x^4+y^4=100

[sanjana]

If x^4 + y^4 = 100,then the greatest possible value of x is between?
a)0 and 3
b)3 and 6
c)6 and 9
d)9 and 12
e)12 and 15

OA : B

For this question I chose A because I included 3 in the range between 0 and 3. But looks like 3 is included in Between 3 and 6.
i.e does between 3 and 6 mean 3<=x<=6 or 3<x<6?

Can someone clarify?

[xcusemeplz2009]

i think b/n means 0.1 to 2.9;3.1 to 5.9

for this as long as value of x^4 <100 eqn holds true and x can be b/n 3 and 4

[mridul_dave]

i think b/n means 0.1 to 2.9;3.1 to 5.9

for this as long as value of x^4 <100 eqn holds true and x can be b/n 3 and 4

You dont have to worry about the definition of between here. The key is that 'x' or 'y' may not be integers. so assume a value of y = 0.01

x^4 will have to be 99.9999. THis is definitely more than 3 (because 3^4 is only 81 )
X is definitely cannot exceed 4 because 4 ^4 is way more than 100.

So x can be more than 3, but is definitely less than 4. Therefore B is the most correct answer.

Confession: When I first read the question I first thought the answer is A.

[xcusemeplz2009]

i think b/n means 0.1 to 2.9;3.1 to 5.9

for this as long as value of x^4 <100 eqn holds true and x can be b/n 3 and 4

You dont have to worry about the definition of between here. The key is that 'x' or 'y' may not be integers. so assume a value of y = 0.01

x^4 will have to be 99.9999. THis is definitely more than 3 (because 3^4 is only 81 )
X is definitely cannot exceed 4 because 4 ^4 is way more than 100.

So x can be more than 3, but is definitely less than 4. Therefore B is the most correct answer.

Confession: When I first read the question I fir
st thought the answer is A.

very true but what if x and y are int. then which option to go for......

[Stuart@KaplanGMAT]

very true but what if x and y are int. then which option to go for......

Then there would be no correct answer choice among those listed. In other words, if x and y had to be integers, then there would have to be a different answer listed.

[mridul_dave]

very true but what if x and y are int. then which option to go for......

Then there would be no correct answer choice among those listed. In other words, if x and y had to be integers, then there would have to be a different answer listed.

Agree with Stuart.
Also I always assume that in general, 'between' always 'includes' the range limits.

[yoshimihoku]

y could be 0
so 0<=x^4<=100
0<=x^2<=10
0<=x<=√10

√9=3,√16=4
so √10 is between 3 and 4 because 10 is between 9 and 16

so 0<=x<=3.xxxxx