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# The smallest of three consecutive even integers is 40 less than three

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Math Expert
Joined: 02 Sep 2009
Posts: 60460
The smallest of three consecutive even integers is 40 less than three  [#permalink]

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10 Jan 2016, 08:53
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45% (medium)

Question Stats:

63% (01:37) correct 37% (01:42) wrong based on 83 sessions

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The smallest of three consecutive even integers is 40 less than three times the largest. What is the largest of these integers?

A. 14
B. 17
C. 18
D. 19
E. 20

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Re: The smallest of three consecutive even integers is 40 less than three  [#permalink]

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15 Jan 2016, 00:31
2
Hi All,

This question can be solved by TESTing THE ANSWERS.

We're told a couple of facts about a group of integers:
1) They are 3 CONSECUTIVE EVEN INTEGERS,
2) The smallest is 40 LESS than 3 times the LARGEST.

We're asked for the LARGEST of the 3 integers.

To start, we know that all 3 integers are EVEN, so we can eliminate Answers B and D (since they're ODD integers).

IF...
The LARGEST INTEGER = 18....
The 3 integers are 14, 16, 18
3(18) = 54
14 = 40 less than 54
Thus the smallest is 40 less than 3 times the largest, so this Answer 'fits' everything we were told. Thus, this MUST be the answer.

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Re: The smallest of three consecutive even integers is 40 less than three  [#permalink]

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11 Jan 2016, 06:01
1
xLUCAJx wrote:
chetan2u wrote:
Bunuel wrote:
The smallest of three consecutive even integers is 40 less than three times the largest. What is the largest of these integers?

A. 14
B. 17
C. 18
D. 19
E. 20

let the three numbers be a,b and c..
now The smallest of three consecutive even integers is 40 less than three times the largest means 3c-40=a..
3c-a=40..
2c+c-a=40..
c-a=4, as a,b,and c are consecutive even integers..
2c+4=40..
2c=36 or c=18..
C

is 18 the largest integer? I got 20 because I added 2 to 18 to get the largest?

No, 18 is the correct answer. From 3c-40=a , you can clearly see that 'a' is the smallest of the 3 even integers and 'c' is the largest.

Hope this helps.
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Joined: 02 Aug 2009
Posts: 8341
Re: The smallest of three consecutive even integers is 40 less than three  [#permalink]

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11 Jan 2016, 06:05
1
xLUCAJx wrote:
chetan2u wrote:
Bunuel wrote:
The smallest of three consecutive even integers is 40 less than three times the largest. What is the largest of these integers?

A. 14
B. 17
C. 18
D. 19
E. 20

let the three numbers be a,b and c..
now The smallest of three consecutive even integers is 40 less than three times the largest means 3c-40=a..
3c-a=40..
2c+c-a=40..
c-a=4, as a,b,and c are consecutive even integers..
2c+4=40..
2c=36 or c=18..
C

is 18 the largest integer? I got 20 because I added 2 to 18 to get the largest?

hi,
why did you add 2 to 18? did you too do the Q the same way? If these are known, one would be able to say where did you go wrong
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The smallest of three consecutive even integers is 40 less than three  [#permalink]

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20 Jan 2016, 15:21
1
Bunuel wrote:
The smallest of three consecutive even integers is 40 less than three times the largest. What is the largest of these integers?

A. 14
B. 17
C. 18
D. 19
E. 20

Algebraic approach
x = first consecutive even integer
x+ 2 = second consecutive even integer
x + 4 = third consecutive even integer.

Therefore,
$$x = 3(x+4) - 40$$ $$-->$$ $$-2x = -28$$ $$-->$$ $$x = 14$$
$$x + 4 = 14 + 4 = 18$$

Math Expert
Joined: 02 Aug 2009
Posts: 8341
Re: The smallest of three consecutive even integers is 40 less than three  [#permalink]

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11 Jan 2016, 00:54
Bunuel wrote:
The smallest of three consecutive even integers is 40 less than three times the largest. What is the largest of these integers?

A. 14
B. 17
C. 18
D. 19
E. 20

let the three numbers be a,b and c..
now The smallest of three consecutive even integers is 40 less than three times the largest means 3c-40=a..
3c-a=40..
2c+c-a=40..
c-a=4, as a,b,and c are consecutive even integers..
2c+4=40..
2c=36 or c=18..
C
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Re: The smallest of three consecutive even integers is 40 less than three  [#permalink]

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11 Jan 2016, 05:58
chetan2u wrote:
Bunuel wrote:
The smallest of three consecutive even integers is 40 less than three times the largest. What is the largest of these integers?

A. 14
B. 17
C. 18
D. 19
E. 20

let the three numbers be a,b and c..
now The smallest of three consecutive even integers is 40 less than three times the largest means 3c-40=a..
3c-a=40..
2c+c-a=40..
c-a=4, as a,b,and c are consecutive even integers..
2c+4=40..
2c=36 or c=18..
C

is 18 the largest integer? I got 20 because I added 2 to 18 to get the largest?
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Re: The smallest of three consecutive even integers is 40 less than three  [#permalink]

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11 Jan 2016, 06:15
hi,
why did you add 2 to 18? did you too do the Q the same way? If these are known, one would be able to say where did you go wrong[/quote]

I figured out what I did wrong. I missed consecutive EVEN integers so I was getting 18 on the first try. Redid the problem with even integers got 18. Thanks for the help.
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Re: The smallest of three consecutive even integers is 40 less than three  [#permalink]

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05 Apr 2016, 07:24
saiesta wrote:
Bunuel wrote:
The smallest of three consecutive even integers is 40 less than three times the largest. What is the largest of these integers?

A. 14
B. 17
C. 18
D. 19
E. 20

Algebraic approach
x = first consecutive even integer
x+ 2 = second consecutive even integer
x + 4 = third consecutive even integer.

Therefore,
$$x = 3(x+4) - 40$$ $$-->$$ $$-2x = -28$$ $$-->$$ $$x = 14$$
$$x + 4 = 14 + 4 = 18$$

You got the right answer but with a wrong approach. How do you make sure that x, x+2 and x+4 are even?
We should rather consider 2x, 2x+2, 2x+4.
(Though this is not gonna have any impact on the final answer as the they are consecutive and the sum is not gnna change).
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Re: The smallest of three consecutive even integers is 40 less than three  [#permalink]

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05 Apr 2016, 07:33
Consider the 3 consecutive even integers to be $$2K, 2K+2$$ and $$2K+4$$
Now, we are given that the smallest is 40 less than three times the largest.
i.e. $$2K+40 = 3 (2k+4) => 2K+40 = 6K+12 => 4K = 28 => K = 7$$

Hence, the largest would be
$$2(7)+4 = 18$$

Option C
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Re: The smallest of three consecutive even integers is 40 less than three  [#permalink]

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05 Oct 2016, 16:58
Bunuel wrote:
The smallest of three consecutive even integers is 40 less than three times the largest. What is the largest of these integers?

A. 14
B. 17
C. 18
D. 19
E. 20

-let a, b and c be 3 consecutive even integers where a=smallest and c=largest
-we know that a=3c-40
I knew E was out immediately since 3 * 20 - 40 = 20.
I next tried C: a=3*18 - 40 = 54-40 = 14.
14 is the smallest and thus 18 would be the largest....B and D are out since they produce odd, not even, integers.
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Re: The smallest of three consecutive even integers is 40 less than three  [#permalink]

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Re: The smallest of three consecutive even integers is 40 less than three   [#permalink] 26 Nov 2019, 01:02
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