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If xy = 10, what is the value of x + y?
1. x and y are positive numbers.
2. 1/x + 1/y = 3
1. x and y are positive numbers.
2. 1/x + 1/y = 3
Source: McGraw Hill's GMAT
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
Posts: 240
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.
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.
Posts: 6,727
SajjadAhmad
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
Mo2men
Joined: 26 Mar 2013
Last visit: 09 May 2023
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Posts: 2,425
GMATPrepNow
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
Posts: 6,727
Mo2men
That's a perfect solution!
I don't believe there are any restrictions on this technique.
Cheers,
Brent
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