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31 Jan 2020, 11:42
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
52% (02:34) correct
48%
(02:43)
wrong
based on 279
sessions
History
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Not Attempted Yet
If |x - 5| = 2|x - 8|, then what is the value of x?
(1) \(|x^2 – 100| > 50\)
(2) \(|x^2 – 49| =0\)
(1) \(|x^2 – 100| > 50\)
(2) \(|x^2 – 49| =0\)
31 Jan 2020, 12:24
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If |x - 5| = 2|x - 8|, then what is the value of x?
--> square the both sides:
\((x-5)^{2} = (2(x-8))^{2}\)
--> \(x^{2}-10x+25= 4(x^{2}-16x+64)= 4x^{2}-64x+ 256\)
\(3x^{2}-54x+231=0\)
\(x^{2}-18x+77=0\)
--> (x-7)(x-11)=0
x could be 7 or 11.
(Statement1): \(|x^{2}–100|>50\)
--> if x=7, then |49-100|=51 >50 (√)
--> if x=11, then |121-100|= 21 >50 (ø)
x is equal to 7
Sufficient
(Statement2): \(|x^{2}–49|=0\)
--> if x=7, then |49-49| =0 (√)
--> if x=11, then |121-49| ≠0
x is equal to 7
Sufficient
The answer is D.
--> square the both sides:
\((x-5)^{2} = (2(x-8))^{2}\)
--> \(x^{2}-10x+25= 4(x^{2}-16x+64)= 4x^{2}-64x+ 256\)
\(3x^{2}-54x+231=0\)
\(x^{2}-18x+77=0\)
--> (x-7)(x-11)=0
x could be 7 or 11.
(Statement1): \(|x^{2}–100|>50\)
--> if x=7, then |49-100|=51 >50 (√)
--> if x=11, then |121-100|= 21 >50 (ø)
x is equal to 7
Sufficient
(Statement2): \(|x^{2}–49|=0\)
--> if x=7, then |49-49| =0 (√)
--> if x=11, then |121-49| ≠0
x is equal to 7
Sufficient
The answer is D.
31 Jan 2020, 12:40
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lnm87
Let us solve the given equation in the problem stem:
\(|x - 5| = 2|x - 8|\)
Removing the absolute value sign from both sides and introducing \(±\):
\(=> (x - 5) = ± 2(x - 8)\)
\(=> (x - 5) = +2(x - 8)\) OR \((x - 5) = -2(x - 8)\)
\(=> x - 5 = 2x - 16\) OR \(x - 5 = -2x + 16\)
\(=> x = 11\) OR \(x = 7\) ... (i)
Let us now check the statements:
Statement 1: \(|x^2 – 100| > 50\)
Verifying with the values of \(x\) obtained in (i):
\(x = 11: |121 - 100| = 21 > 50\) --- false
\(x = 7: |49 - 100| = |-51| = 51 > 50\) --- true
Thus, we have \(x = 7\) (unique) - Sufficient
Statement 2: \(|x^2 – 49| =0\)
Verifying with the values of \(x\) obtained in (i):
\(x = 11: |121 - 49| = 0\) --- false
\(x = 7: |49 - 49| = 0\) --- true
Thus, we have \(x = 7\) (unique) - Sufficient
Answer D
