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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? _________________

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

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16 Jul 2016, 02:23

1

This post received KUDOS

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

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.
_________________

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

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16 Jul 2016, 04:49

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This post was BOOKMARKED

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.

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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GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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

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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.

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

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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.