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If 3x(52) is divided by 35(53), the quotient terminates with one decimal digit. If x > 0, which of the following
statements must be true?
(A) x is even
(B) x is odd
© x < 5
(D) x 5
(E) x = 5 -
abc is a three-digit number in which a is the hundreds digit, b is the tens digit, and c is the units digit. Let &(abc)&= (2a)(3b)(5c). For example, &(203)& = (22)(30)(53) = 500. For how many three-digit numbers abc will thefunction &(abc)& yield a prime number?
(A) 0
(B) 1
© 2
(D) 3
(E)
Were you copying pasting questions? What’s going on with that C? Can you please ensure that all the answer choices you posted are complete? Also, please fix the mathematical form in your questions; try wrapping your mathematical expressions with $$ so that would be eaiser for others to decipher your question.
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- We discussed this problem months ago, you can try to search keywords in searching bar to find the solution out.
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Man, I wasted a lot of time only because of the poor way in which the question has been copy pasted. Why not post a picture instead?
For quotient to terminate with one decimal, the denominator must have factors of 2’s or 5’s. If we divide these two, we’re left with 3^x/(3^5.5), in order to cancel out 3 in denominator completely, x should be greater than or equal to 5.
Answer is D.
2,3 and 5 are all prime numbers, for the product to be prime, only one of three should have power of 1 and rest should be 0. eg - (2^1).(3^0).(5^0) = 2.1.1 = 2. Likewise for 3 and 5. So, the combinations of powers will be, 100, 010 ,001 but it has to be a 3-digit number, so answer is only 100.
Answer is B.
(Greg has covered this question in one of the prime factorization videos).
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