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505-555 (Easy)|   Arithmetic|      
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Bunuel
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What is the largest integer if the sum of three consecutive even integ 17 Jan 2016, 12:05
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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15% (low)

Question Stats:

80% (01:09) correct 20% (01:21) wrong based on 313 sessions

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What is the largest integer if the sum of three consecutive even integers is 318?

A. 100
B. 104
C. 106
D. 108
E. 111
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D
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BrentGMATPrepNow
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What is the largest integer if the sum of three consecutive even integ 03 May 2018, 15:38
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Bunuel
What is the largest integer if the sum of three consecutive even integers is 318?

A. 100
B. 104
C. 106
D. 108
E. 111
Show more

Let x = the smallest value
So, x + 2 = the middle value
And x + 4 = the biggest value

The sum is 318
So, we can write x + (x+2) + (x+4) = 318
Simplify: 3x + 6 = 318
Subtract 6 from both sides to get: 3x = 312
Solve: x = 104
So, the SMALLEST value = 104
This means 106 is the MIDDLE value and 108 is the BIGGEST value

Answer: D

Cheers,
Brent
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Mo2men
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What is the largest integer if the sum of three consecutive even integ 20 Jan 2016, 02:51
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Bunuel
What is the largest integer if the sum of three consecutive even integers is 318?

A. 100
B. 104
C. 106
D. 108
E. 111
Show more


Solving The question using 2 approaches:

1- Algebraic Approach

Let largest even number = X

(X-4)+(X-2)+X = 318 ......> X =108

Answer: D


2- Testing the Answers

This approach may take longer time if tried to do every number, So we can just use the unit-digit

A) 100......Sum of even numbers=0+8+6= 4 does match unit digit of 318

B) 104.....4+2+0=6

D) 108.....8+6+4=8.... match the unit digit of 318

Answer D
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What is the largest integer if the sum of three consecutive even integ 20 Jan 2016, 14:12
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Mo2men
Bunuel
What is the largest integer if the sum of three consecutive even integers is 318?

A. 100
B. 104
C. 106
D. 108
E. 111


Solving The question using 2 approaches:

1- Algebraic Approach

Let largest even number = X

(X-4)+(X-2)+X = 318 ......> X =108

Answer: D


2- Testing the Answers

This approach may take longer time if tried to do every number, So we can just use the unit-digit

A) 100......Sum of even numbers=0+8+6= 4 does match unit digit of 318

B) 104.....4+2+0=6

D) 108.....8+6+4=8.... match the unit digit of 318

Answer D
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Edit: Nvm I did not read the question correctly.
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What is the largest integer if the sum of three consecutive even integ Updated on: 21 Jan 2016, 09:06
Originally posted by saiesta on 20 Jan 2016, 14:30.
Last edited by saiesta on 21 Jan 2016, 09:06, edited 1 time in total.
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This is how I tried to solve the problem. We can already cross off answer choice E since it is not an even integer. Furthermore, The arithmetic mean and median in evenly spaced sets are equal to each other. The median for this evenly spaced set is 106. (318/3 = 106). The next larger integer greater than 106 is 108. Answer choice D.
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What is the largest integer if the sum of three consecutive even integ 20 Jan 2016, 18:57
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saiesta
This is how I tried to solve the problem. We can already cross off answer choice E since it is not an even integer. Furthermore, The arithmetic mean and median in evenly spaced sets are equal to each other. The median for this evenly spaced set is 106. (308/3 = 106). The next larger integer greater than 106 is 108. Answer choice D.
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There is Typo error. it is 318 :)
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What is the largest integer if the sum of three consecutive even integ 21 Jan 2016, 09:08
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Mo2men
saiesta
This is how I tried to solve the problem. We can already cross off answer choice E since it is not an even integer. Furthermore, The arithmetic mean and median in evenly spaced sets are equal to each other. The median for this evenly spaced set is 106. (308/3 = 106). The next larger integer greater than 106 is 108. Answer choice D.


There is Typo error. it is 318 :)
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Changed it. Thanks for pointing it out.
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What is the largest integer if the sum of three consecutive even integ 21 Jan 2016, 09:46
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Bunuel
What is the largest integer if the sum of three consecutive even integers is 318?

A. 100
B. 104
C. 106
D. 108
E. 111
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2k-2 + 2k + 2k+2 = 318
6k = 318
2k = 106
2k+2 = 108
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What is the largest integer if the sum of three consecutive even integ 21 Jan 2016, 10:01
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[/quote]

2k-2 + 2k + 2k+2 = 318
6k = 318
2k = 106
2k+2 = 108[/quote]


Why pick 2k?

k-2+k+k+2=318
3k=318
k=106
k+2=108
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What is the largest integer if the sum of three consecutive even integ 23 Jan 2016, 00:52
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paidlukkha
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2k-2 + 2k + 2k+2 = 318
6k = 318
2k = 106
2k+2 = 108[/quote]


Why pick 2k?

k-2+k+k+2=318
3k=318
k=106
k+2=108[/quote]

habit. i pick 2k as soon as see "even" mentioned in the question. :)
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What is the largest integer if the sum of three consecutive even integ 07 May 2018, 10:32
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Bunuel
What is the largest integer if the sum of three consecutive even integers is 318?

A. 100
B. 104
C. 106
D. 108
E. 111
Show more

If we let n = the first even integer, then the next consecutive even integer is (n + 2), and the one after that is (n + 4). W create the equation:

n + n + 2 + n + 4 = 318

3n = 312

n = 104

So the largest integer is 104 + 4 = 108.

Answer: D
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What is the largest integer if the sum of three consecutive even integ 15 Feb 2024, 14:15
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