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01 Oct 2018, 15:39
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
72% (02:01) correct
28%
(02:00)
wrong
based on 86
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For all values of \(x\) and \(y\), let \(x\blacktriangle y\) be defined by \(x\blacktriangle y = xy - x + 1\). If \(\left( {a - 2} \right)\blacktriangle \,a\,\, = \,\,a\,\blacktriangle \left( {a + 1} \right)\), which of the following numbers is closest to the value of \(a\) ?
(A) 0.66
(B) 0.83
(C) 0.95
(D) 1.14
(E) 1.43
Source: https://www.GMATH.net
(Exercise 18 of the Quant Class #04 included in our free test drive!)
(A) 0.66
(B) 0.83
(C) 0.95
(D) 1.14
(E) 1.43
Source: https://www.GMATH.net
(Exercise 18 of the Quant Class #04 included in our free test drive!)
Chethan92
Joined: 18 Jul 2018
Last visit: 21 Apr 2022
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Location: India
Concentration: Operations, General Management
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GMAT 1: 590 Q46 V25
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01 Oct 2018, 18:35
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(a−2)▲a = a▲(a+1)
(a−2)a-(a−2)+1 = a(a+1)-a+1
\(a^2\)-2a-a+2+1 = \(a^2\)+a-a+1
-3a = -2
Or
a = 2/3 = 0.66
A is the answer.
(a−2)a-(a−2)+1 = a(a+1)-a+1
\(a^2\)-2a-a+2+1 = \(a^2\)+a-a+1
-3a = -2
Or
a = 2/3 = 0.66
A is the answer.
02 Oct 2018, 11:40
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fskilnik
Thank you for your contribution, Afc0892!
The solution I present below is the same, just to follow my method´s style (for the interested readers).
\(?\,\,\,:\,\,a\,\,\left( {{\rm{approx}}.} \right)\,\)
\({\text{LHS}} = \left( {a - 2} \right)\blacktriangle \,a = \left( {a - 2} \right)a - \left( {a - 2} \right) + 1 = {a^2} - 3a + 3\)
\({\text{RHS}} = a\,\blacktriangle \left( {a + 1} \right) = a\left( {a + 1} \right) - a + 1 = {a^2} + 1\)
\({\rm{LHS}} = {\rm{RHS}}\,\,\,\,\, \Rightarrow \,\,\,\,\, - 3a + 3 = 1\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,?\,\,\,:\,\,\,a = {2 \over 3} \cong \,\,0.66\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
