Last visit was: 17 Jun 2024, 01:23 It is currently 17 Jun 2024, 01:23
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30567 [39]
Given Kudos: 799
Location: Canada
Send PM
Most Helpful Reply
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11443
Own Kudos [?]: 33518 [8]
Given Kudos: 317
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30567 [6]
Given Kudos: 799
Location: Canada
Send PM
General Discussion
Intern
Intern
Joined: 20 Feb 2017
Posts: 14
Own Kudos [?]: 14 [1]
Given Kudos: 19
Location: India
Concentration: Operations, International Business
GMAT 1: 560 Q47 V21
GPA: 3.05
WE:Other (Entertainment and Sports)
Send PM
Re: If x and y are positive integers, what is the value of x? [#permalink]
1
Kudos
Option D.
1) sufficient
3x+2y = 12
x=2 and y=3

2) sufficient
we can reduce the eq to = (3x +5y)^2 = 21^2; 3x+5y = 21
x=2 and y=3
Director
Director
Joined: 05 Mar 2015
Posts: 840
Own Kudos [?]: 870 [1]
Given Kudos: 45
Send PM
Re: If x and y are positive integers, what is the value of x? [#permalink]
1
Kudos
GMATPrepNow wrote:
If x and y are positive integers, what is the value of x?

1) 3x + 2y = 12
2) |9x² + 30xy + 25y²| = 21²

*kudos for all correct solutions



similar question for practice

https://gmatclub.com/forum/peter-went-to-the-store-to-buy-paint-small-cans-cost-164747.html
Manager
Manager
Joined: 25 Apr 2016
Posts: 56
Own Kudos [?]: 40 [1]
Given Kudos: 308
Send PM
Re: If x and y are positive integers, what is the value of x? [#permalink]
1
Kudos
x and y are positive integer
statement 1st 3x+2y =12 , considering the question stem, it will result in only one solution i.e(2,3)
statement 2nd will water down to 3x +5y =21 , considering question stem, it will result in only one solution (2,3)-> option D
Intern
Intern
Joined: 27 Apr 2016
Posts: 5
Own Kudos [?]: 1 [0]
Given Kudos: 7
Send PM
Re: If x and y are positive integers, what is the value of x? [#permalink]
hi Brent - thanks for posting this question and providing the explanation. when working with absolute values, I thought we would have to consider all possibilities as follows - please help me understand why this approach is incorrect (and since I ended up with 4 possibilities as shown below - I concluded that this statement was insufficient). I can see why case 2 and case 3 are invalid as RHS and LHS are not equal - but what about cases 1 and 4?:

case 1: 3x + 5y = 21

case 2: -(3x + 5y) = 21

and since we took the square root of both sides we were left with + / - 21 on the RHS, so we have two more cases:

case 3: 3x + 5y = -21

case 4: -(3x + 5y) = -21
Retired Moderator
Joined: 22 Aug 2013
Posts: 1183
Own Kudos [?]: 2526 [0]
Given Kudos: 459
Location: India
Send PM
Re: If x and y are positive integers, what is the value of x? [#permalink]
hudhudaa wrote:
hi Brent - thanks for posting this question and providing the explanation. when working with absolute values, I thought we would have to consider all possibilities as follows - please help me understand why this approach is incorrect (and since I ended up with 4 possibilities as shown below - I concluded that this statement was insufficient). I can see why case 2 and case 3 are invalid as RHS and LHS are not equal - but what about cases 1 and 4?:

case 1: 3x + 5y = 21

case 2: -(3x + 5y) = 21

and since we took the square root of both sides we were left with + / - 21 on the RHS, so we have two more cases:

case 3: 3x + 5y = -21

case 4: -(3x + 5y) = -21



Hi

You are right that when we are given (3x+5y)^2 = 21^2 then we have to consider 4 possibilities.

But here in this question we are also given that x/y are positive integers, so 3x+5y has to be a positive integer only, and it cannot be anything else. So we just go with the case 3x+5y = 21, and then we try for positive integer values of x/y (not even 0) which will satisfy the equation. We will see that the only possibility is x=2, y=3
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30567 [0]
Given Kudos: 799
Location: Canada
Send PM
Re: If x and y are positive integers, what is the value of x? [#permalink]
Expert Reply
Top Contributor
hudhudaa wrote:
hi Brent - thanks for posting this question and providing the explanation. when working with absolute values, I thought we would have to consider all possibilities as follows - please help me understand why this approach is incorrect (and since I ended up with 4 possibilities as shown below - I concluded that this statement was insufficient). I can see why case 2 and case 3 are invalid as RHS and LHS are not equal - but what about cases 1 and 4?:

case 1: 3x + 5y = 21

case 2: -(3x + 5y) = 21

and since we took the square root of both sides we were left with + / - 21 on the RHS, so we have two more cases:

case 3: 3x + 5y = -21

case 4: -(3x + 5y) = -21


Good question.

