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705-805 (Hard)|   Algebra|      
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Bunuel
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If (x−2.5)(x+0.5)=4, what is the value of x? 25 Feb 2021, 01:15
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A
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75% (hard)

Question Stats:

44% (02:04) correct 56% (02:16) wrong based on 109 sessions

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If (x−2.5)(x+0.5)=4, what is the value of x?

(1) (x+1.5)(x−1.5)=0

(2) (x−3.5)(x+1.5)=0


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A
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If (x−2.5)(x+0.5)=4, what is the value of x? 25 Feb 2021, 02:01
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(x -2.5) (x + 0.5) = 4
gives you: x^2- 2x- 5.25 = 0
which is (x-3.5) (x+1.5) = 0

Answer B
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If (x−2.5)(x+0.5)=4, what is the value of x? 25 Feb 2021, 02:16
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rohantewari I think answer should be A.

Given (x-2.5)(x+0.5)=4

Expanding, x^2+2x-5.25=0
(x-3.5)(x+1.5)=0

x=3.5 or x=-1.5

We need to find one unique value of x.

Statement 1: (x+1.5)(x-1.5)=0

x=1.5 or -1.5

Given x is either 3.5 or -1.5,

We can conclude x= -1.5. SUFFICIENT

Statement 2: (x-3.5)(x+1.5)=0

Repetition of what is given and no additional info. INSUFFICIENT

ANS:A

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If (x−2.5)(x+0.5)=4, what is the value of x? 25 Feb 2021, 06:11
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I do not know whether my method is correct or not.

Question Stem : \( (x−2.5)(x+0.5)=4\).

\(x = 4+2.5 => 6.5 || x = 4-0.5 => 3.5\)

Now going through both statements

Statement 1 : \((x+1.5)(x−1.5)=0\)

value of x can be -1.5 or 1.5 which do not match the values we got from simplifying the question stem.

Not Sufficient.

Statement 2 : \((x−3.5)(x+1.5)=0\)

Value of \(x\) can be \(3.5\) or \(-1.5\).

The first value of \(x\) does match with the values we got from simplifying the question stem.

Sufficient.

The OA is B.
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If (x−2.5)(x+0.5)=4, what is the value of x? 25 Feb 2021, 08:43
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kntombat
I do not know whether my method is correct or not.

Question Stem : \( (x−2.5)(x+0.5)=4\).

\(x = 4+2.5 => 6.5 || x = 4-0.5 => 3.5\)

Now going through both statements

Statement 1 : \((x+1.5)(x−1.5)=0\)

value of x can be -1.5 or 1.5 which do not match the values we got from simplifying the question stem.

Not Sufficient.

Statement 2 : \((x−3.5)(x+1.5)=0\)

Value of \(x\) can be \(3.5\) or \(-1.5\).

The first value of \(x\) does match with the values we got from simplifying the question stem.

Sufficient.

The OA is B.
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kntombat

Pls substitute x as 6.5 in the equation
(x-2.5)(x+0.5)=4

We get, 4*7=4, which is not true. 6.5 is not a solution for the given equation.

Whereas if you substitute - 1.5 for x , we get -4*-1= 4. -1.5 is a possible solution for x and not 6.5.

Hope this was useful.

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If (x−2.5)(x+0.5)=4, what is the value of x? 25 Feb 2021, 10:51
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If (x−2.5)(x+0.5)=4, what is the value of x?

Stat 1: (x+1.5)(x−1.5)=0; if x = 1.5, then, (x−2.5)(x+0.5) = (-1)*2 =-2 not equal to 4.; but if x = -1.5, then, (x−2.5)(x+0.5) = (-4)*(-1) = 4. Sufficient

Stat 2: (x−3.5)(x+1.5)=0; at x= 3.5, (x−2.5)(x+0.5) =4 and at x = -1.5, (x−2.5)(x+0.5) = 4, so we don't have unique value of x. Not Sufficient

So, I think A. :)
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If (x−2.5)(x+0.5)=4, what is the value of x? 25 Feb 2021, 23:42
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If (x−2.5)(x+0.5)=4, what is the value of x?

(1) (x+1.5)(x−1.5)=0
x = 1.5 or -1.5
Only -1.5 satisfies (x−2.5)(x+0.5)=4
Sufficient

(2) (x−3.5)(x+1.5)=0
x = 3.5 or -1.5
Both satisfy (x−2.5)(x+0.5)=4
No unique answer
Not sufficient

Option A

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If (x−2.5)(x+0.5)=4, what is the value of x? 28 Feb 2021, 01:50
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Solution



Given
In this question, we are given that
    • (x−2.5)(x+0.5)=4

To find
We need to determine
    • The value of x

Approach and Working out

    • Statement 1: (x+1.5)(x−1.5)=0
      o (x+1.5) = 0 or (x−1.5)=0
      o x = -1.5 or x = 1.5
         If x = -1.5,
    • (x−2.5)(x+0.5) = (-4)(-1) = 4
    • So, x can be -1.5.
       If x = 1.5,
    • (x−2.5)(x+0.5) = (-1)(2) = -2
    • So, x cannot be 1.5.
      o We get a unique value of x.

Statement 1 is sufficient alone.

    • Statement 2: (x-3.5)(x+1.5)=0
      o (x-3.5) = 0 or (x+1.5)=0
      o x = 3.5 or x = -1.5
         If x = 3.5,
    • (x−2.5)(x+0.5) = (1)(4) = 4
    • So, x can be 3.5.
       If x = -1.5,
    • (x−2.5)(x+0.5) = (-4)(-1) = 4
    • So, x can be -1.5.
      o We do not get a unique value of x.
Statement 2 alone is insufficient.

Thus, option A is the correct answer.

Correct Answer: Option A
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If (x−2.5)(x+0.5)=4, what is the value of x? 05 Aug 2023, 01:16
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