Find the fourth consecutive even number: (I) The sum of the

Question

Find the fourth consecutive even number:
(I) The sum of the last two numbers is 30
(II) The sum of the first two numbers is 22

(A) Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient

(B) Statement (II) ALONE is sufficient, but statement (I) is not sufficient

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient

(D) Each statement ALONE is sufficient

(E) Statements (I) and (II) TOGETHER are NOT sufficient

There is no indication whatsoever about how many numbers there are... so if you are able to come up with the answer then please explain to me how that came about.

fluke · Answer

(I) 
Let third number be 'x'
Fourth number will be x+2

x+x+2=30
2x=28
x=14=Third Number, Fourth Number=x+2=16

Sufficient.

(II) 
Let first number be 'f'
Second number will be f+2

f+f+2=22
2f=20
f=10=First Number, Fourth Number=f+(n-1)*d=10+3*2=16

Sufficient.

Ans: "D"

gmat1220 · Answer

1) not sufficient. Unless the questions says how many total consecutive integers are 1) is NOT sufficient.

2) is sufficient. lets say numbers are n, n+2

2n + 2 = 22
n = 10
so first two numbers are 10,12. Hence we can find the fourth consecutive even. Sufficient.

Unless the questions says how many total consecutive integers are 1) is NOT sufficient. hence B

Bunuel · Answer

Poorly worded question. If the question were:

Find the largest of 4 consecutive even numbers of a set X.
(1) The sum of the largest two numbers of the set is 30
(2) The sum of the smallest two numbers of the set is 22

Then the answer would indeed be D.

mariyea · Answer

That's exactly what I thought! i answered B too... but the q says that I'm wrong.
This is the OE.
"From Statement 1, we get the sum of last two of the four consecutive even numbers are 30. ( This is an assumption that the only amount of numbers there are is four... That is not stated in the q.) 
If x be the last number, the second last number would be x - 2 as the numbers are even and consecutive.
Now, x + x - 2 = 30
or x = 16
Now, if 16 is the last number in the series of even consecutive numbers, the others are 14, 12, and 10.
Thus statement 1 alone is sufficient to answer the question.

Statement 2 gives the sum of the first two numbers as 22.
If x and x + 2 are the first two numbers, 
x + x + 2 = 22
and x = 10.
The other numbers in the series are 12, 14 and 16. Thus the question can also be answered using statement 2 alone.

Therefore, both the statements are individually able to answer the question,

Hence (D) is the correct answer."

mariyea · Answer

That's what I thought too...

fluke · Answer

I concur with Maryea, Bunuel and gmat1220.

With given info: Answer should be "B".

GMAT01 · Answer

What could be possible scenarios that show statement 1 has multiple solutions?

Example,

One would be assuming only four terms in this sequence to arrive at the same value as statement 2.

Posted from my mobile device

PerfectScores · Answer

Find the fourth consecutive even number:
(I) The sum of the last two numbers is 30
(II) The sum of the first two numbers is 22

Either of the statement is sufficient. If we know even one number we know everything.

If sum of last two numbers is 30 that means that x + x + 2 = 30 hence 2x = 28 and x =14 so the series is 10 12 14 16

Krabhay · Answer

Let the consecutive even numbers be x , x+2 , x+4 & x +6
Statement 1. x+4 + x + 6 = 30 This gives, x = 10. Hence, Sufficient.
Statement 2. x + x + 2 = 22. This gives, x = 10. Hence, Sufficient.

Find the fourth consecutive even number: (I) The sum of the

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