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

 It is currently 12 Dec 2019, 20:00

### 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

# If s, u, and v are positive integers and 2s = 2u + 2v, which of the fo

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59712
If s, u, and v are positive integers and 2s = 2u + 2v, which of the fo  [#permalink]

### Show Tags

03 Mar 2014, 01:24
3
11
00:00

Difficulty:

15% (low)

Question Stats:

77% (01:03) correct 23% (01:11) wrong based on 629 sessions

### HideShow timer Statistics

If s, u, and v are positive integers and 2s = 2u + 2v, which of the following must be true?

I. s = u
II. $$u\neq{v}$$
III. s > v

(A) None
(B) I only
(C) II only
(D) III only
(E) II and III

Problem Solving
Question: 122
Category: Arithmetic Operations on rational numbers
Page: 77
Difficulty: 600

The Official Guide For GMAT® Quantitative Review, 2ND Edition

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 59712
Re: If s, u, and v are positive integers and 2s = 2u + 2v, which of the fo  [#permalink]

### Show Tags

03 Mar 2014, 01:25
SOLUTION

If s, u, and v are positive integers and 2s = 2u + 2v, which of the following must be true?

I. s = u
II. $$u\neq{v}$$
III. s > v

(A) None
(B) I only
(C) II only
(D) III only
(E) II and III

Notice two things:
1. we are asked to find out which of the following MUST be true, not COULD be true
2. s, u, and v are positive integers.

Given: $$2s=2u+2v$$ --> $$s=u+v$$. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true.

As for II: it's not necessarily true, for example 4=2+2. So, we have that only option III must be true.

_________________
Manager
Status: GMATting
Joined: 21 Mar 2011
Posts: 105
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
Re: If s, u, and v are positive integers and 2s = 2u + 2v, which of the fo  [#permalink]

### Show Tags

03 Mar 2014, 22:57
1
2s = 2u + 2v;
s = u + v;

Since we are told that all are positive integers, we can definitely say that s is greater than u and v.
I. s = u; Not true - since all are positive integers, s>u will be true.
II. u#v; Not true - As u and v can either hold the same positive integer value(ex., u=3 & v=3) or different values;
III. s>v; True - Since all are positive integers, s>v will hold true.

Ans is (D)
Math Expert
Joined: 02 Sep 2009
Posts: 59712
Re: If s, u, and v are positive integers and 2s = 2u + 2v, which of the fo  [#permalink]

### Show Tags

08 Mar 2014, 11:37
1
SOLUTION

If s, u, and v are positive integers and 2s = 2u + 2v, which of the following must be true?

I. s = u
II. $$u\neq{v}$$
III. s > v

(A) None
(B) I only
(C) II only
(D) III only
(E) II and III

Notice two things:
1. we are asked to find out which of the following MUST be true, not COULD be true
2. s, u, and v are positive integers.

Given: $$2s=2u+2v$$ --> $$s=u+v$$. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true.

As for II: it's not necessarily true, for example 4=2+2. So, we have that only option III must be true.

_________________
Manager
Joined: 20 Dec 2013
Posts: 222
Location: India
Re: If s, u, and v are positive integers and 2s = 2u + 2v, which of the fo  [#permalink]

### Show Tags

08 Mar 2014, 20:00
Option D.
s,u,v can't be equal to 0
And s=u+v
So s>v definitely.
II statement could be or couldn't be true.
And I statement can never be true because if s=u,then v=0 which is not possible as v is +ve integer.

Posted from my mobile device
Intern
Joined: 03 Aug 2012
Posts: 19
Location: United States (OR)
GPA: 3.53
WE: Analyst (Entertainment and Sports)
Re: If s, u, and v are positive integers and 2s = 2u + 2v, which of the fo  [#permalink]

### Show Tags

08 Mar 2014, 20:28
I got this one wrong at first but figured it out after. Here's what helped me.

I set up each equation,

S = U + V
V = U + S
U = V - S

I. From above we can plug zero in for V, and tell right away that S and U do not equal one another. FALSE
II. From above we can plug zero in for S, and in that instance it would tell us that U can equal V. FALSE
III. From the equation S = U + V, we can incur that S is a product of V + something else. So S is always greater than V. TRUE

Intern
Joined: 24 Mar 2014
Posts: 4
Location: India
Concentration: General Management, Technology
GMAT Date: 07-18-2014
GPA: 3.53
WE: Information Technology (Computer Software)
Re: If s, u, and v are positive integers and 2s = 2u + 2v, which of the fo  [#permalink]

### Show Tags

04 May 2014, 13:23
Hi,

why we can't consider 0 as a value for U - as 0 is a positive integer. If U = 0 then S = V thus option 3 will not hold true.

Following post from tells that we can consider 0 as non-negative integer.

Bunuel Math Expert

Joined: 02 Sep 2009
Posts: 17496
Followers: 2923
Kudos [?]: 18736 [0], given: 2371

follow send pm Re: PS-which of the following must be true [#permalink] 22 May 2012, 01:23 Expert's post Joy111 wrote:
Bunuel wrote:
LM wrote:
If x and y are integers such that ,and z is non negative integer then which of the following must be true?

A)

B)

C)

D)

E)

Note that we are asked "which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

Given: and .

