wrong explaination?

[anand0408]

Here's a question i encountered in MCAT #2:

If x, y, and z are integers greater than 1, and (327)(510)(z) = (58)(914)(xy), then what is the value of x?

(1) y is prime

(2) x is prime

Explaination is:

The best way to answer this question is to use the rules of exponents to simplify the question stem, then analyze each statement based on the simplified equation.

(327)(510)(z) = (58)(914)(xy) Simplify the 914
(327)(510)(z) = (58)(328)(xy) Divide both sides by common terms 58, 327
(52)(z) = 3xy

(1) INSUFFICIENT: Analyzing the simplified equation above, we can conclude that z must have a factor of 3 to balance the 3 on the right side of the equation. Similarly, x must have at least one factor of 5. Statement (1) says that y is prime, which does no tell us how many fives are contained in x and z.

For example, it is possible that x = 5, y = 2, and z = 3:
52 · 3 = 3 · 52

It is also possible that x = 25, y = 2, and z = 75:
52 · 75 = 3 · 252
52 · 52 · 3 = 3 · 252

(2) SUFFICIENT: Analyzing the simplified equation above, we can conclude that x must have a factor of 5 to balance out the 52 on the left side. Since statement (2) says that x is prime, x cannot have any other factors, so x = 5. Therefore statement (2) is sufficient.

The correct answer is B.

I think this is wrong because:

The condition says nothing about Z

What if Z = 2 (5^-2)(3)

Then we have:

3(X^Y) = 2 (5^-2) (3) (5^2)

=> (X^Y) = 2

Since X is prime: If X = 2, Y = 1, this is satisfied.

Similarly by playing with Z we can get n number of answers

Hence insufficient and IMO answer is (E)....anybody?

[Ben Ku]

I think the question is correctly stated:

If x, y, and z are integers greater than 1, and (3^27)(5^10)(z) = (5^8)(9^14)(x^y), then what is the value of x?

(1) y is prime
(2) x is prime


We can simplify the 9^14 as 3^28. In this case, our equation is
(3^27)(5^10)(z) = (5^8)(3^28)(x^y)
(5^2)(z) = 3(x^y)

We know that z must be divisible by 3 and x^y must be divisible by 25.

I think this is wrong because:
The condition says nothing about Z
What if Z = 2 (5^-2)(3)
Then we have:
3(X^Y) = 2 (5^-2) (3) (5^2)
=> (X^Y) = 2

This value for Z is not possible because 2(5^-2)(3) = 0.24, which is NOT an integer, as specified in the question stem.

I hope that helps.

[enniguy]

Hi,

I have a question regarding the explanation for this question.
The answer claims that it's B, as in, X is prime is enough.

After simplification the equation will be,
(X^Y)3 = Z(5^2).
Consider following values for X, Y and Z.
(1) --- (5^2)3 = 3(5^2). Here X=5,Y=2,Z=3. X is prime.
(2) --- (5^4)3 = (3*5^2)(5^2). Here X=5,Y=4,Z=75. X is still prime.

So, shouldn't the answer be C instead of B?

[esledge]

Hi,

I have a question regarding the explanation for this question.
The answer claims that it's B, as in, X is prime is enough.

After simplification the equation will be,
(X^Y)3 = Z(5^2).
Consider following values for X, Y and Z.
(1) --- (5^2)3 = 3(5^2). Here X=5,Y=2,Z=3. X is prime.
(2) --- (5^4)3 = (3*5^2)(5^2). Here X=5,Y=4,Z=75. X is still prime.

So, shouldn't the answer be C instead of B?

I think you are getting turned around in the logic.

If the question were something like "what is z?" then your two examples would indicate that we could have at least two different answers (z = 3 or 75) based on the constraint that x is prime.

But remember, we are not checking whether x could be prime, or whether there's only one such scenario. We are starting from the fact that x is prime, considering the possible scenarios, then answering the final question for each/all of them, which in this case is "what is x?" In both of your examples, x = 5. SUFFICIENT.