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If A>B are two odd numbers, how many even numbers are the

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If A>B are two odd numbers, how many even numbers are the

by fskilnik@GMATH » Sun Mar 17, 2019 12:29 pm

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GMATH practice exercise (Quant Class 16)

If A>B are two odd numbers, how many even numbers are there between them?

(A) (A+B)/2
(B) A-B+1
(C) A-B
(D) A-B-1
(E) (A-B)/2

Answer: [spoiler]_____(E)__[/spoiler]
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by fskilnik@GMATH » Sun Mar 17, 2019 4:33 pm
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 16)

If A>B are two odd numbers, how many even numbers are there between them?

(A) (A+B)/2
(B) A-B+1
(C) A-B
(D) A-B-1
(E) (A-B)/2
$$?\,\, = \,\,\# \,\,{\rm{even}}\,\,{\rm{numbers}}\,\,{\rm{in}}\,\,\left[ {B,A} \right]\,\,\,\,\,\,\left( {B < A\,,\,\,{\rm{odds}}} \right)$$

First Approach ("the smart way"):

$${\rm{Take}}\,\,\left( {B,A} \right) = \left( {1,5} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{Target}} = 2\,\,\,\,\,\left[ {2,4} \right]$$
$$\left. \matrix{
\left( A \right)\,\,3\,\,\, \to \,\,\,{\rm{refuted}} \hfill \cr
\left( B \right)\,\,5\,\,\, \to \,\,\,{\rm{refuted}} \hfill \cr
\left( C \right)\,\,4\,\,\, \to \,\,\,{\rm{refuted}} \hfill \cr
\left( D \right)\,\,3\,\,\, \to \,\,\,{\rm{refuted}}\,\,\, \hfill \cr} \right\}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( E \right)\,\,\,{\rm{by}}\,\,{\rm{exclusion}}$$

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


Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by fskilnik@GMATH » Sun Mar 17, 2019 4:35 pm
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 16)

If A>B are two odd numbers, how many even numbers are there between them?

(A) (A+B)/2
(B) A-B+1
(C) A-B
(D) A-B-1
(E) (A-B)/2
$$?\,\, = \,\,\# \,\,{\rm{even}}\,\,{\rm{numbers}}\,\,{\rm{in}}\,\,\left[ {B,A} \right]\,\,\,\,\,\,\left( {B < A\,,\,\,{\rm{odds}}} \right)$$

Second Approach ("the technical way"):

$$? = \# \,\,{\rm{even}}\,\,{\rm{numbers}}\,\,{\rm{in}}\,\,I = \left[ {B,A - 1} \right] = \,\,{1 \over 2}\left( {{\rm{\# }}\,\,{\rm{integers}}\,\,{\rm{in}}\,\,I} \right)$$
$$\left( {{\rm{\# }}\,\,{\rm{integers}}\,\,{\rm{in}}\,\,I} \right)\,\, = \,\,\left( {A - 1 - B} \right) + 1 = A - B\,\,\,\,\,\,\,\left[ {{\rm{fingers}}\,\,{\rm{technique}}} \right]$$
$$? = {{A - B} \over 2}$$

The correct answer is (E).


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

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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