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Vasya wrote down several consecutive integers

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Joined: 11 Jul 2015
Posts: 1
Vasya wrote down several consecutive integers  [#permalink]

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11 Jul 2015, 21:48
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75% (hard)

Question Stats:

47% (02:06) correct 53% (01:50) wrong based on 98 sessions

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Vasya wrote down several consecutive integers. Which of the following could not be the percentage of odd numbers among them?

(A) 40
(B) 45
(C) 48
(D) 50
(E) 60
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Joined: 02 Aug 2009
Posts: 8632
Vasya wrote down several consecutive integers  [#permalink]

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11 Jul 2015, 22:58
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A2A2 wrote:
Vasya wrote down several consecutive integers. Which of the following could not be the percentage of odd numbers among them?

(A) 40
(B) 45
(C) 48
(D) 50
(E) 60

what you have to check is if the (answer given: 100-answer given) is either equal or two consecutive values..
reason for this is that there are only three possiblities of numbers of odd numbers in consecutive integers
1) equal to number of even numbers
2)one more than number of even numbers
3)one more than number of even numbers

(A) 40:60=2:3 possible
(B) 45:55=9:11not possible
(C) 48:52=12:13 possible
(D) 50:50=1:1 possible
(E) 60:40=3:2 possible
ans B
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Vasya wrote down several consecutive integers  [#permalink]

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11 Jul 2015, 23:03
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A2A2 wrote:
Vasya wrote down several consecutive integers. Which of the following could not be the percentage of odd numbers among them?

(A) 40
(B) 45
(C) 48
(D) 50
(E) 60

Case 1: Either no. of odd Numbers will be equal to No. of Even Integers i.e. 50%
Case 2: Or no. of odd Numbers will be ONE Greater than No. of Even Integers i.e. (a)*100/(2a-1)
Case 3: Or no. of odd Numbers will be ONE Less than No. of Even Integers i.e. (a)*100/(2a+1)

Option A: 40% = 40/100 = 2/5 i.e. (a)*100/(2a+1) i.e. POSSIBLE
Option B: 45% = 45/100 = 9/20 i.e. NOT POSSIBLE
Option C: 48% = 48/100 = 12/25 i.e. (a)*100/(2a+1) i.e. POSSIBLE
Option D: 50% i.e. POSSIBLE
Option E: 40% = 60/100 = 3/5 i.e. (a)*100/(2a-1) i.e. POSSIBLE

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Re: Vasya wrote down several consecutive integers  [#permalink]

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25 Jun 2016, 22:59
A2A2 wrote:
Vasya wrote down several consecutive integers. Which of the following could not be the percentage of odd numbers among them?

(A) 40
(B) 45
(C) 48
(D) 50
(E) 60

Quick approach..

Well I started solving with the approach that everybody has followed here..but midway..I realized something..
Let's start..

There are in total Three possibilities

1. Odd and Even numbers are equal --> So (D) out.

2. Even numbers one more than Odd numbers

So Odd numbers by Total numbers..

$$\frac{x}{2x+1}$$

3. Odd Numbers one more than Even numbers..

$$\frac{x+1}{2x+1}$$

So the percentage values in both the cases will respectively be..

$$\frac{x}{2x+1}*100 = N$$

$$\frac{x+1}{2x+1}*100 = N$$

In both the expressions, the numerator and denominator of x terms will never have any common factor(as you can easily see in the first that the denominator will leave a remainder of 1 when divided by the numerator, so no canceling out will be possible; and in the second the numerator and denominator are consecutive integers, with denominator being an odd number).
Thus, 2x+1 has to be Odd and a factor of 100 for N to be an integer, in other words it will be an odd multiple of 5 that also divides 100. What's important to notice is that the expression

$$\frac{100}{2x+1}$$ will always give us an Even Integer.

Thus, N can never be an odd number, and your answer is (B)
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Re: Vasya wrote down several consecutive integers  [#permalink]

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11 Aug 2019, 07:48
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Re: Vasya wrote down several consecutive integers   [#permalink] 11 Aug 2019, 07:48