If a/b > 4, is a > 8?
(1) b > 2
(2) a > 7
[spoiler]OA=A[/spoiler]
Source: Princeton Review
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If a/b > 4, is a > 8?
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Jay@ManhattanReview
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Given: a/b > 4VJesus12 wrote:If a/b > 4, is a > 8?
(1) b > 2
(2) a > 7
[spoiler]OA=A[/spoiler]
Source: Princeton Review
We have to determine whether a > 8.
Let's take each statement one by one.
(1) b > 2
Given b > 2 means that b is positive, thus, we can multiply b to both the sides of a/b > 4.
Thus, we have a/b > 4 => (a/b)*b > 4*b => a > 4b. Say b = 2.001, then a > 4*2.001 => a > 8. Suiificient.
(2) a > 7
Case 1: Say a = 7.5 < 8. Thus, from a/b > 4, we have 7.5/b > 4 => 7.5/4 > b. Since b can have any value, it is a valid case. The answer is No.
Case 2: Say a = 10. Thus, from a/b > 4, we have 10/b > 4 => 10/4 > b. Since b can have any value, it is a valid case. The answer is Yes.
No unique answer. Insufficient.
The correct answer: A
Hope this helps!
-Jay
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fskilnik@GMATH
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$${a \over b} > 4$$VJesus12 wrote:If a/b > 4, is a > 8?
(1) b > 2
(2) a > 7
Source: Princeton Review
$$a\,\,\mathop > \limits^? \,\,8$$
$$\left( 1 \right)\,\,\,\left\{ \matrix{
\,b > 2 \hfill \cr
\,{a \over b} > 4 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,a\,\,\, = \,\,\,b \cdot {a \over b}\,\,\, > \,\,\,2 \cdot 4\,\,\, = \,\,\,8\,\,\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.\,\,$$
$$\left( 2 \right)\,\,a > 7\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {8,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {9,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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