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

Question

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

chetan2u · Answer

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

xLUCAJx · Answer

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

ENGRTOMBA2018 · Answer

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.

chetan2u · Answer

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

xLUCAJx · Answer

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

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.

EMPOWERgmatRichC · Answer

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).

Let's TEST Answer C: 18

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.

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

saiesta · Answer

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

Answer C.

arhumsid · Answer

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).

arhumsid · Answer

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

mikeyg51 · Answer

I tested the answers:
-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.

Nahid1521017 · Answer

Let,
1st even number x
2nd even number x+2
3rd even number x+4 (as they are consecutive numbers)

According to the question:
3(x+4)-40=x
or, 3x+12-40=x
or, 3x-x=28
or, x=28/2
or, x=14

Hence, Largest of these integers= x+4= 14+4=18 (Answer)

bumpbot · Answer

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

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

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