · Answer

j=0  satisfies  |\frac{7 - 3j}{2}| \leq 4 .
Since the correct range must include 0, eliminate A, D and E.

j=1  satisfies  |\frac{7 - 3j}{2}| \leq 4 .
Since the correct range must include 1, eliminate B.

C

Varane · Answer

I have a doubt with this. If it is <= 5 then it can also be a value that is - infinity. And if we suppose that then the equation j>= -1/3 will be invalid. Hence what is the logic behind this?

Posted from my mobile device

GMATGuruNY · Answer

You have correctly determined that the following statement is not valid:
If  j ≤ 5 , then  |\frac{7 - 3j}{2}| \leq 4 .
Since values less than -1/3 do not satisfy the given equation, the statement above is not justified.

However, option C implies the following statement:
If  |\frac{7 - 3j}{2}| \leq 4 , then  j ≤ 5 .
The statement above is true, since every value that satisfies the given equation is less than or equal to 5.

bumpbot · Answer

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If |(7 - 3j)/2| <= 4, then which of the following must be true?

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