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Manager  Joined: 23 Oct 2014
Posts: 84
Concentration: Marketing
Which of the following integers represents a sum of 3  [#permalink]

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3 00:00

Difficulty:   55% (hard)

Question Stats: 60% (01:23) correct 40% (01:09) wrong based on 117 sessions

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Which of the following integers represents a sum of 3 consecutive even integers?

A. 200
B. 303
C. 400
D. 554
E. 570

I'm ashamed to say that I don't understand this. This question came from the flashcards from GMATclub.

I figured I'd just list out the possible integers that can occupy the ones place: 0, 2, 4, 6, 8 and add any three consecutively to see what answer matched any of the answer choices' ones place.

0+2+4 = 6
2+4+6 = 12
4+6+8 = 18
6+8+0 = 14

I wanted to say the answer is D but they said the answer was E.
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Re: Which of the following integers represents a sum of 3  [#permalink]

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BassanioGratiano wrote:
Which of the following integers represents a sum of 3 consecutive even integers?

A. 200
B. 303
C. 400
D. 554
E. 570

I'm ashamed to say that I don't understand this. This question came from the flashcards from GMATclub.

I figured I'd just list out the possible integers that can occupy the ones place: 0, 2, 4, 6, 8 and add any three consecutively to see what answer matched any of the answer choices' ones place.

0+2+4 = 6
2+4+6 = 12
4+6+8 = 18
6+8+0 = 14

I wanted to say the answer is D but they said the answer was E.

Sum of three consecutive Even Integers must be a multiple of 2 as well as a multiple of 3 because such a sum is always 3 times the middle number (applicable to all equally spaced numbers)

Divisibility of 3: Sum of the digits of the number must be divisible by 3
Divisibility of 2: Unit digit of the number must be divisible by 2

A. 200 NOT A MULTIPLE OF 3 SO RULED OUT
B. 303 NOT A MULTIPLE OF 2 SO RULED OUT
C. 400 NOT A MULTIPLE OF 3 SO RULED OUT
D. 554 NOT A MULTIPLE OF 3 SO RULED OUT
E. 570 A MULTIPLE OF BOTH 2 AND 3 SO THE CORRECT ANSWER!!!
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Manager  Joined: 23 Oct 2014
Posts: 84
Concentration: Marketing
Re: Which of the following integers represents a sum of 3  [#permalink]

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GMATinsight wrote:
BassanioGratiano wrote:
Which of the following integers represents a sum of 3 consecutive even integers?

A. 200
B. 303
C. 400
D. 554
E. 570

I'm ashamed to say that I don't understand this. This question came from the flashcards from GMATclub.

I figured I'd just list out the possible integers that can occupy the ones place: 0, 2, 4, 6, 8 and add any three consecutively to see what answer matched any of the answer choices' ones place.

0+2+4 = 6
2+4+6 = 12
4+6+8 = 18
6+8+0 = 14

I wanted to say the answer is D but they said the answer was E.

Sum of three consecutive Even Integers must be a multiple of 2 as well as a multiple of 3 because such a sum is always 3 times the middle number (applicable to all equally spaced numbers)

Divisibility of 3: Sum of the digits of the number must be divisible by 3
Divisibility of 2: Unit digit of the number must be divisible by 2

A. 200 NOT A MULTIPLE OF 3 SO RULED OUT
B. 303 NOT A MULTIPLE OF 2 SO RULED OUT
C. 400 NOT A MULTIPLE OF 3 SO RULED OUT
D. 554 NOT A MULTIPLE OF 3 SO RULED OUT
E. 570 A MULTIPLE OF BOTH 2 AND 3 SO THE CORRECT ANSWER!!!

I didn't even think of that. So with that we know the three consecutive even integers are.

188 190 192

Thank you.
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Joined: 19 Dec 2014
Posts: 16169
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GRE 1: Q170 V170
Re: Which of the following integers represents a sum of 3  [#permalink]

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Hi All,

In these types of prompts, it's certainly helpful if you know your Number Property Rules (in this case, the rules of division). Even if you didn't know those rules those, you could solve with algebra and a bit more work.

We're told that there are 3 CONSECUTIVE EVEN integers. We can call those integers:
X
X + 2
X + 4

The sum of those integers = 3X + 6

From here, you can check all five answers. The correct answer will leave you with an EVEN INTEGER value for X... And at this point you might more easily recognize the "rule of 3" for division....

Answer A: 3X + 6 = 200 --> 3X = 194 194 is NOT a multiple of 3. Eliminate A.

Answer B: 3X + 6 = 303 --> 3X =297 X = 99 which is NOT an even integer. Eliminate B.

Answer C: 3X + 6 = 400 --> 3X = 394 394 is NOT a multiple of 3. Eliminate C.

Answer D: 3X + 6 = 554 --> 3X = 548 548 is NOT a multiple of 3. Eliminate D.

Answer E: 3X + 6 = 570 --> 3X = 564 X = 188 which IS an even integer.

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Rich
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_________________ Re: Which of the following integers represents a sum of 3   [#permalink] 14 Dec 2018, 07:57
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