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Manager  Joined: 08 Dec 2012
Posts: 60
Location: United Kingdom
WE: Engineering (Consulting)
If 3|3 – x| = 7, what is the product of all the possible va  [#permalink]

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Difficulty:   15% (low)

Question Stats: 77% (01:29) correct 23% (01:47) wrong based on 704 sessions

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If 3|3 – x| = 7, what is the product of all the possible values of x?

A. 1/9
B. 1/3
C. 2/3
D. 16/9
E. 32/9
Intern  Status: Attending Duke in May!
Joined: 07 Jan 2013
Posts: 23
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Re: If 3|3 – x| = 7, what is the product of all the possible va  [#permalink]

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nave81 wrote:
If 3|3 – x| = 7, what is the product of all the possible values of x?

A. 1/9
B. 1/3
C. 2/3
D. 16/9
E. 32/9

3|3-x| = 7 can be rewritten as: $$|3-x| = \frac{7}{3}$$

So

$$|\frac{9}{3} - x| = \frac{7}{3}$$

x has two possible solutions $$\frac{2}{3}$$ and $$\frac{16}{3}$$ that satisfy the equation

$$\frac{2}{3}*\frac{16}{3} = \frac{32}{9}$$

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Re: If 3|3 – x| = 7, what is the product of all the possible va  [#permalink]

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$$3|3 - x| = 7$$
case $$3-x>0$$
$$3(3-x)=7$$
$$9-3x=7, x=\frac{2}{3}$$
case $$3-x<0$$
$$3(-3+x)=7$$
$$-9+3x=7, x= 16/3$$

$$\frac{2}{3}*\frac{16}{3}=\frac{32}{9}$$
E
Intern  Joined: 15 Jan 2013
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Concentration: Finance, Operations
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Re: If 3|3 – x| = 7, what is the product of all the possible va  [#permalink]

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nave81 wrote:
If 3|3 – x| = 7, what is the product of all the possible values of x?

A. 1/9
B. 1/3
C. 2/3
D. 16/9
E. 32/9

3|3 – x| = 7 So, |3 – x| = 7/3 or (3-x) = +7/3 or -7/3
Solving we get x = 2/3 or 16/3
product = $$2/3 * 16/3 = 32/9$$
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Re: If 3|3 – x| = 7, what is the product of all the possible va  [#permalink]

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If 3|3 – x| = 7, what is the product of all the possible values of x?

x≥3, x<3

x≥3:
3|3 – x| = 7
3 -(3-x) = 7
3 (-3+x) = 7
-9 + 3x = 7
3x = 16
x=16/3 Valid

x<3
3(3-x) = 7
9-3x = 7
-3x=-2
x=2/3

(16/3)*(2/3) = 32/9

(E)
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Re: If 3|3 – x| = 7, what is the product of all the possible va  [#permalink]

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I don't agree with E. 16/3, when substituted in the original equation doesn't satisfy it. you would get |-9/3| = 7/3 which is not legit. So we should discard 16/3 as a solution of the equation. That leaves us with 2/3 which is option C

Best Regards
Dheeraj Rekula
Math Expert V
Joined: 02 Sep 2009
Posts: 64117
Re: If 3|3 – x| = 7, what is the product of all the possible va  [#permalink]

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Math Expert V
Joined: 02 Sep 2009
Posts: 64117
If 3|3 – x| = 7, what is the product of all the possible va  [#permalink]

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Caesar_1987 wrote:
If 3|3 – x| = 7, what is the product of all the possible values of x?

A. 1/9
B. 1/3
C. 2/3
D. 16/9
E. 32/9

I don't agree with E. 16/3, when substituted in the original equation doesn't satisfy it. you would get|-9/3| = 7/3 which is not legit. So we should discard 16/3 as a solution of the equation. That leaves us with 2/3 which is option C

Best Regards
Dheeraj Rekula

16/3 does satisfy the equation:
3|3 – 16/3| = 7;
3*7/3 = 7.

Hope it's clear.
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Re: If 3|3 – x| = 7, what is the product of all the possible va  [#permalink]

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3|3-x| = 7 can be rewritten as: |3−x|=7/3
so we have
1. 3-x =7/3
x=2/3

2. 3-x=-7/3
x=16/3

so product will be
32/9
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Re: If 3|3 – x| = 7, what is the product of all the possible va  [#permalink]

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nave wrote:
If 3|3 – x| = 7, what is the product of all the possible values of x?

A. 1/9
B. 1/3
C. 2/3
D. 16/9
E. 32/9

Given : 3|3 – x| = 7

3 – x = 7/3 or 3 – x = -7/3

x = 2/3 or 16/3

Product of all the possible values of x = 2/3 * 16*3 = 32/9

(E)
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Intern  B
Joined: 29 Oct 2012
Posts: 21
Re: If 3|3 – x| = 7, what is the product of all the possible va  [#permalink]

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the equation leads to two values of x
2/3 , 16/3
their product equals to 32/9 i.e. E
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Re: If 3|3 – x| = 7, what is the product of all the possible va  [#permalink]

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_________________ Re: If 3|3 – x| = 7, what is the product of all the possible va   [#permalink] 21 Mar 2020, 14:38

# If 3|3 – x| = 7, what is the product of all the possible va  