is a perfect square.
(A) 7
(B) 8
(C) 9
(D) 10
(E) None of the above
\(2^6+2^{10}+2^𝑥=2^6(1+2^4+2^{𝑥−6})\) Karena \(2^6\) kuadrat sempurna maka \((1+2^4+2^{𝑥−6})\) juga merupakan kuadrat sempurna \((1+2^4+2^{𝑥−6})=17+2^{𝑥−6}\) Nilai \(2^{𝑥−6}\) yang memenuhi adalah \(2^{𝑥−6}=8 ⟹2^{𝑥−6}=2^3⟹𝑥=9\)
16. Given that a, b and c are positive real numbers and \(a+ b + c = 1\), evaluate
\(\sqrt{4a + 1} + \sqrt{4b + 1} + \sqrt{4c + 1}\)
(A) 4
(B) 5
(C) < 4
(D) > 5
(E) None of the above
17. A bag contains 20 balls numbered 1 to 20. If 2 balls are randomly chosen from the bag, find the probability that the sum of the two numbers is prime.
(A) \(\frac{23}{40}\)
(B) \(\frac{29}{40}\)
(C) \(\frac{31}{380}\)
(D) \(\frac{17}{190}\)
(E) None of the above
Ruang sampel \(𝑛(𝑆)={20\choose 2}=\frac{20!}{18!.2!}=\frac{20.19.18!}{18!.2}=190\) cara Banyak kemungkin jumlah angka pada \(2\) bola adalah bilangan prima. • Berjumlah \(3, (1, 2)\) ada \(1\) • Berjumlah \(5, (1, 4), (2, 3)\) ada \(2\) • Berjumlah \(7, (1, 6), (2, 5), (3, 4)\) ada \(3\) • Berjumlah \(11, (1,10), (2, 9), (3, 8), (4, 7), (5, 6)\) ada \(5\) • Berjumlah \(13, (1, 12), (2, 10), …, (6, 7)\) ada \(6\) • Berjumlah \(17, (1, 16), … (8, 9)\) ada \(8\) • Berjumlah \(19, (1, 18), …, (9, 10)\) ada \(9\) • Berjumlah \(23, (4, 19), …, (11, 12) ada [latex]8\) • Berjumlah \(29, (9, 20), (10, 19), …., (14,15)\) ada \(6\) • Berjumlah \(31, (11, 20), …., (15, 16)\) ada \(5\) • Berjumlah \(37, (17, 20), (18, 19)\) ada \(2\) Banyaknya ada \(55\) Jadi peluangnya adalah \(\frac{55}{190}=\frac{11}{38}\)
18. Mr. Woodley paid $650,000 for two commercial properties. A year later, the market value of the 1st property rose by 20%, while that of the 2nd dropped by 25%. The two properties then had the same market value. Of what market value was the 1st property at first?
(A) $220,000
(B) $230,000
(C) $240,000
(D) $250,000
(E) None of the above
Misalkan harga Property pertama adalah \(A\) dan harga Property kedua adalah \(B\)