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

 It is currently 24 Apr 2019, 13:04

### 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

# For how many ordered pairs of positive integers (x,y) is x + 2y = 100?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 54496
For how many ordered pairs of positive integers (x,y) is x + 2y = 100?  [#permalink]

### Show Tags

21 Mar 2019, 04:04
1
1
00:00

Difficulty:

45% (medium)

Question Stats:

57% (01:35) correct 43% (01:21) wrong based on 47 sessions

### HideShow timer Statistics

For how many ordered pairs of positive integers (x,y) is x + 2y = 100?

(A) 33
(B) 49
(C) 50
(D) 99
(E) 100

_________________
CEO
Joined: 18 Aug 2017
Posts: 3041
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
For how many ordered pairs of positive integers (x,y) is x + 2y = 100?  [#permalink]

### Show Tags

Updated on: 21 Mar 2019, 08:26
1
1
Bunuel wrote:
For how many ordered pairs of positive integers (x,y) is x + 2y = 100?

(A) 33
(B) 49
(C) 50
(D) 99
(E) 100

pair series will go on from x,y = (2,49), (4,48),(6,47)...... (98,1)
total such pairs 49
IMO B
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.

Originally posted by Archit3110 on 21 Mar 2019, 04:09.
Last edited by Archit3110 on 21 Mar 2019, 08:26, edited 1 time in total.
VP
Joined: 31 Oct 2013
Posts: 1323
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: For how many ordered pairs of positive integers (x,y) is x + 2y = 100?  [#permalink]

### Show Tags

21 Mar 2019, 05:49
Archit3110 wrote:
Bunuel wrote:
For how many ordered pairs of positive integers (x,y) is x + 2y = 100?

(A) 33
(B) 49
(C) 50
(D) 99
(E) 100

pair series will go on from x,y = (100,0 ) to (0,50)
total such pairs = 50
(100,0) to (2,49)
total values of y=49
IMO B

Bro, x and y can't be 0.

x and y are positive integers.
Intern
Joined: 05 Mar 2019
Posts: 17
Re: For how many ordered pairs of positive integers (x,y) is x + 2y = 100?  [#permalink]

### Show Tags

21 Mar 2019, 05:59
Since x cannot be 0 y must be smaller than 50, therefore there are 49 different possible values of y.
Answer B is correct since pairs are ordered?
Intern
Status: Custom Boxes Zone
Joined: 13 Mar 2019
Posts: 6
Location: United States
Re: For how many ordered pairs of positive integers (x,y) is x + 2y = 100?  [#permalink]

### Show Tags

21 Mar 2019, 06:28
I'm supposing the appropriate solution is 16. Since it is x+2y=100 this suggests x is even. so x=2,4, 6, 8, 10, ..., 30, 32. There are 16 requested sets.
Intern
Joined: 05 Mar 2019
Posts: 17
Re: For how many ordered pairs of positive integers (x,y) is x + 2y = 100?  [#permalink]

### Show Tags

21 Mar 2019, 06:31
1
jackharrywa wrote:
I'm supposing the appropriate solution is 16. Since it is x+2y=100 this suggests x is even. so x=2,4, 6, 8, 10, ..., 30, 32. There are 16 requested sets.

Why do you stop at 32?

x could also have the value 98 and y=1, by your logic that's 49 possible values of x
Intern
Status: Custom Boxes Zone
Joined: 13 Mar 2019
Posts: 6
Location: United States
Re: For how many ordered pairs of positive integers (x,y) is x + 2y = 100?  [#permalink]

### Show Tags

21 Mar 2019, 06:59
Berlin92 wrote:
jackharrywa wrote:
I'm supposing the appropriate solution is 16. Since it is x+2y=100 this suggests x is even. so x=2,4, 6, 8, 10, ..., 30, 32. There are 16 requested sets.

Why do you stop at 32?

x could also have the value 98 and y=1, by your logic that's 49 possible values of x

yes, you are saying absolutely right, it is 49 possible value.
Intern
Joined: 01 Feb 2019
Posts: 20
Location: India
Re: For how many ordered pairs of positive integers (x,y) is x + 2y = 100?  [#permalink]

### Show Tags

21 Mar 2019, 07:32
Here is how i am going to solve it...

x + 2y = 100 for positive pair of x and y..

Lets assume that y = 49 then 2y = 98. Then x will be 2. y can't be 50 because then 2y will be 100 and x will become zero. As per problem statement x cant be zero.

now lets reduce the value of y

case 1 - if y = 48 then x becomes 4
case 2 - if y = 47 then x becomes 6
case 3 - if y = 46 then x becomes 8
and so on..

so y can have values from 49 to 1. It will change x values accordingly as well.

Manager
Joined: 12 Sep 2017
Posts: 227
For how many ordered pairs of positive integers (x,y) is x + 2y = 100?  [#permalink]

### Show Tags

Updated on: 25 Mar 2019, 13:05
Hello!

It can be solved with arithmetic progression.

$$nth = a + d(n-1)$$

$$nth = 98$$
$$a = 2$$

Applying the formula $$n = 49$$.

49.

B

Originally posted by jfranciscocuencag on 21 Mar 2019, 18:38.
Last edited by jfranciscocuencag on 25 Mar 2019, 13:05, edited 1 time in total.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5852
Location: United States (CA)
Re: For how many ordered pairs of positive integers (x,y) is x + 2y = 100?  [#permalink]

### Show Tags

24 Mar 2019, 18:24
Bunuel wrote:
For how many ordered pairs of positive integers (x,y) is x + 2y = 100?

(A) 33
(B) 49
(C) 50
(D) 99
(E) 100

We see that the smallest integer value for y is 1 (and x will then be 98), and the largest value of y is 49 (and x will then be 2). Since y can be any integer from 1 to 49, there are 49 values for y and hence 49 ordered pairs of (x, y).

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@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

Director
Joined: 27 May 2012
Posts: 735
For how many ordered pairs of positive integers (x,y) is x + 2y = 100?  [#permalink]

### Show Tags

29 Mar 2019, 13:03
1
Bunuel wrote:
For how many ordered pairs of positive integers (x,y) is x + 2y = 100?

(A) 33
(B) 49
(C) 50
(D) 99
(E) 100

x + 2y = 100
x=100-2y
x=2(50-y)
Since x and y have to be positive integers, smallest value of y = 1, and largest value of y=49, hence there are 49 such pairs.

Hope this helps .
_________________
- Stne
For how many ordered pairs of positive integers (x,y) is x + 2y = 100?   [#permalink] 29 Mar 2019, 13:03
Display posts from previous: Sort by