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04 Dec 2018, 08:54
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
78% (01:31) correct
22%
(01:43)
wrong
based on 174
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What is the value of \(|y|*|y - 3|\) ?
(1) \((|y| - 7)(y + 5) = 0\)
(2) \(5|y| - 10 = 0\), \(y > 0\)
(1) \((|y| - 7)(y + 5) = 0\)
(2) \(5|y| - 10 = 0\), \(y > 0\)
04 Dec 2018, 09:26
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|y|∗|y−3|= \(y^2\) * \((y-3)^2\) = \(y^4\) - \(6y^3\) + \(9y^2\)......so we need to find this.
(1) (|y|−7)(y+5)=0
Case 1: y>=0 (y-7)(y+5)=0
(y-7)=0 or (y+5)=0
y=7 or y=-5(this is not possible as y>=0 )
Case 2: y<0
(-y-7)(y+5)=0
(-y-7)=0 or (y+5)=0
y=-7 or y=-5
As per case 1 & 2, y=-7,-5 and 7. NOT SUFFICIENT
(2) 5|y|−10, y>0
Case 1: y>=0
5y-10=0 =>y=2
Case 2: y<0
-5y-10=0 =>y=-2
But y>0. So, y=2 SUFFICIENT
IMO answer is option B
(1) (|y|−7)(y+5)=0
Case 1: y>=0 (y-7)(y+5)=0
(y-7)=0 or (y+5)=0
y=7 or y=-5(this is not possible as y>=0 )
Case 2: y<0
(-y-7)(y+5)=0
(-y-7)=0 or (y+5)=0
y=-7 or y=-5
As per case 1 & 2, y=-7,-5 and 7. NOT SUFFICIENT
(2) 5|y|−10, y>0
Case 1: y>=0
5y-10=0 =>y=2
Case 2: y<0
-5y-10=0 =>y=-2
But y>0. So, y=2 SUFFICIENT
IMO answer is option B
04 Dec 2018, 19:22
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Harshgmat
\(?\,\, = \,\,\left| {y \cdot \left( {y - 3} \right)} \right|\)
\(\left( 1 \right)\,\,\left| y \right| - 7 = 0\,\,\,{\rm{or}}\,\,\,y + 5 = 0\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,y = 7\,\,\,\, \Rightarrow \,\,\,\,? = 28 \hfill \cr \\
\,{\rm{Take}}\,\,y = - 7\,\,\,\, \Rightarrow \,\,\,\,? = 70 \hfill \cr} \right.\)
\(\left( 2 \right)\,\,\left\{ \matrix{\\
\,\left| y \right| = 2 \hfill \cr \\
\,y > 0 \hfill \cr} \right.\,\,\,\, \Rightarrow \,\,\,\,y = 2\,\,\,\, \Rightarrow \,\,\,\,? = 2\)
The correct answer is therefore (B).
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
