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Solusi Tryout 4 TPS Kuantitatif

Nomor 1.

Nomor 2.

Nomor 3.

Nomor 4.

Nomor 5.

Nomor 6.

Nomor 7.

Nomor 8.

Nomor 9.

Nomor 10.

Nomor 11.

Nomor 12.

Nomor 13.

Nomor 14.

Nomor 15.

Nomor 16.

Nomor 17.

Nomor 18.

Nomor 19.

Nomor 20.

Demikian share tentang
At certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling
tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of
sleep no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what
percent of the interns report no feelings of tiredness during their shifts ?

A). $ 6 \, $

B). $ 14 \, $

C). $ 19 \, $

D). $ 20 \, $

E). $ 81 $

A). $ 6 \, $

B). $ 14 \, $

C). $ 19 \, $

D). $ 20 \, $

E). $ 81 $

A school's annual budget for the purchase of student computers increased by 60% this year over
last year. If the price of student computers inceased by 20% this year, then the number of
computers it can purchase this year is what percent greater than the number of computers
it purchase last year ?

A). $ 33\frac{1}{3} \, $

B). $ 40 \, $

C). $ 42\frac{1}{3} \, $

D). $ 48 \, $

E). $ 60 $

A). $ 33\frac{1}{3} \, $

B). $ 40 \, $

C). $ 42\frac{1}{3} \, $

D). $ 48 \, $

E). $ 60 $

Machine A and machine B can produce 1 widget in 3 hours working together at their respective
constant rates. If machine A's speed were doubled, the two machines could produce 1 widget in 2
hours working together at their respective rates. How many hours does it currently take machine
A to produce 1 widget on its own ?

A). $ 1 \, $

B). $ 2 \, $

C). $ 3 \, $

D). $ 5 \, $

E). $ 6 $

A). $ 1 \, $

B). $ 2 \, $

C). $ 3 \, $

D). $ 5 \, $

E). $ 6 $

Wati walks 5 miles from point A to point B in ane hour, then bicyles back to point A along the
same route at 15 miles per hour. Budi makes the same round trip, but does so at half of Wati's
average speed. How many minutes does Budi spend on his round trip ?

A). $ 40 \, $

B). $ 80 \, $

C). $ 120 \, $

D). $ 160 \, $

E). $ 180 $

A). $ 40 \, $

B). $ 80 \, $

C). $ 120 \, $

D). $ 160 \, $

E). $ 180 $

At Denpasar Utara Elementary School, the number of teachers and students totals 510
(there are six grade levels). The ratio of students to teachers is 16 to 1. SD Tulang ampiang
students (SD Tulang ampiang is one of the school in Denpasar Utara) make up $ \frac{1}{5} $ of
the student population. Fifth and sixth graders account for $ \frac{1}{3} $ of the remainder.
Student in first and second grades account for $ \frac{1}{4} $ of all the students. If there
are an equal number of students in the third and fourth grades, then the number of students in
third grade is how many greater or fewer than the number of students in SD Tulang ampiang ?

A). 12 greater

B). 17 fewer

C). 28 fewer

D). 36 fewer

E). 44 fewer

A). 12 greater

B). 17 fewer

C). 28 fewer

D). 36 fewer

E). 44 fewer

Nomor 6.

Set S consist of integers 7, 8, 10, 12, and 13. If integer $ n $ is included in the set, the
average (arithmetic mean) of the set S will increase by 20%. What is the value of
integer $ n $ ?

A). 16

B). 20

C). 22

D). 23

E). 24

A). 16

B). 20

C). 22

D). 23

E). 24

If $ x $ and $ n $ are integers, is the sum of $ x $ and $ n $ less than zero ?

Decide whether the following statements (1) and (2) are sufficient to answer the question.

(1). $ x + 3 < n - 1 $

(2). $ - 2x > 2n $

A). Statement (1) alone is sufficient, but statement (2) alone is not sufficient

B). Statement (2) alone is sufficient, but statement (1) alone is not sufficient

C). Both statements together are sufficient, but neither statement alone is sufficient

D). Each statement alone is sufficient

E). Statement (1) and (2) together are not sufficient

Decide whether the following statements (1) and (2) are sufficient to answer the question.

(1). $ x + 3 < n - 1 $

(2). $ - 2x > 2n $

A). Statement (1) alone is sufficient, but statement (2) alone is not sufficient

B). Statement (2) alone is sufficient, but statement (1) alone is not sufficient

C). Both statements together are sufficient, but neither statement alone is sufficient

D). Each statement alone is sufficient

E). Statement (1) and (2) together are not sufficient

if $ n $ is a multiple of 5 and $ n = p^2q$, where $ p $ and $ q $ are prime numbers,
which of the following must be a multiple of 25 ?

