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

Question

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

Skywalker18 · Accepted Answer

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 !!

TheKingInTheNorth · Answer

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

BrainLab · Answer

-5,-4,-3,-2,-1,0,1,2 Answer (C)

Skywalker18 · Answer

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

colorblind · Answer

Hey Skywalker,

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

KariLouise · Answer

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!

Bunuel · Answer

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

AyushCrackVerbal · Answer

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

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=IYNfx2meiJo

ScottTargetTestPrep · Answer

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

GMATinsight · Answer

Answer: Option C

Video solution by  GMATinsight

https://www.youtube.com/watch?v=6njo6_JQKmA

Wei915 · Answer

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?

Bunuel · Answer

_______________________
No, GMAT does not have its own "math", so I think it's just a typo there.

raghav1708 · Answer

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

Thanks  Bunuel

Bunuel · Answer

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.
 https://gmatclub.com/forum/download/file.php?id=68099

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  
     Theory   
 Math: Number Theory 
 Number Properties: Tips and hints 
 Advanced Number Properties on GMAT (All 5 parts) 
 Do you make these 3 mistakes in GMAT Even-Odd Questions?  
 Everything about Factorials on the GMAT 
 Solving Complex Problems Using Number Line 
     Questions   
 Tough New Set: Number Properties Set 
 Power of a Number in a Factorial Problems 
 Number Properties Ability Quiz 
 Special Numbers and Sequences Problems 
 The E-GMAT Number Properties Knockout: 10 Great 700+ Ques for you! 
 Trailing Zeros Problems 
 DS Questions 
 PS Questions

For more check  Ultimate GMAT Quantitative Megathread

Hope it helps.

raghav1708 · Answer

Thank you for the help  Bunuel ! Loved the explanation! 
Thank you!

wadhwakaran · Answer

-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

bumpbot · Answer

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

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