Is the sum of four particular integers even? (1) Two of the integers

Question

Is the sum of four particular integers even?

(1) Two of the integers are odd and two are even.
(2) The average (arithmetic mean) of the four integers is an integer.

DS21602.01
OG2020 NEW QUESTION

BrentGMATPrepNow · Accepted Answer

Some important rules: 
#1. ODD +/- ODD = EVEN
#2. ODD +/- EVEN = ODD
#3. EVEN +/- EVEN = EVEN

#4. (ODD)(ODD) = ODD
#5. (ODD)(EVEN) = EVEN
#6. (EVEN)(EVEN) = EVEN

Target question :    Is the sum of four particular integers even?

Statement 1 : Two of the integers are odd and two are even.  
We have: SUM = ODD + ODD + EVEN + EVEN
= (ODD + ODD) + (EVEN + EVEN)
= EVEN + EVEN
= EVEN
The answer to the target question is  YES, the sum is even 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : The average (arithmetic mean) of the four integers is an integer. 
Let the 4 numbers be a, b, c, and d
We can write: (a + b + c + d)/4 = k, where k is some integer
So, we can also write: a + b + c + d = 4k
Since 4k is EVEN, we know that a + b + c + d is EVEN
The answer to the target question is  YES, the sum is even 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

LevanKhukhunashvili · Answer

To get the sum of four integers even, several cases are possible
1) all of them are even
2) There are even number of odd integers

1 stm: odd+odd+even+even=even.  Suff 
2 stm:  \frac{sum of four integers}{4} =integer --> sum of four integers=4*integer.  suff

IMO
Ans:  D

Archit3110 · Answer

#1
o+o+e+e= e
sufficient
#2
avg of 4 integers is integers means sum of 4 intgers is even
sufficient
IMO D

EMPOWERgmatRichC · Answer

Hi All,

We're told that we have four INTEGERS. We're asked if the sum of those four integers is EVEN. This is a YES/NO question and can be solved with either Number Property rules or TESTing VALUES.

(1) Two of the integers are ODD and two are EVEN.

Fact 1 gives us enough information to deal with some specific Number Properties. 
Adding two ODD numbers will give us a sum that is EVEN (for example, 3+5 = 8) 
Adding two EVEN numbers will give us a sum that is EVEN (for example, 2+4 = 6)

Thus, adding two ODDs and two EVENs will give us EVEN+EVEN = EVEN. The answer to the question is ALWAYS YES. 
Fact 1 is SUFFICIENT

(2) The average (arithmetic mean) of the four integers is an integer.

Fact 2 references the 'Average Formula', so we should think in those terms. If we refer to the values as A, B, C and D, we can set up an average as:

(A+B+C+D)/4 = Integer 
(A+B+C+D) = (4)(Integer)

From this equation, we know that the sum of the four integers will be 4 times an integer. Multiplying ANY integer by an EVEN number will give us a product that is EVEN. For example: 
4(-1) = -4 
4(0) = 0 
4(1) = 4 
4(2) = 8 
4(3) = 12 
Etc. 
Thus, the answer to the question is ALWAYS YES. 
Fact 2 is SUFFICIENT

Final Answer:  D

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

ScottTargetTestPrep · Answer

Statement One Alone:

Two of the integers are odd, and two are even.

Since we have two even and two odd integers, we have:

odd + odd + even + even = even + even = even

Statement one alone is sufficient to answer the question.

Statement Two Alone:

The average (arithmetic mean) of the four integers is an integer.

Since the average of the 4 numbers is an integer:

sum/4 = integer

sum = 4 * integer

Thus, we see that the sum must be even.

Statement two alone is sufficient to answer the question.

Answer: D

EgmatQuantExpert · Answer

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are asked to determine
 • Whether the sum of four particular integers even or not.

To determine this, we need to know either the values of the integers, or the even-odd nature of them.
With this understanding, let us now analyse the individual statement.

Step 3: Analyse Statement 1

As per the information given in statement 1, two of the integers are odd and two are even.
 • Therefore, the sum of the four integers = (odd + odd) + (even + even) = even + even = even 
As we can determine that the sum of the four integers is even, statement 1 is sufficient to answer the question.

Step 4: Analyse Statement 2

As per the information given in statement 2, the average (arithmetic mean) of the four integers is an integer.
 • Hence, we can say, sum of the four integers = average of the four integers × 4
• As any multiple of 4 is an even number, the sum of the four integers is also an even number 
Hence, statement 2 is sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)

Since we can determine the answer from either of the statements individually, this step is not required.
Hence, the correct answer choice is option D.

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-NP-e1533292144892.png

Nistha86 · Answer

What are particular integers?what is we take values as -2.2,3,-3? ) is neither positive or negative?Please explain.

Bunuel · Answer

The question says that there are four particular integers, say a, b, c, and d, and asks whether their sum is even, so whether a + b + c + d = even.

If the integers are -2, 2, 3 and -3, then their sum is 0, which is even number. 0 is neither positive nor negative but it's definitely even.

Hope it's clear.

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=SBiciL_PS1Q

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=ZbF0UzCxcL4

bumpbot · Answer

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Is the sum of four particular integers even? (1) Two of the integers

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Is the sum of four particular integers even? (1) Two of the integers

Prep Toolkit

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