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Given a positive integer c, how many integers are greater [#permalink]
07 Oct 2017, 10:05
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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. \(c + 1\)
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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 C1 = 21= 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 c1.



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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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answer: C 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, …, 2c1. So there are (2c1)(c+1)+1 = c1 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. FatemehAsgarinejad wrote: answer: C 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, …, 2c1. 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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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. Answer: C
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Re: Given a positive integer c, how many integers are greater
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10 May 2018, 06:43





