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

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The sum of 4 different odd integers is 64. What is the value of the [#permalink]

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New post 16 Jul 2016, 01:59
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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.
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Re: The sum of 4 different odd integers is 64. What is the value of the [#permalink]

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New post 16 Jul 2016, 02:07
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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.

P.S. Which Official Guide is this question from?
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Re: The sum of 4 different odd integers is 64. What is the value of the [#permalink]

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New post 17 Jul 2016, 05:04
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AneesShaik wrote:
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
(2) Of these integers, the greatest is 6 more than the least.


(1) The consecutive integers must be (15-2,15,15+2,15+4) so that the sum could be 64,So the greatest number is 19,Sufficient

(2) The range of the integers is 6,within this range to get sum 64 the integers must be (13,15,17,19) as statement (1),Sufficient

Correct Answer D
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Re: The sum of 4 different odd integers is 64. What is the value of the [#permalink]

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New post 16 Jul 2016, 02:23
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Bunuel wrote:
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.

P.S. Which Official Guide is this question from?



Bunuel : can you just help me understand why from the first statement we are taking x= x + (x + 2) + (x + 4) + (x + 6) = 64. Can't it be x + (x - 2) + (x - 4) + (x - 6) = 64 ..won't the greatest number be different
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Re: The sum of 4 different odd integers is 64. What is the value of the [#permalink]

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New post 16 Jul 2016, 02:28
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nikhilbansal08 wrote:
Bunuel wrote:
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.

P.S. Which Official Guide is this question from?



Bunuel : can you just help me understand why from the first statement we are taking x= x + (x + 2) + (x + 4) + (x + 6) = 64. Can't it be x + (x - 2) + (x - 4) + (x - 6) = 64 ..won't the greatest number be different


In my solution the smallest number is x and the greatest is x + 6.

In your case the smallest number is x - 6 and the greatest is x.

In any case the answer is the same.
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Re: The sum of 4 different odd integers is 64. What is the value of the [#permalink]

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New post 16 Jul 2016, 04:49
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Bunuel wrote:
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.

P.S. Which Official Guide is this question from?


This is from OG 2017 Bunuel.
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Re: The sum of 4 different odd integers is 64. What is the value of the [#permalink]

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New post 06 Dec 2016, 18:15
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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.


We are given that the sum of 4 different odd integers is 64 and need to determine the value of the greatest of these integers.

Statement One Alone:

The integers are consecutive odd numbers

Since we know that the integers are consecutive odd integers, we can denote the integers as x, x + 2, x + 4, and x + 6 (notice that the largest integer is x + 6).

Since the sum of these integers is 64, we can create the following equation and determine x:

x + (x + 2) + (x + 4) + (x + 6) = 64

4x + 12 = 64

4x = 52

x = 13

Thus, the largest integer is 13 + 6 = 19.

Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

Of these integers, the greatest is 6 more than the least.

Using the information in statement two, we can determine that the four integers are consecutive odd integers. Let’s further elaborate on this idea. If we take any set of four consecutive odd integers, {1, 3, 5, 7}, {9, 11, 13, 15}, or {19, 21, 23, 25}, notice that in ALL CASES the greatest integer in the set is always 6 more than the least integer. In other words, the only way to fit two odd integers between the odd integers n and n + 6 is if the two added odd integers are n + 2 and n +4, thus making them consecutive odd integers. Since we have determined that we have a set of four consecutive odd integers and that their sum is 64, we can determine the value of all the integers in the set, including the value of the greatest one, in the same way we did in statement one. Thus, statement two is also sufficient to answer the question.

Answer: D
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Re: The sum of 4 different odd integers is 64. What is the value of the [#permalink]

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New post 12 Oct 2017, 06:49
nikhilbansal08 wrote:
Bunuel wrote:
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.

P.S. Which Official Guide is this question from?



Bunuel : can you just help me understand why from the first statement we are taking x= x + (x + 2) + (x + 4) + (x + 6) = 64. Can't it be x + (x - 2) + (x - 4) + (x - 6) = 64 ..won't the greatest number be different





Bunuel, I think nikhilbansal08 is right in this case.The question asks for :"What is the value of the greatest of these integers? "

now if we consider, clue no : 1,the we get

(2n+1) + (2n+3)+(2n+5)+(2n+7)=64
8(n+2)=64
n=6
so numbers are 13,15,17,19
greatest value is 19 in this case.

but if we consider

(2n+3)+(2n+5)+(2n+7)+(2n+9)=64
8(n+3)=64
n=5
numbers are 11,13,15,17

so the greatest value is 17

clearly,depending on the values of n the greatest value varies.
1 alone is insufficient.

clue 2 says ,greatest is 6 more the least,which means they are consecutive odd,but does not say any thing about greats value. 2 alone insufficient

if we combine clue 1+2 ,2 is redundant as from 1 we already know that they are consecutive odd.

