Problem And Solution SEAMO 2017 Paper D

SEAMO

19. Arrange \(3^{50}, 4^{40}, 5^{30}\) in ascending order.
(A) \(3^{50}<4^{40}<5^{30}\)
(B) \(5^{30}<3^{50}<4^{40}\)
(C) \(5^{30}<4^{40}<3^{50}\)
(D) \(4^{40}<5^{30}<3^{50}\)
(E) None of the above


Belum tersedia


20. Sara picked 2 oranges from a basket of 15 oranges in which 10 oranges are good, 5 oranges are bad. The probability she pick up at least one good orange is \(\frac{m}{n}\). Find the value of \((m + n)\).
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42


Belum tersedia


21. In an equilateral ΔABC, D and E are points on BC and AB respectively. Given that BD = AE and AD and CE intersect at point F, find ∠DFC.


(A) 30°
(B) 36°
(C) 42°
(D) 54°
(E) 60°


karena \(AE = BD, AB = AC\) dan \(∠𝐴𝐵𝐷 = ∠𝐶𝐸𝐴\) maka \(Δ𝐴𝐵𝐷 ≅ Δ𝐴𝐸𝐶\)
Karena \(Δ𝐴𝐵𝐷 ≅ Δ𝐴𝐸𝐶\) maka \(∠𝐵𝐴𝐷 = ∠𝐸𝐶𝐴 = 𝑦°\)
Karena \(∠𝐴𝐵𝐷 = 60°\) dan \(∠𝐵𝐴𝐷 = 𝑦°\) maka \(∠𝐴𝐷𝐶 = (60 + 𝑦)°\)
Karena \(∠𝐴𝐶𝐷 = 60°\) dan \(∠𝐴𝐸𝐶 = 𝑦°\) maka \(∠𝐹𝐶𝐷 = (60 − 𝑦)°\)
Jumlah sudut segitiga
\(𝑥° + (60 + 𝑦)° + (60 − 𝑦)° = 180°\)
\(⇒𝑥° + (120)° = 180° ⟹ 𝑥 = 60°\)


22. The number which, when subtracted from
the terms of ratio a : b makes it equal to c : d is
(A) \(\frac{ab-cd}{ab+cd}\)
(B) \(\frac{bc-ad}{c-d}\)
(C) \(\frac{ab+cd}{c+d}\)
(D) \(\frac{ab-cd}{b-c}\)
(E) None of the above


Belum tersedia


23. a, b, c are three positive real numbers. The second number is greater than the first by the amount the third number is greater than the second. The product of the two smaller numbers is 85 and that of the two bigger numbers is 115. Then the value of (2012a – 1006c) is
(A) 3355
(B) 4433
(C) 5533
(D) 3344
(E) 5454


\(𝑎 < 𝑏 < 𝑐\)
\(𝑎𝑏 = 85\)
\(𝑏𝑐 = 115\)
Bagi kedua persamaan di atas
\(\frac{𝑏𝑐}{𝑎𝑏}=\frac{115}{85}⟹\frac{𝑐}{𝑎}=\frac{23}{17}\)
Pilih \(𝑏 = 5\), maka nilai \(𝑐 = 23\) dan \(𝑎 = 17\), tidak memenuhi syarat \(𝑎 < 𝑏 < 𝑐\)
Pilih \(𝑏 = 10\), maka nilai \(𝑐 =\frac{23}{2}\) dan \(𝑎 =\frac{17}{2}\), memenuhi
Jadi nilai dari \(2012𝑎 – 1006𝑐\) adalah 
\(2012(\frac{17}{2}) – 1006(\frac{23}{2})=17102-11569=5533\)


24. If \(x=\frac{y}{y+1}\) and \(y=\frac{a-2}{2}\) then value of \(x(y+2)+\frac{x}{y}+\frac{y}{x}\), when \(a=2017\) is

(A) 2016
(B) 2015
(C) 2018
(D) 2017
(E) 2019


\(\begin{align}
x(y+2)+\frac{x}{y}+\frac{y}{x} &= 𝑥(𝑦 + 2 +\frac{1}{𝑦}) +\frac{𝑦}{𝑥}\\
&= 𝑥(\frac{𝑎−2}{2}+\frac{2}{𝑎−1}+ 2) + 𝑦(\frac{𝑦+1}{𝑦})\\
&= (\frac{𝑦}{𝑦+1})(\frac{𝑎}{2}− 1 +\frac{2}{𝑎−1}+ 2) + 𝑦 + 1\\
&= (\frac{𝑎−2}{𝑎}) (\frac{𝑎}{2}+ 1 +\frac{2}{𝑎−1}) +\frac{𝑎−2}{2}+ 1\\
&=\frac{𝑎−2}{2}+\frac{𝑎−2}{𝑎}+\frac{2}{𝑎}+\frac{𝑎−2}{2}+ 1\\
&= 𝑎 − 2 +\frac{𝑎−2}{𝑎}+\frac{2}{𝑎}+ 1\\
&= 𝑎 − 2 + 2\\
&= 𝑎 = 2017\\
\end{align}\)


25. A triangular pyramid is made of 4 equilateral triangles as faces. If
each side of equilateral triangular face is 1 unit. Find the height of the pyramid.

(A) \(\sqrt{\frac{2}{3}}\)
(B) \(\sqrt{\frac{3}{2}}\)
(C) \(\frac{2}{\sqrt 3}\)
(D) \(\frac{\sqrt 3}{2}\)
(E) None of the above


Belum tersedia


Baca juga
SEAMO PAPER D 2021
SEAMO PAPER D 2020
SEAMO PAPER D 2019 

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