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15^x + 15^(x+1) = (15^y)(4^y).If x and y are integers and 15^x + 15^(x+1)/ 4^y = 15^y, what is the value of x?
a. 2
b. 3
c. 4
d. 5
e. Cannot be determined
Note however that if you expand this you get:GMATGuruNY wrote:This question was posted previously with the answer choices shown here:
15^x + 15^(x+1) = (15^y)(4^y).If x and y are integers and 15^x + 15^(x+1)/ 4y = 15y, what is the value of x?
a. 2
b. 3
c. 4
d. 5
e. Cannot be determined
We can plug in the answers, which represent the value of x.
Answer choice C: 4
15� + 15� = (15^y)(4^y)
15�(1+15) = (15^y)(4^y)
(15�)(4²) = (15^y)(4^y).
The values in red imply that y=2.
Thus, on the left-hand side, 15� needs to decrease to 15², implying that the value of x must be 2 LESS than answer choice C.
The correct answer is A.
Answer choice A: 2
15² + 15³ = (15^y)(4^y)
15²(1+15) = (15^y)(4^y)
(15²)(4²) = (15^y)(4^y).
Success!
I just found my own mistake. I can't believe it!Mathsbuddy wrote:Note however that if you expand this you get:GMATGuruNY wrote:This question was posted previously with the answer choices shown here:
15^x + 15^(x+1) = (15^y)(4^y).If x and y are integers and 15^x + 15^(x+1)/ 4y = 15y, what is the value of x?
a. 2
b. 3
c. 4
d. 5
e. Cannot be determined
We can plug in the answers, which represent the value of x.
Answer choice C: 4
15� + 15� = (15^y)(4^y)
15�(1+15) = (15^y)(4^y)
(15�)(4²) = (15^y)(4^y).
The values in red imply that y=2.
Thus, on the left-hand side, 15� needs to decrease to 15², implying that the value of x must be 2 LESS than answer choice C.
The correct answer is A.
Answer choice A: 2
15² + 15³ = (15^y)(4^y)
15²(1+15) = (15^y)(4^y)
(15²)(4²) = (15^y)(4^y).
Success!
3600 = 60 * y^2
so y^2 = 60
but y = SQRT(60)is non-integer (contrary to the condition in the question).
Therefore answer E - cannot be determined!
I've made an algebraic solution to match this on a separate reply, if you are interested.
I know I've made a mistake here, because y should equal 2.Mathsbuddy wrote:15^x + 15^(x+1)/ 4y = 15y
15^x * (1 + 15) = 60y^2
15^x = 60/16 * y^2 = 15/4 * y^2 = (SQRT(15/4) * y)^2
If 15^x = p^2 where p = SQRT(15/4) * y
then when p = 15, x = 2.
However, this is only if y is an integer (as per the rules of the question):
p = 15 = SQRT(15/4) * y
so y^2 = 4 * 225/15 = 60
so y = SQRT(60) which is non-integer.
Therefore answer E - cannot be determined.