You'll find that the solution to the case 1 equation is identical to the case 4 equation, and the solution to the case 2 equation is identical to the case 3 equation. The reason for this is that equations 1 and 4 are equivalent equations, and equations 2 and 3 are equivalent equations.

Take, for example, case 1: 3x + 5y = 21
If we multiply both sides of this equation by -1, we get -(3x + 5y) = -21 (the case 4 equation).

The same holds true for equations 2 and 3

Cheers,
Brent
Intern
Intern
Joined: 17 Apr 2017
Posts: 11
Own Kudos [?]: 3 [1]
Given Kudos: 26
Send PM
Re: If x and y are positive integers, what is the value of x? [#permalink]
1
Kudos
is zero a positive integer ?
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30567 [0]
Given Kudos: 799
Location: Canada
Send PM
Re: If x and y are positive integers, what is the value of x? [#permalink]
Expert Reply
Top Contributor
anmolsd1995 wrote:
is zero a positive integer ?

Zero is an integer.
Zero is neither positive nor negative.
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6015
Own Kudos [?]: 13630 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Re: If x and y are positive integers, what is the value of x? [#permalink]
Expert Reply
anmolsd1995 wrote:
is zero a positive integer ?


anmolsd1995

Zero is
1) Neither Positive, nor a Negative integer but Yes it's an integer
2) Zero is an Even integer
3) Zero is a special highlight of Non-negative integers over positive integers.

:) :thumbsup:
Senior Manager
Senior Manager
Joined: 16 Nov 2021
Posts: 472
Own Kudos [?]: 28 [0]
Given Kudos: 5901
Location: United Kingdom
Send PM
Re: If x and y are positive integers, what is the value of x? [#permalink]
BrentGMATPrepNow wrote:
GMATPrepNow wrote:
If x and y are positive integers, what is the value of x?

1) 3x + 2y = 12
2) |9x² + 30xy + 25y²| = 21²


IMPORTANT: I created this question to highlight a common myth about Data Sufficiency questions as well as highlight a common mistake that students make.

Target question: What is the value of x?

Given: x and y are positive integers

Statement 1: 3x + 2y = 12
Some students will see this equation with 2 variables and automatically conclude that there are infinitely many solutions, in which case, statement 1 is not sufficient.
Under most conditions, this conclusion would be correct. However, in this question, we have the given condition that x and y are positive integers, which severely limits the possible solutions.
In fact, there is only ONE pair of positive integers that satisfy the equation: x = 2 and y = 3.
So, we can be certain that x = 2
Since we can answer the target question with certainty, statement 1 is SUFFICIENT


Statement 2: |9x² + 30xy + 25y²| = 21²
First factor the part inside the absolute value to get: |(3x + 5y)²| = 21²
This means that EITHER (3x + 5y)² = 21² OR (3x + 5y)² = -(21²)
We can quickly dismiss the second case, (3x + 5y)² = -(21²), since (3x + 5y)² must be greater than or equal to zero. So, it could never equal -(21²)

So, what about (3x + 5y)² = 21²?
This means that either 3x + 5y = 21 or 3x + 5y = -21
If x and y are both positive, we know that 3x + 5y will be positive, which means there are no solutions to the equation 3x + 5y = -21
What about the equation 3x + 5y = 21?
Under the restriction that x and y are POSITIVE INTEGERS, there is only ONE pair of positive integers that satisfy the equation: x = 2 and y = 3.
So, once again, we can be certain that x = 2
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

RELATED VIDEOS






Hi Brent BrentGMATPrepNow, at this stage since we are squaring both sides, so shouldn't it be just 3x + 5y = 21 only? Have I missed something here?
(3x + 5y)² = 21²?
This means that either 3x + 5y = 21 or 3x + 5y = -21
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30567 [0]
Given Kudos: 799
Location: Canada
Send PM
Re: If x and y are positive integers, what is the value of x? [#permalink]
Expert Reply
Top Contributor
Kimberly77 wrote:

Hi Brent BrentGMATPrepNow, at this stage since we are squaring both sides, so shouldn't it be just 3x + 5y = 21 only? Have I missed something here?
(3x + 5y)² = 21²?
This means that either 3x + 5y = 21 or 3x + 5y = -21


Here's an example to show why that reasoning is incorrect:
We know that 3² = (-3)², since both sides of the equation evaluate to be 9
However, we can't just remove the exponents and conclude that 3 = -3

Similarly, if x² = 9, we can't conclude x = 3 is only one solution, since x = -3 also satisfies the equation.
Senior Manager
Senior Manager
Joined: 16 Nov 2021
Posts: 472
Own Kudos [?]: 28 [0]
Given Kudos: 5901
Location: United Kingdom
Send PM
Re: If x and y are positive integers, what is the value of x? [#permalink]
Great explanation. Thanks Brent BrentGMATPrepNow.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33616
Own Kudos [?]: 838 [0]
Given Kudos: 0
Send PM
Re: If x and y are positive integers, what is the value of x? [#permalink]
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.
GMAT Club Bot
Re: If x and y are positive integers, what is the value of x? [#permalink]
Moderator:
Math Expert
93696 posts