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In a certain sequence of 8 numbers, each number after the first is 1

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Bunuel
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In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   15 Oct 2015, 21:56
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In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?

(A) None
(B) One
(C) Two
(D) Three
(E) Four
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C
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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   31 Dec 2015, 00:09
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colorblind wrote:
Skywalker18 wrote:
First term , a1 = -5
Common difference ,d =1
An= a1+(n-1)d
0 = -5 +(n-1)1 = -5 + n - 1 = n - 6
=> n = 6
Therefore, the number of terms which are positive is 8-6 =2

The list is -5 , -4 , -3 , -2 , -1 , 0 , 1 , 2
Number of terms which are positive = 2

Hey Skywalker,

appreciate if you could explain the first part of your solution??


Hi colorblind ,
Please find the highlighted explanation in Blue .

First term , a1 = -5
Common difference ,d =1 (each number after the first is 1 more than the previous number )
The below is the formula for A.P
An= a1+(n-1)d
To find number of positive terms in the sequence we need to need number of integers equal to or less than 0.
So , i have calculated the position of 0 in the sequence . Zero is the 6th term in the sequence
0 = -5 +(n-1)1 = -5 + n - 1 = n - 6
=> n = 6
Therefore, the number of terms which are positive is 8-6 =2

Hope it helps !! :)
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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   16 Oct 2015, 02:39
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First term , a1 = -5
Common difference ,d =1
An= a1+(n-1)d
0 = -5 +(n-1)1 = -5 + n - 1 = n - 6
=> n = 6
Therefore, the number of terms which are positive is 8-6 =2

The list is -5 , -4 , -3 , -2 , -1 , 0 , 1 , 2
Number of terms which are positive = 2
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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   16 Oct 2015, 22:51
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In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?

(A) None
(B) One
(C) Two
(D) Three
(E) Four

In GMAT Zero is considered as an integer which is neither positive nor negative.

Non - Negative ( zero to positive infinity )

Solution to the question :
-5,-4,-3,-2,-1,0 , 1,2

Hence ans is 2 ..option C
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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   21 Aug 2022, 05:24
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raghav1708 wrote:
Bunuel wrote:
In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?

(A) None
(B) One
(C) Two
(D) Three
(E) Four


Hi Bunuel
Why are we not counting Zero?, Zero is a positive Integer, right?

Thanks Bunuel


Every real number other than zero is either positive or negative. Numbers to the left of 0 are negative and numbers to the right of 0 are positive.


Notice that:
  • Zero is neither positive nor negative (the only one of this kind)!


ZERO:

1. Zero is an INTEGER.

2. Zero is an EVEN integer.

3. Zero is neither positive nor negative (the only one of this kind)

4. Zero is divisible by EVERY integer except 0 itself (\(\frac{x}{0} = 0\), so 0 is a divisible by every number, x).

5. Zero is a multiple of EVERY integer (\(x*0 = 0\), so 0 is a multiple of any number, x)

6. Zero is NOT a prime number (neither is 1 by the way; the smallest prime number is 2).

7. Division by zero is NOT allowed: anything/0 is undefined.

8. Any non-zero number to the power of 0 equals 1 (\(x^0 = 1\))

9. \(0^0\) case is NOT tested on the GMAT.

10. If the exponent n is positive (n > 0), \(0^n = 0\).

11. If the exponent n is negative (n < 0), \(0^n\) is undefined, because \(0^{negative}=0^n=\frac{1}{0^{(-n)}} = \frac{1}{0}\), which is undefined. You CANNOT take 0 to the negative power.

12. \(0! = 1! = 1\).



2. Properties of Integers



For more check Ultimate GMAT Quantitative Megathread



Hope it helps.
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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   15 Oct 2015, 23:55
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Bunuel wrote:
In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?

(A) None
(B) One
(C) Two
(D) Three
(E) Four


Kudos for a correct solution.

-5,-4,-3,-2,-1,0,1,2 Answer (C)
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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   10 Jan 2016, 10:55
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KariLouise wrote:
Hi Bunuel, thank you for your valuable posts, they are well explained and very complete! I have one question about 0 number in the GMAT: According to GMAT rules, 0 is considered as non negative and non positive, but in this example above, it is considered as positive number. Could you please exaplin me in which conditions can we consider it as positive?
Also, is it an even or odd number?
Thank you for your help!


Where above is 0 considered as positive???

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Check more here: number-properties-tips-and-hints-174996.html
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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   01 May 2021, 07:14
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Bunuel wrote:
In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?

(A) None
(B) One
(C) Two
(D) Three
(E) Four

Solution:

According to the rule of the sequence, we can see that the 8 numbers are:

-5, -4, -3, -2, -1, 0, 1, and 2

Recalling that 0 is neither positive nor negative, we see that there are two positive numbers in the sequence.

