2. A box contains five cards, numbered 1, 2, 3, 4 and 5. Three cards are randomly selected without replacement from the box. What is the probability that “4” is the largest value selected?
(A) \(\frac{1}{5}\)
(B) \(\frac{3}{10}\)
(C) \(\frac{2}{5}\)
(D) \(\frac{1}{2}\)
(E) None of the above
Dari ketiga kartu, nomor kartu terbesar adalah 4 dan dua lainnya bernomor selain 5 Peluangnya adalah \(\frac{3\choose 2}{5\choose 3}=\frac{3}{10}\)
3. What fraction of all the 9-digit numbers formed using the digits 1 to 9, without repetition, is divisible by 36?
(A) \(\frac{1}{9}\)
(B) \(\frac{2}{9}\)
(C) \(\frac{1}{3}\)
(D) \(\frac{4}{9}\)
(E) None of the above
Habis dibagi 36, sama saja dengan habis dibagi 4 dan habis dibagi 9. Bilangan 9 digit berbeda yang dibentuk dari angka {1, 2, 3, …,9} masing-masing digunakan sekali pasti habis dibagi 9 karena jumlah digitnya kelipatan 9. Kita tinjau yang habis dibagi 4, Syarat habis dibagi 4 adalah 2 angka terakhir habis dibagi 4 yaitu \(\{12, 16, 24, 28, 32, 36, 48, 52, 56, 64, 68, 72, 76, 84, 92, 96\}\) ada \(16\) bilangan Peluang habis dibagi 36 adalah \(\frac{16×7!}{9!}=\frac{16×7!}{9×8×7!}=\frac{16}{9×8}=\frac{2}{9}\)
4. Find the remainder when
\((x − 2)^{10} + (x − 3)^{20}\)
is divided by
\(x^2 − 5x + 6\)
(A) \(x + 1\)
(B) \(x\)
(C) \(1\)
(D) \(2\)
(E) None of the above
8. Gary wrote some numbers on each side of 3 cards, and laid them on a table, as shown.
Given that the sum of numbers on each card are equal and the numbers on the hidden sides are prime, find the sum of the three hidden numbers.
(A) 44
(B) 43
(C) 42
(D) 41
(E) None of the above
9. Find the number of positive integers x, such that \(4x^4 + 1\) is prime.
(A) 0
(B) 1
(C) 2
(D) 3
(E) None of the above