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If x and y are positive, which of the following ...

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If x and y are positive, which of the following ...

by mitzwillrockgmat » Thu May 27, 2010 3:15 am
Hi can someone explain how to solve this??

i read somewhere cross multiplication. if this is true can someone show me the process how i can cross multiply sqrt (x+y)/2x with 1/sq rt(x+y) ??

i dont know how to conclude which is greater, sqtr (x+y)*sqtr (x+y) or 2x??

also read somewhere to pick values of x & y that are perfect squares...why is that so??

thanks!! :)



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by gmatmachoman » Thu May 27, 2010 3:24 am
mitzwillrockgmat wrote:Hi can someone explain how to solve this??

i read somewhere cross multiplication. if this is true can someone show me the process how i can cross multiply sqrt (x+y)/2x with 1/sq rt(x+y) ??

i dont know how to conclude which is greater, sqtr (x+y)*sqtr (x+y) or 2x??

also read somewhere to pick values of x & y that are perfect squares...why is that so??

thanks!! :)



Image

Pick B!!

1/ sqrt (x+y)

= sqrt (x+y) /(x+y)

I tried plugging in x= y =10

and picked B
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by gmatjedi » Thu May 27, 2010 3:39 am
my approach:

1/sqrt(x+y) = (x+y)/(x^2+2xy+y^2)

square option 2= (x+sqrt(xy)+y)/(x^2+2xy+y^2)
larger than above

square option 3=(x-sqrt(xy)+y)/(x^2+2xy+y^2)
smaller than above

for option 1, best option seems to be choosing numbers:
try both x=16 and y=9
and
x=9 and y=16
this shows that value depends on which is larger x or y
if x>y then above larger than option 1
if x<y then above smaller than option 1

choose b only
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by mitzwillrockgmat » Thu May 27, 2010 3:41 am
gmatmachoman wrote:
mitzwillrockgmat wrote:Hi can someone explain how to solve this??

i read somewhere cross multiplication. if this is true can someone show me the process how i can cross multiply sqrt (x+y)/2x with 1/sq rt(x+y) ??

i dont know how to conclude which is greater, sqtr (x+y)*sqtr (x+y) or 2x??

also read somewhere to pick values of x & y that are perfect squares...why is that so??

thanks!! :)



Image

Pick B!!

1/ sqrt (x+y)

= sqrt (x+y) /(x+y)

I tried plugging in x= y =10

and picked B

how is 1/ sqrt (x+y) = sqrt (x+y) /(x+y) ? can u show how u deduced that? also why pick 10 for both?
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by gmatmachoman » Thu May 27, 2010 3:52 am
Ok let me do that!!

rule 1 : sqrt (x) * sqrt (x) = x

apply this in our equation. we need to achieve unity when doing so that operation on numbers!

1/ sqrt (x+y) = sqrt (x+y)/{(sqrt (x+y) * sqrt (x+y)}

=sqrt (x+y) /(x+y)

U can plz refer some book dealing with radicals/ surds/ that will help u a lot!
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by mitzwillrockgmat » Thu May 27, 2010 4:35 am
gmatmachoman wrote:Ok let me do that!!

rule 1 : sqrt (x) * sqrt (x) = x

apply this in our equation. we need to achieve unity when doing so that operation on numbers!

1/ sqrt (x+y) = sqrt (x+y)/{(sqrt (x+y) * sqrt (x+y)}

=sqrt (x+y) /(x+y)

U can plz refer some book dealing with radicals/ surds/ that will help u a lot!
thanks got that but how do i proceed further to determine which value is greater?
u didnt mention why you picked x=y=10
thanks :)
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by kevincanspain » Thu May 27, 2010 5:19 am
mitzwillrockgmat wrote:
gmatmachoman wrote:Ok let me do that!!

rule 1 : sqrt (x) * sqrt (x) = x

apply this in our equation. we need to achieve unity when doing so that operation on numbers!

1/ sqrt (x+y) = sqrt (x+y)/{(sqrt (x+y) * sqrt (x+y)}

=sqrt (x+y) /(x+y)

U can plz refer some book dealing with radicals/ surds/ that will help u a lot!
thanks got that but how do i proceed further to determine which value is greater?
u didnt mention why you picked x=y=10
thanks :)

If you want to compare fractions, it's best to get a common numerator or denominator

If we compare sqrt(x+y)/(x+y) with sqrt(x + y)/2x, the greater fraction will have the smaller numerator

2x < x + y is equivalent to x < y, so the latter fraction will be greater if and only if x < y
Kevin Armstrong
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