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

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GMATH Teacher
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Joined: 12 Oct 2010
Posts: 935
If A>B are two odd numbers, how many even numbers are there between A  [#permalink]

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17 Mar 2019, 13:41
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Difficulty:

15% (low)

Question Stats:

76% (00:54) correct 24% (01:05) wrong based on 34 sessions

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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

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Re: If A>B are two odd numbers, how many even numbers are there between A  [#permalink]

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17 Mar 2019, 16:32
Odd number: $$2n + 1$$.

Since $$A > B$$, the difference $$A - B$$ indicates all the numbers between them. $$\frac{A - B}{2}$$ indicates all the even numbers between $$A$$ and $$B$$.
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: If A>B are two odd numbers, how many even numbers are there between A  [#permalink]

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17 Mar 2019, 17:41
fskilnik 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)
Our high-level "quant" preparation starts here: https://gmath.net
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: If A>B are two odd numbers, how many even numbers are there between A  [#permalink]

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17 Mar 2019, 17:44
fskilnik 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

Second Approach ("the technical way"):

$$?\,\, = \,\,\# \,\,{\rm{even}}\,\,{\rm{numbers}}\,\,{\rm{in}}\,\,\left[ {B,A} \right]\,\,\,\,\,\,\left( {B < A\,,\,\,{\rm{odds}}} \right)$$

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

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

$$? = {{A - B} \over 2}$$

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: If A>B are two odd numbers, how many even numbers are there between A   [#permalink] 17 Mar 2019, 17:44
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