# GMAT 650 Level Arithmetic Practice Question #40

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The given question is a challenging GMAT 650 level quant problem solving question combining concepts in the Algebra and Number Properties.

Question 40: If x and y are non-negative integers such that 4x + 7y = 68, how many values are possible for (x + y)?

1. A. 11
2. B. 3
3. C. 5
4. D. 17
5. E. 14

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### Explanatory Answer | GMAT Equations & Numbers

Given data:
x and y are non-negative integers.
So, both x and y can take 0 or positive integer values.

4x + 7y = 68
=> 4x = 68 - 7y
Because x is an integer, 4x is divisible by 4. So, (68 - 7y) is divisible by 4.
68 is divisible by 4. So, 7y should also be divisible by 4.

x and y are non-negative integers.
So, the least possible value for y is 0.
So, 7y = 0. Note: 0 is divisible by 4.
Subsequently, let us plug in multiples of 4 for y till such time x remains non-negative.
When y = 0, x = 17
When y = 4, x = 10
When y = 8, x = 3
When y = 12, x = -4 (x is negative)
For values of y that are multiples of 4 and are greater than 8, x will be negative.

Possible values for x + y:
17 + 0 = 17
10 + 4 = 14
8 + 3 = 11
3 values are possible

##### Choice B is the correct answer.

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