Last visit was: 18 May 2024, 21:10 It is currently 18 May 2024, 21:10
Toolkit
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.

Which of the following pairs of numbers (x,y) is NOT a valid solutio

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93334
Own Kudos [?]: 624832 [23]
Given Kudos: 81900
Senior SC Moderator
Joined: 22 May 2016
Posts: 5330
Own Kudos [?]: 35562 [7]
Given Kudos: 9464
General Discussion
Intern
Joined: 16 Jul 2016
Posts: 13
Own Kudos [?]: 31 [0]
Given Kudos: 396
Manager
Joined: 01 Feb 2017
Posts: 244
Own Kudos [?]: 347 [1]
Given Kudos: 148
Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink]
1
Kudos
8933x-5920y=97

For this equation to be valid:
1. x<y as (8933-5920)>97. So, we need to reduce the LHS value.

2. 8933x must be an Odd number because 5920y is an even number and 97 is an odd number.
That means, value of x cannot be an even number.

Hence, Ans C is the only option with x as even

Therefore, Ans C

Posted from my mobile device
Intern
Joined: 29 Aug 2010
Posts: 8
Own Kudos [?]: 45 [0]
Given Kudos: 124
Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink]
8933x-5920y=97

If we don't get the units digit 7 after multiplying by x, then we got the answer:

A. (4749, 7166) ----> ...3* ...9= ....7 May be Valid
B. (10669, 16099)---> ....3*....9= ....7 May be Valid
C. (16588, 25031)---> ....3*....8= ....4 Not Valid hence Answer
D. (22509, 33965)---> ....3*....9= ....7 May be Valid
E. (28429, 42898)---> ....3*....9= ....7 May be Valid

If you like my approach, hit [u]+1Kudos button
Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3042
Own Kudos [?]: 6355 [1]
Given Kudos: 1646
Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink]
1
Kudos
Bunuel wrote:
Which of the following pairs of numbers (x,y) is NOT a valid solution to the equation 8933x − 5920y = 97?

A. (4749, 7166)
B. (10669, 16099)
C. (16588, 25031)
D. (22509, 33965)
E. (28429, 42898)

We can solve this problem using units digits.

We see that the product of 5920 and y will always have a units digit of zero, since the product of any number and a number with a units digit of zero must end in a zero.

Thus, we see that the product of 8933 and x must have a units digit of 7, since 8933x − 5920y = 97.

Of our answer choices, we see that answer choices A, B, D, and E have units digits of 9 for the value of x. Answer choice C is the one that doesn’t have a units digit of 9. Since we are looking for the one that is NOT a valid solution, choice C must be the one that is NOT valid.

Intern
Joined: 28 Nov 2017
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 130
Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink]
Bunuel wrote:
Which of the following pairs of numbers (x,y) is NOT a valid solution to the equation 8933x − 5920y = 97?

A. (4749, 7166)
B. (10669, 16099)
C. (16588, 25031)
D. (22509, 33965)
E. (28429, 42898)

8933*x-5920*y=97
As we can see,the result is an odd number
The product of 8933*x can be either an odd number or even, while 5920*y is always even
To get an odd number 8933*x Must be an odd number ( ODD-EVEN=ODD)

We search for numbers which makes 8933*x even. Only C makes the product even

I hope this is helpful!
VP
Joined: 31 Oct 2013
Posts: 1260
Own Kudos [?]: 1168 [0]
Given Kudos: 635
Concentration: Accounting, Finance
GPA: 3.68
WE:Analyst (Accounting)
Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink]
Bunuel wrote:
Which of the following pairs of numbers (x,y) is NOT a valid solution to the equation 8933x − 5920y = 97?

A. (4749, 7166)
B. (10669, 16099)
C. (16588, 25031)
D. (22509, 33965)
E. (28429, 42898)

8933x − 5920y = 97

97 is odd integer.

5920y = even

8933x must be odd.

Thus x must be odd.

C is the correct answer.
BSchool Moderator
Joined: 08 Dec 2013
Posts: 685
Own Kudos [?]: 518 [0]
Given Kudos: 227
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '23
GMAT 1: 630 Q47 V30
WE:Operations (Non-Profit and Government)
Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink]
Bunuel wrote:
Which of the following pairs of numbers (x,y) is NOT a valid solution to the equation 8933x − 5920y = 97?

A. (4749, 7166)
B. (10669, 16099)
C. (16588, 25031)
D. (22509, 33965)
E. (28429, 42898)

Let us consider all the lat digits of Option C

3*8 - 0*1 = 7, not possible. It has to be 4.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18872
Own Kudos [?]: 22264 [0]
Given Kudos: 285
Location: United States (CA)
Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink]
Bunuel wrote:
Which of the following pairs of numbers (x,y) is NOT a valid solution to the equation 8933x − 5920y = 97?

A. (4749, 7166)
B. (10669, 16099)
C. (16588, 25031)
D. (22509, 33965)
E. (28429, 42898)

We see that coefficients of the given equation 8933x − 5920y = 97 and the coordinates in the given choices are big numbers. So we will analyze them using units digits only.

A) (4749, 7166)
Since 3(9) - 0(6) = 27 has a units digit of 7, the coordinates in choice A can be a solution.

B) (10669, 16099)

Since 3(9) - 0(9) = 27 has a units digit of 7, the coordinates in choice B can be a solution.

C) (16588, 25031)

Since 3(8) - 0(1) = 24 has a units digit of 4 but we need a units digit of 7, the coordinates in choice C CAN’T be a solution.

Non-Human User
Joined: 09 Sep 2013
Posts: 33074
Own Kudos [?]: 828 [0]
Given Kudos: 0
Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#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.
Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink]
Moderators:
Math Expert
93334 posts
Senior Moderator - Masters Forum
3137 posts