GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 12 Dec 2018, 20:04

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### The winning strategy for 700+ on the GMAT

December 13, 2018

December 13, 2018

08:00 AM PST

09:00 AM PST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
• ### GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

December 14, 2018

December 14, 2018

09:00 AM PST

10:00 AM PST

10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

# If a, b, c, d are 4 non-negative integers. Is (a+c) even?

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2291
If a, b, c, d are 4 non-negative integers. Is (a+c) even?  [#permalink]

### Show Tags

Updated on: 13 Aug 2018, 01:46
00:00

Difficulty:

35% (medium)

Question Stats:

69% (02:05) correct 31% (01:55) wrong based on 120 sessions

### HideShow timer Statistics

e-GMAT Question:

If a, b, c, d are 4 non-negative integers. Is (a+c) even?

1. $$a^2 +b^2 + c^2$$ is even
2. $$b^2 + c^2 + d^2$$ is even

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient

This is

Question 4 of The e-GMAT Number Properties Marathon

Go to

Question 5 of the Marathon

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Originally posted by EgmatQuantExpert on 27 Feb 2018, 09:20.
Last edited by EgmatQuantExpert on 13 Aug 2018, 01:46, edited 2 times in total.
BSchool Forum Moderator
Joined: 07 Jan 2016
Posts: 827
Location: India
GMAT 1: 710 Q49 V36
Re: If a, b, c, d are 4 non-negative integers. Is (a+c) even?  [#permalink]

### Show Tags

27 Feb 2018, 11:49
EgmatQuantExpert wrote:

Question:

If a, b, c, d are 4 non-negative integers. Is (a+c) even?

1. $$a^2 +b^2 + c^2$$ is even
2. $$b^2 + c^2 + d^2$$ is even

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient

we know

even + even = even
odd + odd = even

so

1) $$a^2 +b^2 + c^2$$ is even now here a b c are even or 2 out a/b/c are odd and one is even
now a and b even c odd
a+c not even
now a and c odd b even
a+c even
insufficient

2) $$b^2 + c^2 + d^2$$ is even
insufficient similar to
b c even d odd
we don't know value of a

now
combining
$$a^2 +b^2 + c^2$$ + $$b^2 + c^2 + d^2$$ = $$a^2 + 2 b^2 + 2 c^2 + d^2$$
here a^2 + d^2 is even as b/c can be odd or even and still the result is even

we know nothing about C being even/odd

(E) imo
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3325
Location: India
GPA: 3.12
Re: If a, b, c, d are 4 non-negative integers. Is (a+c) even?  [#permalink]

### Show Tags

27 Feb 2018, 12:11
We need to know the following odd-even properties
even^2 = even | odd^2 = odd | even + even = even | odd + odd = even | even + odd = odd

Is a+c even?

1. $$a^2 + b^2 + c^2$$ is even
If $$a^2$$, $$b^2$$,and $$c^2$$ are all even, then a+c is even
If $$a^2$$ and $$b^2$$ are odd and $$c^2$$ is even, a+c is odd (Insufficient)

2. $$b^2 + c^2 + d^2$$ is even
This statement contains no information about a.
We cannot say if a+c is even or not. (Insufficient)

On combining the information in both the statements,
We can have a case where a,b, and d are odd, whereas c is even. Here, a+c is odd
But, if a,b,c, and d are all even, then a+c will be even (Insufficient - Option E)
_________________

You've got what it takes, but it will take everything you've got

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2291
Re: If a, b, c, d are 4 non-negative integers. Is (a+c) even?  [#permalink]

### Show Tags

28 Feb 2018, 10:37

Solution:

Step 1: Analyse Statement 1:
$$a^2 +b^2 + c^2$$ is Even
• If $$a^2 +b^2 + c^2$$ is Even, it gives rise to two possibilities:
o Either one of $$a/b/c$$ is Even and the rest two are Odd
o Or, all the three numbers: $$a, b$$ and $$c$$are Even.
Per our conceptual knowledge, let’s make a table to understand this.

It is clear from the table that the even-odd nature of $$(a + c)$$varies, and we cannot conclude anything about it.
As we do not know the exact even-odd nature of$$(a + c)$$,
Statement 1 alone is NOT sufficient to answer the question.
Hence, we can eliminate answer choices A and D.
Step 2: Analyse Statement 2:
$$b^2 +c^2 + d^2$$ is Even
• If $$b^2 +c^2 + d^2$$ is Even, it gives rise to two possibilities:
o Either one of $$b/c/d$$ is Even and rest two are Odd
o Or, all the three numbers: $$b, c$$ and $$d$$ are Even.
Let’s make a table to understand this.

It is clear from the table that the even-odd nature of $$(a + c)$$ varies, and we cannot conclude anything about it.
As we do not know the exact even-odd nature of $$(a + c)$$,
Statement 2 alone is NOT sufficient to answer the question.
Hence, we can eliminate answer choice B.
Step 3: Combine both Statements:
From the first statement, we have: $$a^2 +b^2 + c^2$$ = Even
From the second statement, we have: $$b^2 +c^2 + d^2$$ = Even
Combining both the statements, we have: a$$^2 +b^2 + c^2 + b^2 +c^2 + d^2$$ = Even + Even = Even
Therefore, $$a^2 +2b^2 + 2c^2 + d^2$$ is even
We know that, $$2b^2 + 2c^2$$ is always even irrespective of the even-odd nature of $$b$$ and $$c$$, since they are multiplied by an even number $$(2)$$
So, our expression reduces to: $$a^2 + d^2$$ is even. This will lead to two possibilities:
• Either both a and d are Odd.
• Or both a and d are Even.
Per our conceptual understanding, let us draw a table combining both the tables from Step 3 and Step 4 to see how will the even odd nature of the numbers affect the even-odd nature of the expression: $$(a + c)$$:

From the table it is evident that the even-odd nature of the expression $$(a + c)$$ cannot be determined uniquely.
By combining both statements we did not get a unique answer.
_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: If a, b, c, d are 4 non-negative integers. Is (a+c) even? &nbs [#permalink] 28 Feb 2018, 10:37
Display posts from previous: Sort by

# If a, b, c, d are 4 non-negative integers. Is (a+c) even?

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.