GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
The product of the sum of five positive integers and the sum of 8 nega
[#permalink]
05 Jul 2023, 03:39
05 Jul 2023, 03:39
Expert Reply
1
Bookmarks
00:00
Question Stats:
28% (01:19) correct
71% (01:14) wrong based on 14 sessions
Hide Show timer Statistics
The product of the sum of five positive integers and the sum of 8 negative integers is odd. If all 13 integers are different, what can be the maximum possible number of odd integers?
A. 5
B. 7
C. 9
D. 12
E. 13
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE NUMBER PROPERTIES
A. 5
B. 7
C. 9
D. 12
E. 13
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE NUMBER PROPERTIES
Re: The product of the sum of five positive integers and the sum of 8 nega
[#permalink]
10 Jul 2023, 23:08
10 Jul 2023, 23:08
1
To find the maximum possible number of odd integers among the 13 given integers, we need to consider the product of the sum of five positive integers and the sum of eight negative integers being odd.
For the product of two numbers to be odd, at least one of the numbers must be odd. Therefore, we need to maximize the number of odd integers in both the positive and negative integers.
Since we have a total of 13 integers, let's consider the extremes for the number of odd integers in each group:
Maximum number of odd integers among the positive integers:
To maximize the number of odd integers, we can have all five positive integers as odd. This gives us a maximum of 5 odd integers among the positive integers.
Maximum number of odd integers among the negative integers:
To maximize the number of odd integers, we can have all eight negative integers as odd. This gives us a maximum of 8 odd integers among the negative integers.
Now, let's calculate the maximum possible number of odd integers in total:
Maximum number of odd integers = Number of odd integers in positive integers + Number of odd integers in negative integers
= 5 + 8
= 13
Therefore, the maximum possible number of odd integers among the 13 given integers is 13.
Hence, the answer is E) 13.
Posted from my mobile device
For the product of two numbers to be odd, at least one of the numbers must be odd. Therefore, we need to maximize the number of odd integers in both the positive and negative integers.
Since we have a total of 13 integers, let's consider the extremes for the number of odd integers in each group:
Maximum number of odd integers among the positive integers:
To maximize the number of odd integers, we can have all five positive integers as odd. This gives us a maximum of 5 odd integers among the positive integers.
Maximum number of odd integers among the negative integers:
To maximize the number of odd integers, we can have all eight negative integers as odd. This gives us a maximum of 8 odd integers among the negative integers.
Now, let's calculate the maximum possible number of odd integers in total:
Maximum number of odd integers = Number of odd integers in positive integers + Number of odd integers in negative integers
= 5 + 8
= 13
Therefore, the maximum possible number of odd integers among the 13 given integers is 13.
Hence, the answer is E) 13.
Posted from my mobile device
Re: The product of the sum of five positive integers and the sum of 8 nega
[#permalink]
05 Oct 2023, 09:47
05 Oct 2023, 09:47
Jakelong wrote:
To find the maximum possible number of odd integers among the 13 given integers, we need to consider the product of the sum of five positive integers and the sum of eight negative integers being odd.
For the product of two numbers to be odd, at least one of the numbers must be odd. Therefore, we need to maximize the number of odd integers in both the positive and negative integers.
Since we have a total of 13 integers, let's consider the extremes for the number of odd integers in each group:
Maximum number of odd integers among the positive integers:
To maximize the number of odd integers, we can have all five positive integers as odd. This gives us a maximum of 5 odd integers among the positive integers.
Maximum number of odd integers among the negative integers:
To maximize the number of odd integers, we can have all eight negative integers as odd. This gives us a maximum of 8 odd integers among the negative integers.
Now, let's calculate the maximum possible number of odd integers in total:
Maximum number of odd integers = Number of odd integers in positive integers + Number of odd integers in negative integers
= 5 + 8
= 13
Therefore, the maximum possible number of odd integers among the 13 given integers is 13.
Hence, the answer is E) 13.
For the product of two numbers to be odd, at least one of the numbers must be odd. Therefore, we need to maximize the number of odd integers in both the positive and negative integers.
Since we have a total of 13 integers, let's consider the extremes for the number of odd integers in each group:
Maximum number of odd integers among the positive integers:
To maximize the number of odd integers, we can have all five positive integers as odd. This gives us a maximum of 5 odd integers among the positive integers.
Maximum number of odd integers among the negative integers:
To maximize the number of odd integers, we can have all eight negative integers as odd. This gives us a maximum of 8 odd integers among the negative integers.
Now, let's calculate the maximum possible number of odd integers in total:
Maximum number of odd integers = Number of odd integers in positive integers + Number of odd integers in negative integers
= 5 + 8
= 13
Therefore, the maximum possible number of odd integers among the 13 given integers is 13.
Hence, the answer is E) 13.
No boss. You are mostly correct. The only thing is that if the second sum had 8 odd numbers, then the sum would have been even. So, the max # of odd nos. in the second sum is 7. 5 + 7 = 12. Answer is D.
Even I first thought the answer will be E.
