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

 It is currently 19 Dec 2018, 08:29

# TODAY:

MIT Sloan R1 Decisions - Join MIT Chat for Live Updates | Chat with UCLA Anderson Adcom @9am PT | Chat with Yale SOM R1 Admit 10am PT

### 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
• ### Happy Christmas 20% Sale! Math Revolution All-In-One Products!

December 20, 2018

December 20, 2018

10:00 PM PST

11:00 PM PST

This is the most inexpensive and attractive price in the market. Get the course now!
• ### Key Strategies to Master GMAT SC

December 22, 2018

December 22, 2018

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

# If x, y, z are three consecutive prime numbers

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2326
If x, y, z are three consecutive prime numbers  [#permalink]

### Show Tags

Updated on: 13 Aug 2018, 01:37
00:00

Difficulty:

45% (medium)

Question Stats:

63% (02:03) correct 37% (01:54) wrong based on 126 sessions

### HideShow timer Statistics

e-GMAT Question:

If x, y, z are three consecutive prime numbers where x<y<z, which of the following is even?

i) $$x^2+y^2+z^2$$
ii) $$(x + y) * (y + z)^2 * (x + z)^3$$
iii) $$(x+3)^2 + y^2 + z$$

A) Only I
B) Only II
C) Only III
D) Both I and II
E) Both II and III

This is

Question 3 of The e-GMAT Number Properties Marathon

Go to

Question 4 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, 08:36.
Last edited by EgmatQuantExpert on 13 Aug 2018, 01:37, edited 2 times in total.
Intern
Joined: 15 Jan 2018
Posts: 11
Concentration: Strategy, General Management
GMAT 1: 630 Q48 V28
GPA: 3.5
Re: If x, y, z are three consecutive prime numbers  [#permalink]

### Show Tags

27 Feb 2018, 08:47
B) Only II, is the correct answer.

i) try to put x=2, y=3 and z=5 => E
Now try to put x=3, y=5 and z=7 => O

ii) this expression will always have one summation even so the complete expression will be even for all the values of x, y and z.

iii) repeat the process done for i, once it will be Odd and in the other it will be even.

Sent from my [device_name] using [url]GMAT Club Forum mobile app[/url]
CEO
Joined: 11 Sep 2015
Posts: 3243
Re: If x, y, z are three consecutive prime numbers  [#permalink]

### Show Tags

27 Feb 2018, 09:56
Top Contributor
EgmatQuantExpert wrote:

Question:

If x, y, z are three consecutive prime numbers where x<y<z, which of the following is even?

i) x² + y² +z²
ii) (x + y)(y + z)²(x + z)³
iii) (x + 3)² + y² + z

A) Only I
B) Only II
C) Only III
D) Both I and II
E) Both II and III

Test some sets of values
Let's start with x = 2, y = 3 and z = 5
We get:
i) x² + y² + z² = 2² + 3² + 5² = 4 + 9 + 25 = 38 = EVEN
ii) (x + y)(y + z)²(x + z)³ = (2 + 3)(3 + 5)²(2 + 5)³ = (5)(8)²(7)³ = EVEN
iii) (x + 3)² + y² + z = (2 + 3)² + 3² + 5 = 25 + 9 + 5 = 39 ODD
Since iii) is not true, we can ELIMINATE C and E

Now let's test x = 3, y = 5 and z = 7
We get:
i) x² + y² + z² = 3² + 5² + 7² = 9 + 25 + 49 = 83 = ODD
Since i) is not true, we can ELIMINATE A and D

By the process of elimination, we are left with B

RELATED VIDEO FROM OUR COURSE

_________________

Test confidently with gmatprepnow.com

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2326
Re: If x, y, z are three consecutive prime numbers  [#permalink]

### Show Tags

27 Feb 2018, 22:48

Solution:

• As per the question stem, x, y, and z are three consecutive prime numbers.
• Since prime numbers can be even or odd, there can be two possibilities, depending on the values that x, y, and z can take:
1. One of the prime numbers is even and other two are odd
a. In this case, x has to be 2, since it is the smallest prime number among x, y and z.
b. y and z would be 3 and 5 respectively.
2. All the three prime numbers are odd.
a. This means that all the prime numbers are greater than or equal to 3.
b. For example: x = 5, y = 7, z = 11

Keeping these 2 possibilities in mind, let us analyze each of the 3 expressions:

Only expression II is even in nature, and hence the correct answer is Option B.
_________________

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

Math Expert
Joined: 02 Aug 2009
Posts: 7117
Re: If x, y, z are three consecutive prime numbers  [#permalink]

### Show Tags

28 Feb 2018, 05:59
EgmatQuantExpert wrote:

Question:

If x, y, z are three consecutive prime numbers where x<y<z, which of the following is even?

i) $$x^2+y^2+z^2$$
ii) $$(x + y) * (y + z)^2 * (x + z)^3$$
iii) $$(x+3)^2 + y^2 + z$$

A) Only I
B) Only II
C) Only III
D) Both I and II
E) Both II and III

firstly what all can be the cases for x<y<z
1) x is 2 so even and y and z will be odd
2) all three are odd

so y and z are ODD for sure

lets check the equations..

i) $$x^2+y^2+z^2$$
a) if x is even and other two odd, E+O+O=E
b) if all three odd, O+O+O=O

so need not be true
..
ii) $$(x + y) * (y + z)^2 * (x + z)^3$$
a) if x is even and other two odd, y+z will be even..so O*E*O=E
b) if all three odd, E*E*E=E..

Always true
..
iii) $$(x+3)^2 + y^2 + z$$
a) if x is even and other two odd, O+O+O=E
b) if all three odd, E+O+O=O

need not be true

only ii

B
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Re: If x, y, z are three consecutive prime numbers &nbs [#permalink] 28 Feb 2018, 05:59
Display posts from previous: Sort by