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Re: If x + y = 36, what is the value of xy? [#permalink]

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24 Aug 2016, 04:26

Bunuel wrote:

If x + y = 36, what is the value of xy?

(1) y − x = 14 (2) y = 2x + 3

Given \(x + y = 36,\) which is the equation of a line that has x and y intercept as 36.

Consider 1) \(y - x = 14\) . This is another line equation and intercepts -14 and 14 and will intersect the line \(x+y =36\). Hence sufficient , Select A and D

Consider 2)\(y = 2x + 3\). This has intercepts \(\frac{-3}{2}\) and 3 and will intersect the line \(x+y =36\). Hence Sufficient.

Statement 1: y − x = 14 So, we have the system: y − x = 14 y + x = 36

Do we need to solve this system to determine the values of x and y and then find the product xy? No. All we need to do is confirm that the two equations are not equivalent.

Here's what I mean: If the equation in statement 1 were 2x + 2y = 72, then this equation is equivalent to the given equation, y + x = 36. Notice that, if we take y + x = 36 and multiply both sides by 2, we get: 2x + 2y = 72. As such, the equations y + x = 36 and 2x + 2y = 72 are equivalent. In cases where the two equations are equivalent, we have an infinite number of solutions, which means we can't solve that particular system.

Since the two equations in our system are not equivalent, we can be certain that there will be only one solution. As such, we COULD solve the system for x and y, which means we COULD find the value of xy with certainty. Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT

Aside: there are cases when two non-equivalent equations can also have ZERO solutions, but this scenario would not appear in a Data Sufficiency question. For more on this, please see the second video below.

Statement 2: y = 2x + 3 So, we have the system: y = 2x + 3 y + x = 36 Since the two equations in this system are not equivalent, we can be certain that there will be only one solution. As such, we COULD solve the system for x and y, which means we COULD find the value of xy with certainty. Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT

Re: If x + y = 36, what is the value of xy? [#permalink]

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24 Aug 2016, 05:48

Senthil1981 wrote:

Bunuel wrote:

If x + y = 36, what is the value of xy?

(1) y − x = 14 (2) y = 2x + 3

Given \(x + y = 36,\) which is the equation of a line that has x and y intercept as 36.

Consider 1) \(y - x = 14\) . This is another line equation and intercepts -14 and 14 and will intersect the line \(x+y =36\). Hence sufficient , Select A and D

Consider 2)\(y = 2x + 3\). This has intercepts \(\frac{-3}{2}\) and 3 and will intersect the line \(x+y =36\). Hence Sufficient.

Answer is D. Both are sufficient.

+1 for kudos

in your explanation or process, we are considering non integer values as well? if yes, then xy will be different for integer & non integer values

Since we know the sum and difference of x and y, we can determine individual values of x and y, and hence their product. Although we already know that statement one alone is sufficient, let’s determine the values of x and y anyway:

Let’s add x + y = 36 and y - x = 14 together:

2y = 50

y = 25

Substituting y = 25 in x + y = 36, we get

x + 25 = 36

x = 11

Thus, xy = 275.

Statement Two Alone:

y = 2x + 3

Since we have an expression of y in terms of x, we can substitute this into x + y = 36 and get the value of x. Once we get the value of x, we can substitute that value in x + y = 36 and find the value of y; hence we can obtain the value of xy. Although we already know statement two alone is sufficient, let’s calculate the values of x and y anyway:

Let’s substitute y = 2x + 3 into x + y = 36:

x + 2x + 3 = 36

3x = 33

x = 11

Let’s substitute x = 11 into x + y = 36:

11 + y = 36

y = 25

Once again, we find xy = 275.

Answer: D
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