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If 22 - |y + 14| = 20, what is the value of y ?

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Bunuel
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If 22 - |y + 14| = 20, what is the value of y ? [#permalink] New post   22 Feb 2022, 09:58
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If 22 - |y + 14| = 20, what is the sum of all possible values of y ?

A. -28
B. -16
C. -12
D. -4
E. 4

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BrentGMATPrepNow
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Re: If 22 - |y + 14| = 20, what is the value of y ? [#permalink] New post   Updated on: 22 Feb 2022, 10:44
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Bunuel wrote:
If 22 - |y + 14| = 20, what is the sum of all possible values of y ?

A. -28
B. -16
C. -12
D. -4
E. 4


Given: 22 - |y + 14| = 20
Subtract 22 from both sides of the equation: -|y + 14| = -2
Multiply both sides of the equation by -1 to get: |y + 14| = 2

Since |2| = 2, and |-2| = 2, we can conclude the following:
Either y + 14 = 2, which means y = -12
Or y + 14 = -2, which means y = -16

So, the sum of the possible solutions = -12 + -16 = -28

Answer: A

Originally posted by BrentGMATPrepNow on 22 Feb 2022, 10:27.
Last edited by BrentGMATPrepNow on 22 Feb 2022, 10:44, edited 1 time in total.
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Re: If 22 - |y + 14| = 20, what is the value of y ? [#permalink] New post   22 Feb 2022, 10:32
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BrentGMATPrepNow wrote:
Bunuel wrote:
If 22 - |y + 14| = 20, what is the sum of all possible values of y ?

A. -28
B. -16
C. -12
D. -4
E. 4


Given: 22 - |y + 14| = 20
Subtract 22 from both sides of the equation: -|y + 14| = -2
Multiply both sides of the equation by -1 to get: |y + 14| = 2

Since |2| = 2, and |-2| = 2, we can conclude the following:
Either y + 14 = 2, which means y = 12
Or y + 14 = -2, which means y = -16

So, the sum of the possible solutions = 12 + -16 = -4

Answer: D



Uhmmm...

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BrentGMATPrepNow
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Re: If 22 - |y + 14| = 20, what is the value of y ? [#permalink] New post   22 Feb 2022, 10:44
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Regor60 wrote:
Uhmmm...

Posted from my mobile device


Ooops!!
All fixed.

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Re: If 22 - |y + 14| = 20, what is the value of y ? [#permalink] New post   28 May 2022, 03:45
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Given that 22 - |y + 14| = 20 and we need to find the the sum of all possible values of y

To open |y + 14| we need to take two cases (Watch this video to know about the Basics of Absolute Value)

Case 1: Assume that whatever is inside the Absolute Value/Modulus is non-negative

=> y + 14 ≥ 0 => y ≥ -14

|y + 14| = y + 14 (as if A ≥ 0 then |A| = A)
=> 22 - (y + 14) = 20
=> 22 - y -14 = 20
=> 8 - 20 = y
=> y = -12
And our condition was y ≥ -14. Definitely -12 ≥ -14
=> y = -12 is a solution

Case 2: Assume that whatever is inside the Absolute Value/Modulus is Negative

y + 14 < 0 => y < -14

|y + 14| = -(y + 14) (as if A < 0 then |A| = -A)
=> 22 - (-(y + 14)) = 20
=> 22 + y + 14 = 20
=> y = 20 - 36
=> y = -16
And our condition was y < -14. Definitely -16 < -14
=> x = -16 is a solution

=> Sum of all possible values of y = -12 + (-16) = -12 -16 = -28

So, Answer will be A
Hope it helps!

Watch the following video to learn How to Solve Absolute Value Problems

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Re: If 22 - |y + 14| = 20, what is the value of y ? [#permalink] New post   28 May 2022, 11:44
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It is given that 22 - |y + 14| = 20

Reorganising the equation, we have, |y + 14| = 22 – 20 OR |y + 14| = 2
This means the expression (y + 14) = 2 or (y + 14) = - 2

Solving for the values of y, the two values of y are -12 and -16.
The sum of the two possible values of y = -12 – 16 = -28

The correct answer option is A.
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Re: If 22 - |y + 14| = 20, what is the value of y ? [#permalink] New post   27 Apr 2023, 10:05
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Official Solution:

If \(22 - |y + 14| = 20\), what is the sum of all possible values of y ?

A. \(-28\)
B. \(-16\)
C. \( -12\)
D. \(-4\)
E. \(4\)


\(22 - |y + 14| = 20\);

\(|y + 14| = 2\);

\(y + 14 = 2\) or \(y + 14 = -2\);

\(y = -12\) or \(y = -16\);

Therefore, the sum of all possible values of \(y\) is \(-12 + (-16) = -28.\)


Answer: A
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Re: If 22 - |y + 14| = 20, what is the value of y ? [#permalink] New post   27 Apr 2023, 17:43
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Bunuel wrote:
If 22 - |y + 14| = 20, what is the sum of all possible values of y ?

A. -28
B. -16
C. -12
D. -4
E. 4


Simplifying the equation, we have:

- |y + 14| = -2

2 = |y + 14|

Solving for when y + 14 is positive, we have:

2 = y + 14

-`12 = y

Solving for when y + 14 is negative, we have:

2 = -y - 14

16 = - y

-16 = y

Thus, the sum of all possible value of y is = -12 + -16 = -28.

Answer: A
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Re: If 22 - |y + 14| = 20, what is the value of y ? [#permalink]
27 Apr 2023, 17:43
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