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

 It is currently 07 Jul 2020, 15:32

### 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 x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 65062
If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are  [#permalink]

### Show Tags

28 May 2020, 02:59
00:00

Difficulty:

85% (hard)

Question Stats:

34% (02:26) correct 66% (02:19) wrong based on 59 sessions

### HideShow timer Statistics

Competition Mode Question

If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are there?

A. 6
B. 5
C. 4
D. 3
E. 2

_________________
PS Forum Moderator
Joined: 18 Jan 2020
Posts: 1078
Location: India
GPA: 4
Re: If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are  [#permalink]

### Show Tags

28 May 2020, 03:15
1
1
IMO B,

3x+4|y|=33 ------(equation)

Putting X = 1,
|Y| = 30/4 =7.5(not integer)

Putting X = 2,
|Y| = 27/4 =6.75(not integer)

Putting X = 3,
|Y| = 24/4 =6(integer)
Therefore y = +-6 -------(1)

Putting X = 4,
|Y| = 21/4 =5.25(not integer)

Putting X = 5,
|Y| = 18/4 =4.5(not integer)

Putting X = 6,
|Y| = 15/4 =3.75(not integer)

Putting X = 7,
|Y| = 12/4 =3(integer)
Therefore Y = -+3 ------(2)

Putting X = 8,
|Y| = 9/4 =2.25(not integer)

Putting X = 9,
|Y| = 6/4 =1.5(not integer)

Putting X = 10,
|Y| = 3/4 =0.75(not integer)

Putting X = 11,
|Y| = 0/4 =0(integer)
Therefore Y = 0 -----(3)

Total values of y = -6,+6,-3,+3,0 (5 values)

Posted from my mobile device
Senior Manager
Joined: 24 Oct 2015
Posts: 496
Location: India
Schools: Sloan '22, ISB, IIM
GMAT 1: 650 Q48 V31
GPA: 4
Re: If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are  [#permalink]

### Show Tags

28 May 2020, 03:17
If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are there?

A. 6
B. 5
C. 4
D. 3
E. 2

Given: x > 0
$$|y| = \frac{3(11-x)}{4}$$

possible values of x,y: [(3,6),(7,3),(11,0)]
we can not go any further as mod can not be less than 0
Ans: D
IESE School Moderator
Joined: 11 Feb 2019
Posts: 308
Re: If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are  [#permalink]

### Show Tags

28 May 2020, 03:27
D.

Given: x > 0 and 3x + 4|y| = 33;

Simplifying the eqn for y; |y| = 3(11-x)/4

Since it given that y is +ve and it is not mentioned that y>0, three values of x satisfies the equation:
(3,6), (7,3), (11, 0)
_________________

Cheers,
NJ
Director
Joined: 16 Jan 2019
Posts: 652
Location: India
Concentration: General Management
WE: Sales (Other)
Re: If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are  [#permalink]

### Show Tags

28 May 2020, 03:34
1
$$3x + 4|y| = 33$$

$$|y|=\frac{33-3x}{4}=\frac{3(11-x)}{4}$$

$$(11-x)$$ is a multiple of $$4$$

So $$x$$ can be $$3, 7 or 11$$

When $$x=3$$ or $$7$$, $$y$$ can take two values (+ve/-ve) for each and when $$x=11,y=0$$

(x,y)=(3,6) (3,-6) (7,3) (7,-3) (11,0)

Posted from my mobile device
Intern
Joined: 01 Mar 2019
Posts: 1
Re: If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are  [#permalink]

### Show Tags

28 May 2020, 04:16
to get an odd answer which is 33, we must add an odd number with an even number and we can get odd number in only multiples of 3 as we can only get even numbers in multiples of 4. We should try with every odd multiples of 3 to add with multiples of 4

Pairs - 21+12 & 24+9

Director
Joined: 30 Sep 2017
Posts: 961
GMAT 1: 720 Q49 V40
GPA: 3.8
Re: If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are  [#permalink]