A). $ p^2 \, $

B). $ q^2 \, $

C). $ pq \, $

D). $ p^2q^2 \, $

E). $ p^3q $

A). $ p^2 \, $

B). $ q^2 \, $

C). $ pq \, $

D). $ p^2q^2 \, $

E). $ p^3q $

if $ a, b, \, $ and $ c $ are integers and $ \frac{ab^2}{c} $ is a positive even integer,
which of the following must be true ?

I. $ ab $ is even

II. $ ab > 0 $

III. $ c $ is even

A). I only

B). II only

C). I and II

D). I and III

E). I, II, and III

I. $ ab $ is even

II. $ ab > 0 $

III. $ c $ is even

A). I only

B). II only

C). I and II

D). I and III

E). I, II, and III

if $(x\# y) $ represents the remainder that results when the positive integer $ x $ is divided
by the positive integer $y$, what is the sum of all the possible values of $ b $ such that
$ (16 \# b) = 1 $ ?

A). $ 23 \, $

B). $ 22 \, $

C). $ 20 \, $

D). $ 16 \, $

E). $ 9 $

A). $ 23 \, $

B). $ 22 \, $

C). $ 20 \, $

D). $ 16 \, $

E). $ 9 $

Nomor 11.

In a certain game, a large bag is filled with blue, green, purple and red chips
worth 1, 5, $ x $ and 11 points each, respectively. The purple chips are worth more than the
green chips, but less than the red chips. A certain number of chips are then selected from the
bag If the product of the point values of the selected chips is 704.000 , how many purple chips
were selectied ?

A). $ 2 \, $

B). $ 3 \, $

C). $ 4 \, $

D). $ 5 \, $

E). $ 6 $

A). $ 2 \, $

B). $ 3 \, $

C). $ 4 \, $

D). $ 5 \, $

E). $ 6 $

In the figure, point D divides side BC of triangle ABC into segments BD and DC of lengths 1 and 2
units respectively. Given that $ \angle ADC = 60^o $ and $ \angle ABD = 45^o $ , what is the
measure of angle $ x $ in degrees ? (Note : Figure is not drawn to scale.)

A). $ 60 \, $

B). $ 70 \, $

C). $ 75 \, $

D). $ 80 \, $

E). $ 85 $

A). $ 60 \, $

B). $ 70 \, $

C). $ 75 \, $

D). $ 80 \, $

E). $ 85 $

In the picture, quadrilateral ABCD is a parallelogram and quadrilateral DEFG is a rectangle.
What is the area of parallelogram ABCD ? (figure not drawn to scale)

Decide whether the following statements (1) and (2) are sufficient to answer the question.

(1). the area of rectangle DEFG is $ 8\sqrt{5} $

(2). Line AH, the altitude of parallelogram ABCD, is 5

A). Statement (1) alone is sufficient, but statement (2) alone is not sufficient

B). Statement (2) alone is sufficient, but statement (1) alone is not sufficient

C). Both statements together are sufficient, but neither statement alone is sufficient

D). Each statement alone is sufficient

E). Statement (1) and (2) together are not sufficient

Decide whether the following statements (1) and (2) are sufficient to answer the question.

(1). the area of rectangle DEFG is $ 8\sqrt{5} $

(2). Line AH, the altitude of parallelogram ABCD, is 5

A). Statement (1) alone is sufficient, but statement (2) alone is not sufficient

B). Statement (2) alone is sufficient, but statement (1) alone is not sufficient

C). Both statements together are sufficient, but neither statement alone is sufficient

D). Each statement alone is sufficient

E). Statement (1) and (2) together are not sufficient

Four spheres and three cubes are arranged in a line according to increasing volume, with no two
solids of the same type adjacent to each ather. The ratio of the volume of one solid to that of
the next largest is constant. If the radius of the smallest sphere is $ \frac{1}{4} $ that of
the largest sphere, what is the radius of the smallest sphere ?

Decide whether the following statements (1) and (2) are sufficient to answer the question.

(1). The volume of the smallest cube is $ 72\pi $

(2). The volume of the second largest sphere is $ 576\pi $

A). Statement (1) alone is sufficient, but statement (2) alone is not sufficient

B). Statement (2) alone is sufficient, but statement (1) alone is not sufficient

C). Both statements together are sufficient, but neither statement alone is sufficient

D). Each statement alone is sufficient

E). Statement (1) and (2) together are not sufficient

Decide whether the following statements (1) and (2) are sufficient to answer the question.

