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If m is an odd integer, which of the following expresses the number of

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If m is an odd integer, which of the following expresses the number of  [#permalink]

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New post 01 Nov 2018, 01:00
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

59% (01:16) correct 41% (01:24) wrong based on 104 sessions

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If m is an odd integer, which of the following expresses the number of  [#permalink]

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New post 01 Nov 2018, 01:19
Bunuel wrote:
If m is an odd integer, which of the following expresses the number of even integers between m and 2m inclusive?


A. m/2 + 1

B. m/2 - 1

C. (m + 1)/2

D. (m - 1)/2

E. 2m + 1



let. m = 1

Number of integers between m and 2m (inclusive) i.e. between 1 and 2 = 1

@m = 1

A. m/2 + 1 = 1/2 +1 = 1.5 INCORRECT

B. m/2 - 1 = 1/2 -1 = -0.5 INCORRECT

C. (m + 1)/2= 1+1/2 = 1 Potentially CORRECT

D. (m - 1)/2= (1-1)/2 = 0 INCORRECT

E. 2m + 1 = 1*2 +1 = 3 INCORRECT


Answer: Option C
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Re: If m is an odd integer, which of the following expresses the number of  [#permalink]

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New post 01 Nov 2018, 02:52
Let M = 3

M & 2M = 3 & 6 = There are 2 even integers(4 & 6) between 3 and 6 inclusive.

C. (M+1)/2 = (3+1)/2 = 4/2 = 2

IMO C
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Re: If m is an odd integer, which of the following expresses the number of  [#permalink]

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New post 01 Nov 2018, 09:40
Another way to quickly eliminate options instead of substituting values in all options:
m is odd, so m/2 is not an integer, so eliminate A, B
We are asked number of even integers between m and 2m, we know the number of even integers cannot be 2m+1, since 2m + 1 is larger than 2m, eliminate E

Then check with m = 1, 2m = 2 for C and D, turns out C is the right answer.

Hence Option C!
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Re: If m is an odd integer, which of the following expresses the number of  [#permalink]

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New post 01 Nov 2018, 10:20
Bunuel wrote:
If m is an odd integer, which of the following expresses the number of even integers between m and 2m inclusive?


A. m/2 + 1

B. m/2 - 1

C. (m + 1)/2

D. (m - 1)/2

E. 2m + 1


i picked number 3 also tested 5 in both cases C was correct
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Re: If m is an odd integer, which of the following expresses the number of  [#permalink]

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New post 01 Nov 2018, 10:31
If m is an odd integer, which of the following expresses the number of even integers between m and 2m inclusive?


A. m/2 + 1

B. m/2 - 1

C. (m + 1)/2

D. (m - 1)/2

E. 2m + 1

Assume value of m to be 3 , so m+2m = 3-6 total 2 even integers , now using value of m check in options where we are getting value as 2 , only option C suffices
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Re: If m is an odd integer, which of the following expresses the number of  [#permalink]

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New post 01 Nov 2018, 10:54
is this really a 600 level question ?
just asking
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Re: If m is an odd integer, which of the following expresses the number of  [#permalink]

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New post 06 Nov 2018, 05:47
The best way to do this question is from the math book notes:

# of terms: (last term - first term)/2 + 1; we use 2 as a divisor since we are looking for even numbers.

last term: 2m
first term: m+1 (since m is odd)

plug and chug and you get (m+1)/2
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If m is an odd integer, which of the following expresses the number of  [#permalink]

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New post 06 Nov 2018, 14:32
Bunuel wrote:
If m is an odd integer, which of the following expresses the number of even integers between m and 2m inclusive?


A. m/2 + 1

B. m/2 - 1

C. (m + 1)/2

D. (m - 1)/2

E. 2m + 1


looking at ratios of number of even integers, e, to m:
1:1
2:3
3:5
note that e=(m+1)/2
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If m is an odd integer, which of the following expresses the number of   [#permalink] 06 Nov 2018, 14:32
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