Official Answer:- AIs x divisible by 39?

Step 1: Analyze the QuestionThis is a Yes/No question. Unlike other remainder questions in which you can pick numbers, the remainders in the

statements would be very tedious and time-consuming to test multiple times individually, let alone to combine. Thus, there

must be a simpler way to determine divisibility. Whenever the numbers given are unwieldy, the easiest and most efficient

way to establish divisibility is to find the prime factors. In this case, 39 breaks down to 3 × 13, so for x to be divisible by

39, it must be divisible by both 3 and 13.

Step 2: Evaluate the StatementsStatement (1) gives the number 65. Consider that 65 is 5 × 13; one of the prime factors of 39 is present. For x to be divisible

by 13, the remainder itself must be a multiple of 13. The remainder 7 is not a multiple of 13, so it is impossible for x to be

divisible by 13 or 39. This makes the answer to the question always no, and Statement (1) is sufficient. Eliminate choices

(B), (C), and (E).

In evaluating Statement (2), you can use the same principle. The number 36 is divisible by 3, one of the necessary primes, so

the remainder must also be divisible by 3. The remainder 15 is divisible by 3, meaning that x is a multiple of 3. Since you

don’t know anything else about x, it’s entirely possible that x is also divisible by 13, while there are certainly values that

would make x not divisible by 13. Statement (2) is insufficient.

The correct answer is (A).

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