fullymooned wrote:
Here is the answer from Kaplan. I dont understand how he gets, If we increase x by 1, then the previous number is multiplied by 7.
This is a Value question. For sufficiency, we need to be able to determine one value for the remainder of 7xyz divided by 4. We need to determine the value of xyz. We are told that x, y, and z are all positive integers.
Evaluate the Statements:
Statement (1): We are given that yz = 3. We know that all of the variables are positive integers, so they must be 1 or greater. If we assume that x = 1, then we get:
The remainder when divided by 4 is 3.
If we increase x by 1, then the previous number is multiplied by 7. If the previous quotient has a remainder of 3 and we multiply that by 7, we get 21. Dividing this by 4, we get a remainder of 1. Increasing x by 1 again, we multiply the remainder of 1 by 7 and get 7. Dividing this by 4 will give us a remainder of 3. This pattern will continue indefinitely. We cannot determine one remainder from these conditions. Therefore, Statement (1) is Insufficient to answer the question. Eliminate choices (A) and (D).
Statement (2): We are told x is odd. This leaves us in the same situation as with Statement (1). When the number of 7s being multiplied is odd, we will get a remainder of 3. When the number of 7s is even, we will get a remainder of 1. Since we do not know the value of y or z, we do not know if the exponent will be odd or even. We cannot determine an answer from this information.
Statement (2) is Insufficient to answer the question. Eliminate choice (B).
Combined: We know that yz = 3 and x is odd. Since an odd number times an odd number is always odd, we know that the exponent will always be odd. An odd exponent will always give us a remainder of 3, as explained in the analysis of Statement (1). We can say that, with these conditions, the remainder will always be 3. Therefore, Statement (1) and Statement (2) combined are Sufficient to answer the question. Eliminate choice (E).
The correct answer is Choice (C).
For (1) we have \(7^{3x}\).
If they mean that if we increase x by 1 in \(7^{3x}\), then the previous number is multiplied by 7, then Kaplan is wrong.
If we increase x by 1 in \(7^{3x}\), then the previous number is multiplied by 7^3, not 7.
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