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What is the number of solutions of the equation 2x + y = 40 where x an

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What is the number of solutions of the equation 2x + y = 40 where x an  [#permalink]

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New post Updated on: 13 May 2017, 07:54
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

79% (01:05) correct 21% (01:28) wrong based on 116 sessions

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What is the number of solutions of the equation 2x + y = 40 where x and y are both positive Integers?

A) 7
B) 13
C) 14
D) 18
E) 19

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Originally posted by GMATinsight on 13 May 2017, 05:59.
Last edited by Bunuel on 13 May 2017, 07:54, edited 1 time in total.
Edited the OA.
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Re: What is the number of solutions of the equation 2x + y = 40 where x an  [#permalink]

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New post 13 May 2017, 07:11
1
GMATinsight wrote:
What is the number of solutions of the equation 2x + y = 40 where x and y are both positive Integers?

A) 7
B) 13
C) 14
D) 18
E) 19


Hi
Again wrong OA..
Ans is E and not B

X and y are POSITIVE so >0..
2x+y=40..
x can take any value from 1 to 19.. as soon as x is 20, y becomes 0..
So solutions are 19..
(x, y) can be (1,38);(2,36);(3,34)(4,32);(5,30)......(19,2)
So ans is 19
E...
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Re: What is the number of solutions of the equation 2x + y = 40 where x an  [#permalink]

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New post 13 May 2017, 08:02
Top Contributor
1
GMATinsight wrote:
What is the number of solutions of the equation 2x + y = 40 where x and y are both positive Integers?

A) 7
B) 13
C) 14
D) 18
E) 19


Let's test some possible solutions, starting with the SMALLEST possible value of x.

1) x = 1 and y = 38
2) x = 2 and y = 36
3) x = 3 and y = 34
4) x = 4 and y = 32
.
.
.
We can see that, for each integer x-value, there is an integer value of y that completes the equation 2x + y = 40
How big can the x-value get?
The biggest possible x-value is 19. Once we get to x = 20, then y = 0, and y is not positive.
.
.
.
19) x = 9 and y = 2
STOP!

Answer:

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Re: What is the number of solutions of the equation 2x + y = 40 where x an  [#permalink]

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New post 26 Aug 2018, 19:15
GMATinsight wrote:
What is the number of solutions of the equation 2x + y = 40 where x and y are both positive Integers?

A) 7
B) 13
C) 14
D) 18
E) 19


We can see the minimum positive integer value of x is 1 and the largest positive integer value of x is 19 (if x is greater than 19, then y would be 0 or negative). Since x can be any positive integer from 1 to 19, inclusive, there are 19 solutions with x and y being both positive integers.

Answer: E
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Re: What is the number of solutions of the equation 2x + y = 40 where x an &nbs [#permalink] 26 Aug 2018, 19:15
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