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The sum of 4 different odd integers is 64. What is the value of the

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raghav1708
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Re: The sum of 4 different odd integers is 64. What is the value of the [#permalink] New post   18 Sep 2022, 03:28
AneesShaik wrote:
The sum of 4 different odd integers is 64. What is the value of the greatest of these integers?

(1) The integers are consecutive odd numbers
(2) Of these integers, the greatest is 6 more than the least.



Hi Bunuel I am not able to understand the second statement. Firstly, all four are different odd numbers, so we can't figure out which is bigger and which is the smallest. Secondly, how can we say that the rest of the two odd numbers are equally distant?

Please help Bunuel

Thanks Bunuel
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Bunuel
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The sum of 4 different odd integers is 64. What is the value of the [#permalink] New post   18 Sep 2022, 03:34
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raghav1708 wrote:
AneesShaik wrote:
The sum of 4 different odd integers is 64. What is the value of the greatest of these integers?

(1) The integers are consecutive odd numbers
(2) Of these integers, the greatest is 6 more than the least.



Hi Bunuel I am not able to understand the second statement. Firstly, all four are different odd numbers, so we can't figure out which is bigger and which is the smallest. Secondly, how can we say that the rest of the two odd numbers are equally distant?

Please help Bunuel

Thanks Bunuel


Here is reasoning for (2):

(2) Of these integers, the greatest is 6 more than the least --> least = x and greatest = x + 6. Between x and x + 6, there are only 2 odd integers x + 2 and x + 4, so we have the same case as above. Sufficient.

Can you please tell me which part is unclear there ? Thank you!
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Re: The sum of 4 different odd integers is 64. What is the value of the [#permalink] New post   18 Sep 2022, 04:23
Bunuel wrote:
raghav1708 wrote:
AneesShaik wrote:
The sum of 4 different odd integers is 64. What is the value of the greatest of these integers?

(1) The integers are consecutive odd numbers
(2) Of these integers, the greatest is 6 more than the least.



Hi Bunuel I am not able to understand the second statement. Firstly, all four are different odd numbers, so we can't figure out which is bigger and which is the smallest. Secondly, how can we say that the rest of the two odd numbers are equally distant?

Please help Bunuel

Thanks Bunuel


Here is reasoning for (2):

(2) Of these integers, the greatest is 6 more than the least --> least = x and greatest = x + 6. Between x and x + 6, there are only 2 odd integers x + 2 and x + 4, so we have the same case as above. Sufficient.

Can you please tell me which part is unclear there ? Thank you!



Okay, now I understand Bunuel , after applying statement 2, the numbers automatically become consecutive odd integers, right?

Correct me If I am wrong Bunuel

Thanks Bunuel
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Re: The sum of 4 different odd integers is 64. What is the value of the [#permalink] New post   18 Sep 2022, 04:46
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raghav1708 wrote:
Okay, now I understand Bunuel , after applying statement 2, the numbers automatically become consecutive odd integers, right?

Correct me If I am wrong Bunuel

Thanks Bunuel


Right. If x is odd, then between x and x + 6, there are only two odd integers: x + 2 and x + 4. For example, between 7 and 7 + 6 = 13, there are two odd integers: x + 2 = 9 and x + 4 = 11. So, in this case the odd integers would be 7, 9, 11, and 13.
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Re: The sum of 4 different odd integers is 64. What is the value of the [#permalink] New post   18 Sep 2022, 05:01
Bunuel wrote:
raghav1708 wrote:
Okay, now I understand Bunuel , after applying statement 2, the numbers automatically become consecutive odd integers, right?

Correct me If I am wrong Bunuel

Thanks Bunuel


Right. If x is odd, then between x and x + 6, there are only two odd integers: x + 2 and x + 4. For example, between 7 and 7 + 6 = 13, there are two odd integers: x + 2 = 9 and x + 4 = 11. So, in this case the odd integers would be 7, 9, 11, and 13.



Thank you so much Bunuel ! Everything is clear now. Always grateful for your help!

Gratitude Bunuel
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Re: The sum of 4 different odd integers is 64. What is the value of the [#permalink] New post   18 Sep 2022, 06:47
Given: The sum of 4 different odd integers is 64.
Asked: What is the value of the greatest of these integers?

(1) The integers are consecutive odd numbers
Let the numbers be a-3,a-1,a+1 & a+3.
The sum of 4 different odd integers is 64.
4a = 64
a = 16
The value of the greatest of these integers = a+3 = 16+ 3 = 19
SUFFICIENT

(2) Of these integers, the greatest is 6 more than the least.
If the least integer is x, the greatest is x+6
Other different odd integers possible are x+2 & x+4
The sum of 4 different odd integers is 64.
x + x+2 + x+4 + x+ 6 = 64
4x + 12 = 64
x = 13
The value of the greatest of these integers = x + 6 = 13 + 6 = 19
SUFFICIENT

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Re: The sum of 4 different odd integers is 64. What is the value of the [#permalink] New post   22 Jul 2023, 01:49
sum of odd I = 16 | greatest odd num(Go)?

1. 2x-3 + 2x-1 + 2x+1 + 2x+3 = 64 | Can be calculated. (Sufficient)
BTW x=8, Go = 19

2. Go - Lo = 6, that means only 2 odd in b/w {1,3,5,7} | 7-1=6.
Same as Case 1. (Sufficient)

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Re: The sum of 4 different odd integers is 64. What is the value of the [#permalink]
22 Jul 2023, 01:49
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