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If xy = 10, what is the value of x + y?

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If xy = 10, what is the value of x + y?  [#permalink]

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New post 12 Apr 2017, 13:22
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Source: McGraw Hill GMAT

If xy = 10, what is the value of x + y?

1. x and y are positive numbers.
2. 1/x + 1/y = 3

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Re: If xy = 10, what is the value of x + y?  [#permalink]

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New post 12 Apr 2017, 13:37
1
1. x and y are positive numbers.

The statement is vague and x and y can take any values (fractions, integers), hence this statement is not sufficient.

2. 1/x + 1/y = 3

Above statement can be written as

(x+y)/xy = 3

Substituting value for xy above

(x+y)/10 = 3

x+y = 30

This statement is sufficient.

Answer is B.
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Re: If xy = 10, what is the value of x + y?  [#permalink]

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New post 12 Apr 2017, 13:39
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Top Contributor
1
SajjadAhmad wrote:
Source: McGraw Hill GMAT

If xy = 10, what is the value of x + y?

1. x and y are positive numbers.
2. 1/x + 1/y = 3


Target question: What is the value of x + y?

Given: xy = 10

Statement 1: x and y are positive numbers.
This statement doesn't feel sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1 and the given information. Here are two:
Case a: x = 1 and y = 10, in which case x + y = 1 + 10 = 11
Case b: x = 2 and y = 5, in which case x + y = 2 + 5 = 7
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 1/x + 1/y = 3
Let's combine these fractions. To do so, we'll need a common denominator.
A common denominator of x and y is xy.
So, 1/x = y/xy and 1/y = x/xy
We can now take: 1/x + 1/y = 3
And rewrite it as: y/xy + x/xy = 3
Combine the fractions: (y + x)/xy = 3
Use the given information to get: (y + x)/10 = 3
Multiply both sides by 10 to get: y + x = 30
PERFECT!
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

Cheers,
Brent
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Re: If xy = 10, what is the value of x + y?  [#permalink]

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New post 13 Apr 2017, 04:23
GMATPrepNow wrote:
Statement 2: 1/x + 1/y = 3
Let's combine these fractions. To do so, we'll need a common denominator.
A common denominator of x and y is xy.
So, 1/x = y/xy and 1/y = x/xy
We can now take: 1/x + 1/y = 3
And rewrite it as: y/xy + x/xy = 3
Combine the fractions: (y + x)/xy = 3
Use the given information to get: (y + x)/10 = 3
Multiply both sides by 10 to get: y + x = 30
PERFECT!
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

Cheers,
Brent


Hi Bent,

IN statement 2, I did it another way and I need your view.

xy=10............(1)

1/x + 1/y = 3...(2)

Multiple both equations

xy(1/x + 1/y)=30

x+ y =30....Perfect.

Is there any restriction for above method?

Thanks
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Re: If xy = 10, what is the value of x + y?  [#permalink]

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New post 13 Apr 2017, 06:13
Top Contributor
Mo2men wrote:
GMATPrepNow wrote:
Statement 2: 1/x + 1/y = 3
Let's combine these fractions. To do so, we'll need a common denominator.
A common denominator of x and y is xy.
So, 1/x = y/xy and 1/y = x/xy
We can now take: 1/x + 1/y = 3
And rewrite it as: y/xy + x/xy = 3
Combine the fractions: (y + x)/xy = 3
Use the given information to get: (y + x)/10 = 3
Multiply both sides by 10 to get: y + x = 30
PERFECT!
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

Cheers,
Brent


Hi Bent,

IN statement 2, I did it another way and I need your view.

xy=10............(1)

1/x + 1/y = 3...(2)

Multiple both equations

xy(1/x + 1/y)=30

x+ y =30....Perfect.

Is there any restriction for above method?

Thanks


That's a perfect solution!
I don't believe there are any restrictions on this technique.

Cheers,
Brent
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Re: If xy = 10, what is the value of x + y?  [#permalink]

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Re: If xy = 10, what is the value of x + y? &nbs [#permalink] 27 Jul 2018, 18:22
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