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If x and y are nonnegative integers and 5x + 2y = 32, how many values

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If x and y are nonnegative integers and 5x + 2y = 32, how many values  [#permalink]

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New post 26 Dec 2016, 11:02
3
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

57% (01:25) correct 43% (01:27) wrong based on 150 sessions

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If x and y are nonnegative integers and 5x + 2y = 32, how many values of x are there?

A. 1
B. 2
C. 3
D. 4
E. 6
Spoiler: OA

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Re: If x and y are nonnegative integers and 5x + 2y = 32, how many values  [#permalink]

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New post 26 Dec 2016, 11:20
1
Bunuel wrote:
If x and y are nonnegative integers and 5x + 2y = 32, how many values of x are there?

A. 1
B. 2
C. 3
D. 4
E. 6


5x + 2y = 32
5x = 2(16 – y)
x = 2n, y = 16 – 5n
x,y >= 0 -------> n = 0, 1, 2, 3 --------> x = 0, 2, 4, 6
Answer D
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Re: If x and y are nonnegative integers and 5x + 2y = 32, how many values  [#permalink]

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New post 30 Sep 2018, 17:17
1
Bunuel wrote:
If x and y are nonnegative integers and 5x + 2y = 32, how many values of x are there?

A. 1
B. 2
C. 3
D. 4
E. 6



we are looking foe the number of x may take . Trail and Error is the best in my sense.

we know that both x and y are integers and they are non-negative in nature.

even - even = even, which is divisible by 2. Plug even values for x only.

5x + 2y = 32.

1. x = 0

5*0 + 2y = 32 = y = 16.

2. x=2

5*2 + 2y = 32

y = 11

3. x = 4

5*4 + 2y = 32

y = 6

4. x = 6

5*6 + 2y = 32

y = 1.


Therefore the equation is true when we put these values of x. one may plug the value of y and look for the integer value of x instead of y.

The best answer is D.
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If x and y are nonnegative integers and 5x + 2y = 32, how many values  [#permalink]

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New post 30 Sep 2018, 21:35
1
Bunuel wrote:
If x and y are nonnegative integers and 5x + 2y = 32, how many values of x are there?

A. 1
B. 2
C. 3
D. 4
E. 6


CONCEPT: Find one solution i.e. values of x and y and for each next solution remember that x always changes by co-efficient of y (i.e. 2 in this case) and y always changes by co-efficient of x (i.e. 5 in this case) and

First solution is x = 0 and y = 16
Second solution is x = 2 and y = 11
Third solution is x = 4 and y = 6
Third solution is x = 6 and y = 1

Answer: Option D
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If x and y are nonnegative integers and 5x + 2y = 32, how many values   [#permalink] 30 Sep 2018, 21:35
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