Answer: C
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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   30 Dec 2015, 23:47
Skywalker18 wrote:
First term , a1 = -5
Common difference ,d =1
An= a1+(n-1)d
0 = -5 +(n-1)1 = -5 + n - 1 = n - 6
=> n = 6
Therefore, the number of terms which are positive is 8-6 =2

The list is -5 , -4 , -3 , -2 , -1 , 0 , 1 , 2
Number of terms which are positive = 2

Hey Skywalker,

appreciate if you could explain the first part of your solution??
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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   10 Jan 2016, 10:12
Hi Bunuel, thank you for your valuable posts, they are well explained and very complete! I have one question about 0 number in the GMAT: According to GMAT rules, 0 is considered as non negative and non positive, but in this example above, it is considered as positive number. Could you please exaplin me in which conditions can we consider it as positive?
Also, is it an even or odd number?
Thank you for your help!
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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   01 Jun 2019, 21:17
Expert Reply
Given:

The first number in a sequence is -5 and each number after the first is 1 more than the previous number.

So the sequence would be :

-5 , -4 , -3 , -2 , -1 , 0 , 1 , 2 (8 numbers are there in the sequence)

There are only two positive numbers in the sequence: 1 and 2 ( 0 is neither positive nor negative )

The correct answer is C
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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   16 Feb 2021, 08:59
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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   07 May 2021, 21:51
Expert Reply
Bunuel wrote:
In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?

(A) None
(B) One
(C) Two
(D) Three
(E) Four


Wanna make solving the Official Questions interesting???


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Answer: Option C

Video solution by GMATinsight



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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   05 Mar 2022, 04:20
Hi all, I've encountered a similar question in the official EA prep that asks "how many of the numbers in the sequence are exact", instead of the more commonly understood question "how many of the numbers in the sequence are positive". Does "exact" mean "positive" in the GMAT or EA?
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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   05 Mar 2022, 04:25
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Wei915 wrote:
Hi all, I've encountered a similar question in the official EA prep that asks "how many of the numbers in the sequence are exact", instead of the more commonly understood question "how many of the numbers in the sequence are positive". Does "exact" mean "positive" in the GMAT or EA?

_______________________
No, GMAT does not have its own "math", so I think it's just a typo there.
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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   21 Aug 2022, 05:19
Bunuel wrote:
In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?

(A) None
(B) One
(C) Two
(D) Three
(E) Four


Hi Bunuel
Why are we not counting Zero?, Zero is a positive Integer, right?

Thanks Bunuel
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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   21 Aug 2022, 22:42
Bunuel wrote:
raghav1708 wrote:
Bunuel wrote:
In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?

(A) None
(B) One
(C) Two
(D) Three
(E) Four


Hi Bunuel
Why are we not counting Zero?, Zero is a positive Integer, right?

Thanks Bunuel


Every real number other than zero is either positive or negative. Numbers to the left of 0 are negative and numbers to the right of 0 are positive.


Notice that:
  • Zero is neither positive nor negative (the only one of this kind)!


ZERO:

1. Zero is an INTEGER.

2. Zero is an EVEN integer.

3. Zero is neither positive nor negative (the only one of this kind)

4. Zero is divisible by EVERY integer except 0 itself (\(\frac{x}{0} = 0\), so 0 is a divisible by every number, x).

5. Zero is a multiple of EVERY integer (\(x*0 = 0\), so 0 is a multiple of any number, x)

6. Zero is NOT a prime number (neither is 1 by the way; the smallest prime number is 2).

7. Division by zero is NOT allowed: anything/0 is undefined.

8. Any non-zero number to the power of 0 equals 1 (\(x^0 = 1\))

9. \(0^0\) case is NOT tested on the GMAT.

10. If the exponent n is positive (n > 0), \(0^n = 0\).

11. If the exponent n is negative (n < 0), \(0^n\) is undefined, because \(0^{negative}=0^n=\frac{1}{0^{(-n)}} = \frac{1}{0}\), which is undefined. You CANNOT take 0 to the negative power.

12. \(0! = 1! = 1\).



2. Properties of Integers



For more check Ultimate GMAT Quantitative Megathread



Hope it helps.



Thank you for the help Bunuel! Loved the explanation!
Thank you!
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Re: In a certain sequence of 8 numbers, each number after the first is 1 [#permalink] New post   21 Aug 2022, 23:04
-5,-4, -3, -2, -1, 0, 1, 2

since 0 is neither positive nor negative
the only positive integers are 1 and 2 (2 in number)
Therefore, option C
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