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GMAT Set 5 Q7

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Source: — Data Sufficiency |
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by Uva@90 » Wed Feb 18, 2015 7:46 am
Abhijit K wrote:What is the value of |x+7|?
1.|x+3|=14
2.(x+2)^2=169
Hi Abhijit,

We need value of X to find the value of |x+7|

Stmt1: |x+3|= 14
x+3 = 14 ==> x = 11
or x+3 = -14 ==> x = -17
since we have two values Insufficient.

Stmt 2: (x+2)^2=169

x+2 = 13 ==> x = 11
or x+2 = -13 ==> x = -15
Since we have two values, Insufficient.

1+2

we have common value of 11. Hence sufficient.
OA is C

Regards,
Uva
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by Brent@GMATPrepNow » Wed Feb 18, 2015 8:22 am
Abhijit K wrote:What is the value of |x+7|?
1. |x+3| = 14
2. (x+2)² = 169


Target question: What is the value of |x+7|?

Statement 1: |x+3| = 14
When solving questions involving ABSOLUTE VALUE, there are 3 steps:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug in the solutions to check for extraneous roots

So, x+3 = 14
OR
x+3 = -14
When we solve the two equations, we get x = 11 OR x = -17

NOTE: Although we got two different answers, we must check whether we get 2 different answers to the target question.

If x = 11, then |x + 7| = |11 + 7| = 18
If x = -17, then |x + 7| = |-17 + 7| = 10
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (x+2)² = 169
This means EITHER (x+2) = 13 OR (x+2) = -13
When we solve the two equations, we get x = 11 OR x = -15
If x = 11, then |x + 7| = |11 + 7| = 18
If x = -15, then |x + 7| = |-15 + 7| = 8
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that |x + 7| = 18 OR 10
Statement 2 tells us that |x + 7| = 18 OR 8
So, if BOTH statements are true, then |x + 7| must equal 18
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
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by Brent@GMATPrepNow » Wed Feb 18, 2015 11:26 am
Uva@90 wrote:
Abhijit K wrote:What is the value of |x+7|?
1.|x+3|=14
2.(x+2)^2=169
Hi Abhijit,

We need value of X to find the value of |x+7|

Stmt1: |x+3|= 14
x+3 = 14 ==> x = 11
or x+3 = -14 ==> x = -17
since we have two values Insufficient.

Stmt 2: (x+2)^2=169

x+2 = 13 ==> x = 11
or x+2 = -13 ==> x = -15
since we have two values Insufficient.

1+2

we have common value of 11. Hence sufficient.
OA is C

Regards,
Uva
Hi Uva@90,

Be careful. Always keep remember that we're trying to answer the target question.
For each statement, we may have 2 possible values for x, BUT that doesn't necessarily mean that there are two different answers to the target question (What is the value of |x+7|?)

Consider, for example, if statement 2 looked like this:

Statement 2: (x+7)² = 100
There are two possible solutions to this equation: x = 3 and x = -17
Does this mean that statement 2 is not sufficient?
No. The target question is NOT asking us to find the value of x. It's asking us to find the value of |x+7|
If x = 3, then |x + 7| = |3 + 7| = |10| = 10
If x = -17, then |x + 7| = |-17 + 7| = |-10| = 10
So, although there are 2 possible values of x, there's ONLY ONE answer to the target question.
So, in this case, statement 2 is SUFFICIENT

Cheers,
Brent
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by Uva@90 » Thu Feb 19, 2015 7:52 am
Brent@GMATPrepNow wrote:
Uva@90 wrote:
Abhijit K wrote:What is the value of |x+7|?
1.|x+3|=14
2.(x+2)^2=169
Hi Abhijit,

We need value of X to find the value of |x+7|

Stmt1: |x+3|= 14
x+3 = 14 ==> x = 11
or x+3 = -14 ==> x = -17
since we have two values Insufficient.

Stmt 2: (x+2)^2=169

x+2 = 13 ==> x = 11
or x+2 = -13 ==> x = -15
since we have two values Insufficient.

1+2

we have common value of 11. Hence sufficient.
OA is C

Regards,
Uva
Hi Uva@90,

Be careful. Always keep remember that we're trying to answer the target question.
For each statement, we may have 2 possible values for x, BUT that doesn't necessarily mean that there are two different answers to the target question (What is the value of |x+7|?)

Consider, for example, if statement 2 looked like this:

Statement 2: (x+7)² = 100
There are two possible solutions to this equation: x = 3 and x = -17
Does this mean that statement 2 is not sufficient?
No. The target question is NOT asking us to find the value of x. It's asking us to find the value of |x+7|
If x = 3, then |x + 7| = |3 + 7| = |10| = 10
If x = -17, then |x + 7| = |-17 + 7| = |-10| = 10
So, although there are 2 possible values of x, there's ONLY ONE answer to the target question.
So, in this case, statement 2 is SUFFICIENT

Cheers,
Brent

Ah yes....
you are correct. ..my bad..:(
Thx for pointing it out :)

Regards
Uva
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by Uva@90 » Thu Feb 19, 2015 7:52 am
Brent@GMATPrepNow wrote:
Uva@90 wrote:
Abhijit K wrote:What is the value of |x+7|?
1.|x+3|=14
2.(x+2)^2=169
Hi Abhijit,

We need value of X to find the value of |x+7|

Stmt1: |x+3|= 14
x+3 = 14 ==> x = 11
or x+3 = -14 ==> x = -17
since we have two values Insufficient.

Stmt 2: (x+2)^2=169

x+2 = 13 ==> x = 11
or x+2 = -13 ==> x = -15
since we have two values Insufficient.

1+2

we have common value of 11. Hence sufficient.
OA is C

Regards,
Uva
Hi Uva@90,

Be careful. Always keep remember that we're trying to answer the target question.
For each statement, we may have 2 possible values for x, BUT that doesn't necessarily mean that there are two different answers to the target question (What is the value of |x+7|?)

Consider, for example, if statement 2 looked like this:

Statement 2: (x+7)² = 100
There are two possible solutions to this equation: x = 3 and x = -17
Does this mean that statement 2 is not sufficient?
No. The target question is NOT asking us to find the value of x. It's asking us to find the value of |x+7|
If x = 3, then |x + 7| = |3 + 7| = |10| = 10
If x = -17, then |x + 7| = |-17 + 7| = |-10| = 10
So, although there are 2 possible values of x, there's ONLY ONE answer to the target question.
So, in this case, statement 2 is SUFFICIENT

Cheers,
Brent

Ah yes....
you are correct. ..my bad..:(
Thx for pointing it out :)

Regards
Uva
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