### Show Tags

28 May 2020, 06:01
x > 0; x and y are both integers.

3x + 4|y| = 33 --> |y| = 3(11-x)/4
(11-x) has to be a multiple of 4, thus x = 11,7,3

For x=11... y=0
For x=7... y=-1 or y=1
For x=3... y=-2 or y=2
Obviously, there are 5 integer pairs (x, y)

Posted from my mobile device
SVP
Joined: 24 Nov 2016
Posts: 1663
Location: United States
Re: If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are  [#permalink]

### Show Tags

28 May 2020, 06:44
Quote:
If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are there?

A. 6
B. 5
C. 4
D. 3
E. 2

x>0, then x=(33-4|y|)/3>0 and an integer

(33-4|y|)/3>0, 33-4|y|>0, 4|y|<33,
|y|<33/4, -33/4<y<33/4,
-8≤y≤8

x=11-4/3|y|>0 and an integer
-8≤|y|=multiple of 3≤8
y={-6,-3,0,3,6}=5
y=-6: x=11-4/3*-6=11+8=19
y=6: x=11-4/3*6=11-8=3
both are in range

(x,y) pairs are 5

Ans (B)
Intern
Joined: 31 Oct 2018
Posts: 7
Re: If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are  [#permalink]

### Show Tags

28 May 2020, 07:14
1
Given x>0, x and you are integers.
3X+4|y|=33
y is integer if x=3 , 7 or 11
So possible ordered pair (x, y) are (3, 6), (3, -6), (7, 3)
(7, -3) &(11,0)i.e total 5 pairs.
So correct ans is (B).

Posted from my mobile device
Manager
Joined: 08 Jan 2018
Posts: 218
Location: India
Concentration: Operations, General Management
GMAT 1: 680 Q50 V32
WE: Project Management (Manufacturing)
Re: If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are  [#permalink]

### Show Tags

28 May 2020, 08:18
IMO B

If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are there?

x = 11 - 4/3|y| >0
|y| < 33/4 =8.25
& for integral values, |y| multiple of 3,
So, possible values are |y| = { 0, 3, 6 }
y = { -6, -3, 0, 3 , 6}
So total 5 pairs of (x,y)

B. 5
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 6430
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are  [#permalink]

### Show Tags

Updated on: 29 May 2020, 03:33
given relation of x > 0 and 3x + 4|y| = 33
would be valid at
y=+/-7 ; x= 2
y=+/-6 ; x=3
y=0 ; x= 11
total pairs ; 5 possible
OPTION B

If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are there?

A. 6
B. 5
C. 4
D. 3
E. 2

Originally posted by Archit3110 on 28 May 2020, 10:16.
Last edited by Archit3110 on 29 May 2020, 03:33, edited 1 time in total.
Stern School Moderator
Joined: 26 May 2020
Posts: 269
Concentration: General Management, Technology
WE: Analyst (Computer Software)
Re: If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are  [#permalink]

### Show Tags

28 May 2020, 15:23
Is it B ?

If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are there?

X > 0 . so 3x + 4|y| = 33 => y = 3/4 (11-x) .. X can be 3 , 7 , 11 and y can be 6 , 3 , 0 respectively .
However as per ques with -ve value of y also the equation will be satisfied .

So total 5 pair of x and y will satisfy the equation.. (3,6) , (3,-6) ,(7,3) , (7,-3) and (11,0)
Hence B , IMO .
_________________
Thank you.
Regards,
Ashish A Das.

The more realistic you are during your practice, the more confident you will be during the CAT.
Manager
Joined: 26 Dec 2017
Posts: 140
GMAT 1: 580 Q42 V27
Re: If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are  [#permalink]

### Show Tags

28 May 2020, 22:06
Ans:C
3x + 4|y| = 33
3x+4y=33..y=(33-3x)/4 as x>0
x=3 y=6
x=7 y=3

3x-4y=33
y=(3x-33)/4
x=3 y=-6
x=7 y=-3
x=15 y=3..no possible as 3*15=45
so total 4 pairs
Re: If x > 0 and 3x + 4|y| = 33, then how many integer pairs of (x, y) are   [#permalink] 28 May 2020, 22:06