Evaluate each option:
A) --> not necessarily true, for example: and ;

B) --> not necessarily true, for example: and ;

C) --> not necessarily true, if then ;

D) --> not necessarily true, it's true only for ;

E) --> as then and as then --> always true.

amazing ! couldn't figure out how option 3 was not necessarily true , forgot that non negative could mean that 0 is possible ,folks : non negative does not mean only positive integers , it could be 0 as well

Hypothetically speaking, Bunuel so if a question says, non positive numbers can we consider 0 as well , rather than only negative numbers.

Set of Non positive numbers { 0,-1,-5,-9 }
Set of Non negative numbers { 0,1, 4, 7, }

is this correct?

Yes, a set of non-positive numbers consists of zero and negative numbers.
Math Expert
Joined: 02 Sep 2009
Posts: 59712
Re: If s, u, and v are positive integers and 2s = 2u + 2v, which of the fo  [#permalink]

### Show Tags

04 May 2014, 23:50
1
DoNow wrote:
Hi,

why we can't consider 0 as a value for U - as 0 is a positive integer. If U = 0 then S = V thus option 3 will not hold true.

Following post from tells that we can consider 0 as non-negative integer.

0 is neither positive nor negative integer.

Also, sets of positive integers {1, 2, 3, 4, ....} and non-negative integers {0, 1, 2, 3, ...} are NOT the same.
_________________
Intern
Joined: 24 Mar 2014
Posts: 4
Location: India
Concentration: General Management, Technology
GMAT Date: 07-18-2014
GPA: 3.53
WE: Information Technology (Computer Software)
Re: If s, u, and v are positive integers and 2s = 2u + 2v, which of the fo  [#permalink]

### Show Tags

05 May 2014, 03:17
Hi Bunuel,

Also I am going through the posts in the quantitative forum for solving the questions and noticed one thing that in almost every post you have provided solution with detailed explanation, which are very helpful. This is a great job considering the huge number of posts we have in the quantitative forum.
Manager
Joined: 25 Mar 2013
Posts: 225
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: If s, u, and v are positive integers and 2s = 2u + 2v, which of the fo  [#permalink]

### Show Tags

14 Jan 2017, 18:12
2S = 2U + 2V
Take out commons
2S = 2 ( U + V )
(2/2) S = U + V
S = U + V
1, S = U may or may not
2, U # V may or may not
3, S > V Must be true
D
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: If s, u, and v are positive integers and 2s = 2u + 2v, which of the fo  [#permalink]

### Show Tags

16 Jan 2017, 18:14
1
Bunuel wrote:

If s, u, and v are positive integers and 2s = 2u + 2v, which of the following must be true?

I. s = u
II. $$u\neq{v}$$
III. s > v

(A) None
(B) I only
(C) II only
(D) III only
(E) II and III

We are given that 2s = 2u + 2v; thus, s = u + v. We need to determine which of the Roman numerals MUST BE true.

I. s = u

We see that s cannot equal u. Since s, u, and v are positive integers, s, the sum of u and v, will always be greater than u. Roman numeral one is NOT true.

II. u ≠ vu ≠ v

Roman numeral two does not have to be true. For example, if u = 1 and v = 1, then we have u = uv = v.

III. s > v

Since s = u + v, and s, u, and v are positive integers, s will ALWAYS be greater than v. Roman numeral three IS true.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
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.

Director
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: If s, u, and v are positive integers and 2s = 2u + 2v, which of the fo  [#permalink]

### Show Tags

06 Feb 2019, 23:29
Bunuel wrote:
If s, u, and v are positive integers and 2s = 2u + 2v, which of the following must be true?

I. s = u
II. $$u\neq{v}$$
III. s > v

(A) None
(B) I only
(C) II only
(D) III only
(E) II and III

Key word: If s, u, and v are positive integers, cant be 0 and -ive integers

Only one statement satisfies this 2s =2(u+v)
s = u + v

III, s > v

D
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
SVP
Joined: 03 Jun 2019
Posts: 1884
Location: India
Re: If s, u, and v are positive integers and 2s = 2u + 2v, which of the fo  [#permalink]

### Show Tags

13 Sep 2019, 23:22
Bunuel wrote:
If s, u, and v are positive integers and 2s = 2u + 2v, which of the following must be true?

I. s = u
II. $$u\neq{v}$$
III. s > v

(A) None
(B) I only
(C) II only
(D) III only
(E) II and III

Problem Solving
Question: 122

Category: Arithmetic Operations on rational numbers
Page: 77
Difficulty: 600

The Official Guide For GMAT® Quantitative Review, 2ND Edition

Given:
1. s, u, and v are positive integers
2. 2s = 2u + 2v
s = u + v
s, u ,v > 0

Asked: Which of the following must be true?

I. s = u
Since v > 0
s > u
NOT TRUE

II. $$u\neq{v}$$
Since there is no restriction on u & v
u may or may not be equal to v
COULD BE TRUE

III. s > v
Since u > 0
s = u + v > v
MUST BE TRUE

IMO D
Re: If s, u, and v are positive integers and 2s = 2u + 2v, which of the fo   [#permalink] 13 Sep 2019, 23:22
Display posts from previous: Sort by