(1). The volume of the smallest cube is $ 72\pi $

(2). The volume of the second largest sphere is $ 576\pi $

A). Statement (1) alone is sufficient, but statement (2) alone is not sufficient

B). Statement (2) alone is sufficient, but statement (1) alone is not sufficient

C). Both statements together are sufficient, but neither statement alone is sufficient

D). Each statement alone is sufficient

E). Statement (1) and (2) together are not sufficient

A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin,
and the square is to have an area of 100. If all coordinates of the vertices must be integers,
how many different ways can this square be drawn ?

A). 4

B). 6

C). 8

D). 10

E). 12

A). 4

B). 6

C). 8

D). 10

E). 12

Nomor 16.

How many different 5-person teams can be formed from a group of $ x $ individuals ?

Decide whether the following statements (1) and (2) are sufficient to answer the question.

(1). If there had been $ x+2 $ individuals in the group, exactly 126 different 5-person teams could have been formed.

(2). If there had been $ x+1 $ individuals in the group, exactly 56 different 3-person teams could have been formed.

A). Statement (1) alone is sufficient, but statement (2) alone is not sufficient

B). Statement (2) alone is sufficient, but statement (1) alone is not sufficient

C). Both statements together are sufficient, but neither statement alone is sufficient

D). Each statement alone is sufficient

E). Statement (1) and (2) together are not sufficient

Decide whether the following statements (1) and (2) are sufficient to answer the question.

(1). If there had been $ x+2 $ individuals in the group, exactly 126 different 5-person teams could have been formed.

(2). If there had been $ x+1 $ individuals in the group, exactly 56 different 3-person teams could have been formed.

A). Statement (1) alone is sufficient, but statement (2) alone is not sufficient

B). Statement (2) alone is sufficient, but statement (1) alone is not sufficient

C). Both statements together are sufficient, but neither statement alone is sufficient

D). Each statement alone is sufficient

E). Statement (1) and (2) together are not sufficient

Ms. Yuli has four children. You are told correctly that she has at least two girls but you are
not told which two of her four children are those girls. What is the probability that she
also has two boys? (Assume that the probability of having a boy is the same as the probability
of having a girl)

A). $ \frac{1}{4} $

B). $ \frac{3}{8} $

C). $ \frac{5}{11} $

D). $ \frac{1}{2} $

E). $ \frac{6}{11} $

A). $ \frac{1}{4} $

B). $ \frac{3}{8} $

C). $ \frac{5}{11} $

D). $ \frac{1}{2} $

E). $ \frac{6}{11} $

A political candidate collected $ \$ 1.749 $ from a fund raising dinner. If each supporter contributed
at least $ \$ 50 $ , what is the greatest possible number of contributors at the dinner ?

A). 33

B). 34

C). 35

D). 36

E). 37

A). 33

B). 34

C). 35

D). 36

E). 37

The three-digit positive integer $ x $ has the hundreds, tens, and units digits of $a$, $b$,
and $c$, respectively. The three-digit positive integer $ y $ has the hundreds, tens, and
units digit of $k$, $l$, and $m$, respectively. If
$(2^a )(3^b )(5^c )= 12(2^k )(3^l )(5^m )$ , then which is the correct relationship between
the following quantities P and Q based on the information provided?

$\begin{array}{|c|c|} \hline \text{P} & \text{Q} \\ \hline \text{The value of } x - y & 200 \\ \hline \end{array} $

A). Quantity P is greater

B). Quantity Q is greater

C). The two quantities are equal

D). The relationship cannot be determined from the information given

$\begin{array}{|c|c|} \hline \text{P} & \text{Q} \\ \hline \text{The value of } x - y & 200 \\ \hline \end{array} $

A). Quantity P is greater

B). Quantity Q is greater

C). The two quantities are equal

D). The relationship cannot be determined from the information given

Which of the following graphs is symmetric with respect to the $y$-axis ?

**Solusi Tryout 4 TPS Kuantitatif**ini. Semoga bisa membantu untuk berlatih dalam mempersiapkan UTBK atau seleksi perguruan tinggi lainnya. Jangan lupa juga untuk mengikuti tryout-tryout lainnya yang akan diadakan secara berkala oleh blog koma. Jika ingin melihat soal dan solusi tryout-tryout sebelumnya, silahkan kunjungi link "Kumpulan Soal dan Solusi Tryout TPS Kuantitatif". Jika ada kritikan dan masukkan yang sifatnya membangun, silahkan tulis di kolom komentar di bawah ini ya. Terimakasih.