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07 Mar 2010, 16:17
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Please kindly provide explanations. Thanks
1. How many hours did it take Helen to drive from her house to her parent's house?
(1) Helen's average speed on this trip was 72km/hr
(2) If Helen's average speed on this trip had been 8km/hr greater, it would have taken her 1 hour less.
2. Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p?
(1) Lines n and p intersect at the point (5,1).
(2) The y-intercept of line n is greater than the y-intercept of line p.
1. How many hours did it take Helen to drive from her house to her parent's house?
(1) Helen's average speed on this trip was 72km/hr
(2) If Helen's average speed on this trip had been 8km/hr greater, it would have taken her 1 hour less.
2. Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p?
(1) Lines n and p intersect at the point (5,1).
(2) The y-intercept of line n is greater than the y-intercept of line p.
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08 Mar 2010, 02:22
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gmatgg
1.
IMO C
1 insuff. 2 insuff.
1 and 2
D = R*T
(72 + 8) * t1 = 72 * (t1 + 1)
80t1 -72t1 = 72 Suff.
2. IMO C
I used drawing approach.
I found the question already solved using the same approach.
ds-geometry-30553.html#p207853
08 Mar 2010, 02:37
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1. How many hours did it take Helen to drive from her house to her parent's house?
(1) Helen's average speed on this trip was 72km/hr
(2) If Helen's average speed on this trip had been 8km/hr greater, it would have taken her 1 hour less.
\(d=rt\), where \(d\) is the distance covered, \(r\) rate and \(t\) time. Question: \(t=?\)
(1) \(r=72\). Clearly not sufficient.
(2) \((r+8)(t-1)=d\). Clearly not sufficient.
(1)+(2) \(r=72\) and \((r+8)(t-1)=d\) --> \(80(t-1)=d\) --> \(d=80(t-1)=rt=72t\) --> \(8t=80\) --> \(t=10\). Sufficient.
Answer: C.
2. Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p?
We have two lines: \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true?
(1) Lines n and p intersect at the point (5,1) --> \(1=5m_1+b_1=5m_2+b_2\) --> \(5(m_1-m_2)=b_2-b_1\). Not sufficient.
(2) The y-intercept of line \(n\) is greater than the y-intercept of line \(p\) --> y-intercept is value of \(y\) for \(x=0\), so it's the value of \(b\) --> \(b_1>b_2\) or \(b_2-b_1<0\). Not sufficient.
(1)+(2) \(5(m_1-m_2)=b_2-b_1\), as from (2) \(b_2-b_1<0\) (RHS), then LHS (left hand side) also is less than zero \(5(m_1-m_2)<0\) --> \(m_1-m_2<0\) --> \(m_1<m_2\). Sufficient.
Answer: C.
(1) Helen's average speed on this trip was 72km/hr
(2) If Helen's average speed on this trip had been 8km/hr greater, it would have taken her 1 hour less.
\(d=rt\), where \(d\) is the distance covered, \(r\) rate and \(t\) time. Question: \(t=?\)
(1) \(r=72\). Clearly not sufficient.
(2) \((r+8)(t-1)=d\). Clearly not sufficient.
(1)+(2) \(r=72\) and \((r+8)(t-1)=d\) --> \(80(t-1)=d\) --> \(d=80(t-1)=rt=72t\) --> \(8t=80\) --> \(t=10\). Sufficient.
Answer: C.
2. Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p?
We have two lines: \(y_n=m_1x+b_1\) and \(y_p=m_2x+b_2\). Q: \(m_1<m_2\) true?
(1) Lines n and p intersect at the point (5,1) --> \(1=5m_1+b_1=5m_2+b_2\) --> \(5(m_1-m_2)=b_2-b_1\). Not sufficient.
(2) The y-intercept of line \(n\) is greater than the y-intercept of line \(p\) --> y-intercept is value of \(y\) for \(x=0\), so it's the value of \(b\) --> \(b_1>b_2\) or \(b_2-b_1<0\). Not sufficient.
(1)+(2) \(5(m_1-m_2)=b_2-b_1\), as from (2) \(b_2-b_1<0\) (RHS), then LHS (left hand side) also is less than zero \(5(m_1-m_2)<0\) --> \(m_1-m_2<0\) --> \(m_1<m_2\). Sufficient.
Answer: C.
