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555-605 Level|   Number Properties|                        
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raghav1708
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The sum of 4 different odd integers is 64. What is the value of the 18 Sep 2022, 04:23
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Bunuel
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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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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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The sum of 4 different odd integers is 64. What is the value of the 18 Sep 2022, 04:46
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raghav1708

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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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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The sum of 4 different odd integers is 64. What is the value of the 18 Sep 2022, 05:01
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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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Thank you so much Bunuel ! Everything is clear now. Always grateful for your help!

Gratitude Bunuel
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The sum of 4 different odd integers is 64. What is the value of the 18 Sep 2022, 06:47
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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

IMO D
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The sum of 4 different odd integers is 64. What is the value of the 22 Jul 2023, 01:49
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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)

Ans D
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The sum of 4 different odd integers is 64. What is the value of the 01 Jul 2025, 00:31
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My issue with this question stems from Statement 2.
For Data sufficiency, we are told that statements 1 & 2 need to always be considered separate from each other until the time comes to combine the 2 statements if both are insufficient. So, when i look at statement 2 on its own, nothing about it tells me that they are consecutive. Yes, we know that the overall sum is 64, and that the greatest term is 6 more than the smallest term but we know nothing about the other 2 terms besides the fact that they are different odd numbers.
I thought the overall point about DS is to determine whether the statements provide enough info to solve the main ask of the question. Statement 1 does that but i dont think statement 2 does. Can someone please explain as to what strategies can be used to approach this question, considering the fact that time runs like a bullet train during the exam? Thanks :)



Bunuel
The sum of 4 different odd integers is 64. What is the value of the greatest these integers?

(1) The integers are consecutive odd numbers --> x + (x + 2) + (x + 4) + (x + 6) = 64. We can find x. Sufficient.

(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.

Answer: D.
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The sum of 4 different odd integers is 64. What is the value of the 01 Jul 2025, 00:56
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My issue with this question stems from Statement 2.
For Data sufficiency, we are told that statements 1 & 2 need to always be considered separate from each other until the time comes to combine the 2 statements if both are insufficient. So, when i look at statement 2 on its own, nothing about it tells me that they are consecutive. Yes, we know that the overall sum is 64, and that the greatest term is 6 more than the smallest term but we know nothing about the other 2 terms besides the fact that they are different odd numbers.
I thought the overall point about DS is to determine whether the statements provide enough info to solve the main ask of the question. Statement 1 does that but i dont think statement 2 does. Can someone please explain as to what strategies can be used to approach this question, considering the fact that time runs like a bullet train during the exam? Thanks :)



Bunuel
The sum of 4 different odd integers is 64. What is the value of the greatest these integers?

(1) The integers are consecutive odd numbers --> x + (x + 2) + (x + 4) + (x + 6) = 64. We can find x. Sufficient.

(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.

Answer: D.
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You are missing a point.

The stem says that we have 4 different odd integers.
(2) says that the greatest is 6 more than the least.

Between any odd number x and x + 6, the only odd integers are x + 2 and x + 4. That gives us exactly four different odd integers: x, x + 2, x + 4, and x + 6, which matches the structure in (1).

So yes, even though it doesn’t say “consecutive,” the condition forces the same four values. Statement (2) is sufficient.
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