GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 16 Feb 2020, 13:18 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If x, y, and z are positive integers, x=?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8556
GMAT 1: 760 Q51 V42
GPA: 3.82
If x, y, and z are positive integers, x=?  [#permalink]

### Show Tags 00:00

Difficulty:   15% (low)

Question Stats: 77% (01:20) correct 23% (01:18) wrong based on 96 sessions

### HideShow timer Statistics

[Math Revolution GMAT math practice question]

If $$x, y$$, and $$z$$ are positive integers, $$x=$$?

1) $$y=x+1$$ and $$z=x+3$$
2) $$x, y$$, and $$z$$ are prime numbers

_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 8283
Re: If x, y, and z are positive integers, x=?  [#permalink]

### Show Tags

1
1
If $$x, y$$, and $$z$$ are positive integers, $$x=$$?

1) $$y=x+1$$ and $$z=x+3$$
Any number of values can be taken...x=1, y=2, and z=4 or 10,11,13 and so on
Insufficient

2) $$x, y$$, and $$z$$ are prime numbers
Can be any combination..
2,3,5 or 5,7,11 and so on
Insufficient

Combined..
X and X+1 are consecutive integers. And only way this is possible is 2 and 3, so X=2
Sufficient

C
_________________
NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1053
Location: India
Concentration: Finance, Marketing
GMAT 1: 590 Q46 V25 GMAT 2: 690 Q49 V34 WE: Engineering (Energy and Utilities)
Re: If x, y, and z are positive integers, x=?  [#permalink]

### Show Tags

Statement 1 is clearly insufficient.
Statement 2 is also insufficient.
Combining both gives Y = 3, Z = 5 and X = 2. V
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 1043
Location: India
GPA: 3.64
Re: If x, y, and z are positive integers, x=?  [#permalink]

### Show Tags

MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x, y$$, and $$z$$ are positive integers, $$x=$$?

1) $$y=x+1$$ and $$z=x+3$$
2) $$x, y$$, and $$z$$ are prime numbers

S1 - y=x+1 and z=x+3
x could be any value from 1,2...
Insufficient.

S2 - x,y,z are prime numbers
Insufficient
Combining S1 and S2
If x=2, y=3 and z=5 (from S1)
all 3 are prime.
Sufficient.
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4318
Re: If x, y, and z are positive integers, x=?  [#permalink]

### Show Tags

Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x, y$$, and $$z$$ are positive integers, $$x=$$?

1) $$y=x+1$$ and $$z=x+3$$
2) $$x, y$$, and $$z$$ are prime numbers

Given: x, y, and z are positive integers

Target question: What is the value of x?

Statement 1: y = x + 1, and z = x + 3
There are infinitely many solutions to the above equations, which means there are infinitely many possible answers to the target question.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x, y, and z are prime numbers
So, x can be ANY prime number.
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that y = x + 1, which means y is 1 greater than x. This means x and y are CONSECUTIVE integers, which also means one value is ODD and one is EVEN
Statement 2 tells us that x and y are prime numbers
Since 2 is the only EVEN prime number, it must be the case that x is 2, and y is 3
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8556
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x, y, and z are positive integers, x=?  [#permalink]

### Show Tags

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (x, y and z) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Since y = x + 1, z = x + 3 and x, y, z are prime numbers, the only possibility is that x = 2, y = 3, and z = 5 because if x is an odd number, then y and z are two different even numbers, which cannot both be prime numbers.
Thus, both conditions together are sufficient.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
There are many different possible values for x, y and z, including x = 1, y = 2, z = 4 and x = 2, y = 3, z = 5. Therefore, we don’t have a unique solution, and condition 1) is not sufficient.

Condition 2)
There are many different possibly values for x, y and z, including x = 2, y = 3 and z = 5, and x = 3, y = 5 and z = 7. So, we don’t have a unique solution, and condition 2) is not sufficient.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 14074
Re: If x, y, and z are positive integers, x=?  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: If x, y, and z are positive integers, x=?   [#permalink] 30 Oct 2019, 10:27
Display posts from previous: Sort by

# If x, y, and z are positive integers, x=?  