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

It is currently 16 Oct 2019, 00:58

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If x, y, and z are positive integers such that 0 < x < y < z and x is

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58371
If x, y, and z are positive integers such that 0 < x < y < z and x is  [#permalink]

Show Tags

New post 13 Mar 2018, 01:06
1
4
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

86% (01:32) correct 14% (01:40) wrong based on 97 sessions

HideShow timer Statistics

examPAL Representative
User avatar
P
Joined: 07 Dec 2017
Posts: 1140
Re: If x, y, and z are positive integers such that 0 < x < y < z and x is  [#permalink]

Show Tags

New post 13 Mar 2018, 01:28
4
Bunuel wrote:
If x, y, and z are positive integers such that 0 < x < y < z and x is even, y is odd, and z is prime, which of the following is a possible value of x + y + z?

A. 4
B. 5
C. 11
D. 15
E. 18


As we're given mostly number-property related information (even, odd, prime) we'll look for a theoretical answer.
This is a Logical approach.

Since a prime number is always odd, then x + y + z is even + odd + odd = even.
(B), (C), (D) are eliminated.
(A) 4 is too small as it can't be the sum of 3 positive integers.

(E) must be our answer.
_________________
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 3545
If x, y, and z are positive integers such that 0 < x < y < z and x is  [#permalink]

Show Tags

New post 13 Mar 2018, 09:45
Bunuel wrote:
If x, y, and z are positive integers such that 0 < x < y < z and x is even, y is odd, and z is prime, which of the following is a possible value of x + y + z?

A. 4
B. 5
C. 11
D. 15
E. 18

I agree with DavidTutorexamPAL that number property theory is very efficient.

We have
0 < x=even < y=odd < z=ODD prime
z must be odd.
All primes after 2 are odd.
If z = 2, y must = 1, and there is no value left for x because (x > 0)

x + y + z =
(E + O\(_1\)) + O\(_2\) =
(O\(_3\) ) + (O\(_2\) ) = E

That said, a few real number trials will establish a pattern. x can be no smaller than 2

2 + 3 + 5 = 10
4 + 5 + 7 = 16
6 + 7 + 11 = 24
8 + 9 + 11 = 26
All are even, and all are > 4

This method is not foolproof for some variable questions (here, number property restrictions do make it foolproof). But if you're stuck, it gives you a basis from which to work.

Answer E
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.




Choose life.
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3074
If x, y, and z are positive integers such that 0 < x < y < z and x is  [#permalink]

Show Tags

New post 19 Mar 2018, 11:23
1

SOLUTION


We know:

    • x is an even number greater than 0.
      o Thus x>=2.

    • y is an odd number.
    • Since z is a prime number greater than x, thus z is an odd number.

Now, we know the nature of x, y, and z, we can easily find the nature of (x + y+ z).

    • x + y + z= Even + odd + odd
    • x + y + z = Even + Even
    • x + y + z = Even
The two even number in the given options are 4 and 18.

The minimum value of x and z are 2 and 3 respectively. And the sum of the minimum values of x and z, that is 2 and 3, is already greater than 4.
Hence, the value of x +y + z cannot be 4.

Therefore, the possible value of (x + y + z) is 18.

Answer: E
_________________
SVP
SVP
User avatar
V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1685
Location: India
Concentration: International Business, Operations
Schools: INSEAD Jan '19
GPA: 3.01
WE: Engineering (Real Estate)
Reviews Badge CAT Tests
Re: If x, y, and z are positive integers such that 0 < x < y < z and x is  [#permalink]

Show Tags

New post 23 Mar 2018, 11:18
Bunuel wrote:
If x, y, and z are positive integers such that 0 < x < y < z and x is even, y is odd, and z is prime, which of the following is a possible value of x + y + z?

A. 4
B. 5
C. 11
D. 15
E. 18


Here logic wins;

Given : 0 < x < y < z and x is even, y is odd, and z is prime

x = even, that means we don't require digit "1" here.

Start with "2" as "x" is even, then next two numbers (y and z) are greater than "2".

This means the sum of x + y + z will always be greater than "9".

Consider 2 + 3 + 4 (without restriction in a sequence), so A and B are out.

Now with given considerations in the question:

x = even, y = odd, and z = prime (this prime will always be odd as we have consumed the only even prime number "2" as "x".

Therefore, even + odd + odd = even.

Our answer should be even so C and D are also out.

(E)
_________________
"Do not watch clock; Do what it does. KEEP GOING."
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2816
Re: If x, y, and z are positive integers such that 0 < x < y < z and x is  [#permalink]

Show Tags

New post 05 Apr 2018, 11:11
Bunuel wrote:
If x, y, and z are positive integers such that 0 < x < y < z and x is even, y is odd, and z is prime, which of the following is a possible value of x + y + z?

A. 4
B. 5
C. 11
D. 15
E. 18


If x is even, y is odd, and z is prime, then the values could be:

x = 2

y = 3

z = 13

So x + y + z = 18.

Answer: E
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4777
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: If x, y, and z are positive integers such that 0 < x < y < z and x is  [#permalink]

Show Tags

New post 31 Aug 2019, 07:32
Bunuel wrote:
If x, y, and z are positive integers such that 0 < x < y < z and x is even, y is odd, and z is prime, which of the following is a possible value of x + y + z?

A. 4
B. 5
C. 11
D. 15
E. 18


x + y + z =Even + Odd + Prime (Odd) = Even

Now the prime number can have 2 possibilities -

1. Odd
2. Even - Not possible as it must be > 2

Thus, the answer must be even, left with option (A) and (E)

(A) can be negated as the least value of x = 2 and considering the other values > 2 , the answer can never be 4, Hence Answer must be (E) 18
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
GMAT Club Bot
Re: If x, y, and z are positive integers such that 0 < x < y < z and x is   [#permalink] 31 Aug 2019, 07:32
Display posts from previous: Sort by

If x, y, and z are positive integers such that 0 < x < y < z and x is

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne