CONSEC

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fruti_yum: Master | Next Rank: 500 Posts; Posts: 128; Joined: Thu Jul 30, 2009 1:46 pm; Thanked: 1 times

by fruti_yum » Sun Aug 02, 2009 11:54 am

If x, y, and z are consecutive even positive integers, which of the following could be equal to x + y + z ?

A. 141
B. 200
C. 318
D. 391
E. 412

I took a long *** method doing this question.. it was easily over 2 mins...
is there a shorter way to do this??

OA is C

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Source: Beat The GMAT — Problem Solving | Sun Aug 02, 2009 11:54 am

truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Sun Aug 02, 2009 12:16 pm

x

y=x+2

z=x+4

x+y+z=3x+6=3(x+2)

Test out the answer choices:

A.) 3(x+2)=141

x+2=47

x=45

45 isn't an even integer.

B.) 3(x+2)=200

200 isn't divisible by 3.

C.) 3(x+2)=318

x=104.

This is our answer.

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ankitns: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Mon Jul 13, 2009 8:58 pm; Thanked: 10 times; GMAT Score:710

Re: CONSEC

by ankitns » Sun Aug 02, 2009 2:27 pm

fruti_yum wrote:If x, y, and z are consecutive even positive integers, which of the following could be equal to x + y + z ?

A. 141
B. 200
C. 318
D. 391
E. 412

I took a long *** method doing this question.. it was easily over 2 mins...
is there a shorter way to do this??

OA is C

This question aims at 2 properties.
1) Sum of even numbers is always even. So this eliminates choices A and D.

2) The average of 3 consecutive even numbers will be the middle number (Say Y is the middle number). Also, the sum of the 3 consecutive numbers 3 * average = 3Y. So this means that the sum MUST be divisible by 3.

Simple check on choices B, C and E will lead us to C as the other two are not divisible by 3.

I dont know any quicker way to it...

hope this helps!

Attempt 1: 710, 92% (Q 42, 63%; V 44, 97%)
Attempt 2: Coming soon!

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shahdevine: Master | Next Rank: 500 Posts; Posts: 197; Joined: Sun May 18, 2008 2:47 am; Thanked: 12 times

Re: CONSEC

by shahdevine » Mon Aug 03, 2009 4:13 pm

fruti_yum wrote:If x, y, and z are consecutive even positive integers, which of the following could be equal to x + y + z ?

A. 141
B. 200
C. 318
D. 391
E. 412

I took a long *** method doing this question.. it was easily over 2 mins...
is there a shorter way to do this??

OA is C

fruiti,

first off you can eliminate answer choices a and d, because they are odd. we are looking for the sum of consecutive even numbers. even+even+even=even.

second, since the problem tells us that x, y and z are even numbers, then the sequence formula is the addition of n, n+2, and n+4 which is 3n+6

third use that formula to check your remaining choices.

3n+6=318
3n=312
n=104

no need to go further...the rest of the options won't work!

you got this!!

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