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# Given a positive integer c, how many integers are greater

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Given a positive integer c, how many integers are greater [#permalink]  07 Oct 2017, 10:05
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Question Stats:

73% (00:41) correct 26% (01:16) wrong based on 15 sessions

Given a positive integer $$c$$, how many integers are greater than c and less than $$2c$$?

A. $$\frac{c}{2}$$

B. $$c$$

C. $$c - 1$$

D. $$c - 2$$

E. $$c + 1$$
[Reveal] Spoiler: OA

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Re: Given a positive integer c, how many integers are greater [#permalink]  09 Oct 2017, 02:00
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Carcass wrote:

Given a positive integer $$c$$, how many integers are greater than c and less than $$2c$$?

A. $$\frac{c}{2}$$

B. $$c$$

C. $$c - 1$$

D. $$c - 2$$

E. $$c + 1$$

Now if we consider C= 2 then

we need a integer greater than 2 and less than 4

There is only one ans i.e 3.

Now to find the ans corresponding to the option we have option C because C-1 = 2-1= 1 i.e we have one option.

If we take other positive integer we will have the same answer i. e option C
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Re: Given a positive integer c, how many integers are greater [#permalink]  22 Feb 2018, 16:08
c+c=2c
2c is exclusive;therefore, subtract 1 from c. answer c-1.
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Re: Given a positive integer c, how many integers are greater [#permalink]  22 Feb 2018, 17:38
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Consider c as 1, then c = 1 and 2c = 2: 0 integer is between 1 and 2, Thus C is correct.
Consider c as 2, then c = 2 and 2c = 4: 1 integer is between 2 and 4 (3), Thus C is correct.
*We know that 2c = c + c. All the values between c and 2c are c+1, c+2, …, 2c-1. So there are (2c-1)-(c+1)+1 = c-1 integers between c and 2c.

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Last edited by Fatemeh on 23 Feb 2018, 12:24, edited 1 time in total.
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Re: Given a positive integer c, how many integers are greater [#permalink]  22 Feb 2018, 23:17
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Very nicely explained. Thanks.

Consider c as 1, then c = 1 and 2c = 2: 0 integer is between 1 and 2, Thus C is correct.
Consider c as 2, then c = 2 and 2c = 4: 1 integer is between 2 and 4 (3), Thus C is correct.
*We know that 2c = c + c. All the values between c and 2c are c+1, c+2, …, 2c-1. So there are integers between c and 2c.
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Re: Given a positive integer c, how many integers are greater [#permalink]  10 May 2018, 06:43
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Expert's post
Carcass wrote:

Given a positive integer $$c$$, how many integers are greater than c and less than $$2c$$?

A. $$\frac{c}{2}$$

B. $$c$$

C. $$c - 1$$

D. $$c - 2$$

E. $$c + 1$$

Recall that the number of integers between two integers a and b, inclusive, is b - a + 1. However, here we want the numbers of integers between c and 2c, excluding themselves. Therefore, the number of integers is 2c - c + 1 - 2 = c - 1. Note that we subtracted 2 on the left side of the equation because we needed to exclude the endpoint values c and 2c.

Alternate Solution:

We can express the integers between c and 2c as c + 1, c + 2, … , c + (c - 1). Since c + 1 is the first integer, c + 2 is the second integer and so on, c + (c - 1) is the c - 1st integer.

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Re: Given a positive integer c, how many integers are greater   [#permalink] 10 May 2018, 06:43
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