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# In the equality above, if A,B, C are positive integers. What is the va

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
In the equality above, if A,B, C are positive integers. What is the va  [#permalink]

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26 Feb 2019, 11:29
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Difficulty:

55% (hard)

Question Stats:

50% (02:33) correct 50% (02:36) wrong based on 8 sessions

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GMATH practice exercise (Quant Class 1)

$${{71} \over {11}} = A + {1 \over {B + {{\left( {C + 1} \right)}^{ - 1}}}}$$

In the equality above, $$A,B,C$$ are positive integers. What is the value of $$2A+3B-4C$$ ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: In the equality above, if A,B, C are positive integers. What is the va  [#permalink]

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27 Feb 2019, 07:43
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fskilnik wrote:
GMATH practice exercise (Quant Class 1)

$${{71} \over {11}} = A + {1 \over {B + {{\left( {C + 1} \right)}^{ - 1}}}}$$

In the equality above, $$A,B,C$$ are positive integers. What is the value of $$2A+3B-4C$$ ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

$$A,B,C\,\, \ge 1\,\,\,{\rm{ints}}\,\,\,\left( * \right)$$

$${{71} \over {11}} = A + {1 \over {B + {{\left( {C + 1} \right)}^{ - 1}}}}$$

$$? = 2A + 3B - 4C$$

$$\left. \matrix{ B + {1 \over {C + 1}}\,\,\mathop > \limits^{\left( * \right)} \,\,1\,\,\,\,\, \Rightarrow \,\,\,\,\,0 < \,{1 \over {B + {{\left( {C + 1} \right)}^{ - 1}}}} < 1\,\,\,\, \hfill \cr {{71} \over {11}} = {{66 + 5} \over {11}} = 6 + {5 \over {11}} \hfill \cr} \right\}\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,A = 6$$

$$\left. \matrix{ {5 \over {11}} = {1 \over {B + {{\left( {C + 1} \right)}^{ - 1}}}}\,\,\,\,\, \Rightarrow \,\,\,\,\,B + {1 \over {C + 1}}\,\, = {{11} \over 5}\,\,\, \hfill \cr C + 1\,\,\mathop > \limits^{\left( * \right)} \,\,1\,\,\,\, \Rightarrow \,\,\,\,\,0 < {1 \over {C + 1}} < 1 \hfill \cr {{11} \over 5} = {{10 + 1} \over 5} = 2 + {1 \over 5} \hfill \cr} \right\}\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,B = 2$$

$${1 \over 5} = {1 \over {C + 1}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,C = 4$$

$$? = 2\left( 6 \right) + 3\left( 2 \right) - 4\left( 4 \right) = 2$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: In the equality above, if A,B, C are positive integers. What is the va   [#permalink] 27 Feb 2019, 07:43
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