Even after combining together they do not say anything about the greatest value.

I think E is the appropriate one.
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The sum of 4 different odd integers is 64. What is the value of the [#permalink]

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New post 12 Oct 2017, 07:01
TYPHOON12 wrote:
nikhilbansal08 wrote:
Bunuel wrote:
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.

P.S. Which Official Guide is this question from?



Bunuel : can you just help me understand why from the first statement we are taking x= x + (x + 2) + (x + 4) + (x + 6) = 64. Can't it be x + (x - 2) + (x - 4) + (x - 6) = 64 ..won't the greatest number be different





Bunuel, I think nikhilbansal08 is right in this case.The question asks for :"What is the value of the greatest of these integers? "

now if we consider, clue no : 1,the we get

(2n+1) + (2n+3)+(2n+5)+(2n+7)=64
8(n+2)=64
n=6
so numbers are 13,15,17,19
greatest value is 19 in this case.

but if we consider

(2n+3)+(2n+5)+(2n+7)+(2n+9)=64
8(n+3)=64
n=5
numbers are 11,13,15,17

so the greatest value is 17

clearly,depending on the values of n the greatest value varies.
1 alone is insufficient.

clue 2 says ,greatest is 6 more the least,which means they are consecutive odd,but does not say any thing about greats value. 2 alone insufficient

if we combine clue 1+2 ,2 is redundant as from 1 we already know that they are consecutive odd.

Even after combining together they do not say anything about the greatest value.

I think E is the appropriate one.



TYPHOON12 The calculation is slightly off (by 2) in this part:
Quote:
(2n+3)+(2n+5)+(2n+7)+(2n+9)=64
8(n+3)=64
n=5
numbers are 11,13,15,17

so the greatest value is 17


If n = 5, then
(2n+3) = 10+3 = 13
(2n+5) = 10+5 = 15
(2n+7) = 10+7 = 17
(2n+9) = 10+9 = 19

The answer will still be the same, no matter how you look at it. Similarly, as you correctly pointed out, option 2 is redundant and thus this solution is also applicable to 2.
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Re: The sum of 4 different odd integers is 64. What is the value of the [#permalink]

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New post 09 Dec 2017, 02:52
For statement 1: take the 4 consecutive odd integers as: 2n-3, 2n-1, 2n+1, 2n+3
Sum = 8n = 64 => n=8;

For statement 2: if we see the above series difference is (2n+3) - (2n-3) =6, as this is the only series which can fit the requirement.

Thus D.
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Re: The sum of 4 different odd integers is 64. What is the value of the [#permalink]

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New post 06 Feb 2018, 12:02
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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.


Target question: What is the value of the greatest of these integers?

Given: The 4 numbers are different odd integers, and their sum is 64.

Statement 1: The integers are consecutive odd numbers
Let x = the first odd integer
So, x + 2 = the 2nd odd integer
So, x + 4 = the 3rd odd integer
So, x + 6 = the 4th odd integer
Since we're told the sum is 64, we can write: x + (x+2) + (x+4) + (x+6) = 64
Since we COULD solve this equation for x, we COULD determine all 4 values, which means we COULD determine the value of the greatest of the 4 odd integers
Of course, we're not going to waste valuable time solving the equation, since our sole goal is to determine whether the statement provides sufficient information.
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Of these integers, the greatest is 6 more than the least.
Notice that the 4 CONSECUTIVE integers (from statement 1) can be written as x, x+2, x+4 and x+6
Notice that the biggest number (x+6) is 6 more than the smallest number (x).
Since the 4 odd integers are different, statement 2 is basically telling us that the 4 integers are CONSECUTIVE
So, for the same reason we found statement 1 to be SUFFICIENT, we can also conclude that statement 2 is SUFFICIENT

Answer: D

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Brent
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Re: The sum of 4 different odd integers is 64. What is the value of the   [#permalink] 06 Feb 2018, 12:02
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