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Qormaata galuumsa kutaa 12ffaa Herregaa, bara 2017 A.L.I (2025), maxxansa 1

Gaaffilee dhugaa qormaata galuumsa yunivarsiitii kutaa 12 kan Herregaa, akkuma barattoonni bara 2017 A.L.I itti fudhatanitti. Tokkoon tokkoon gaaffii deebii sirrii fi ibsa qaba. Qormaanni bara 2017 A.L.I maxxansa adda addaatiin bahe. Fuulli kun maxxansa 1 qaba; kaan gadi aanee tarreeffamaniiru.

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2017 A.L.I (2025), maxxansa 1
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Gaaffii 1

Which one of the following defines prime number?

A.It is a natural number that has an odd number of factors
B.It is an odd natural number that has only two factors
C.It is a natural number that has exactly two distinct factors
D.It is a natural number where one of its factors is 3

Deebii fi ibsa ilaalaa

Deebii: C It is a natural number that has exactly two distinct factors

Maaliif

A prime number is a natural number with exactly two different factors,

1

and the number itself. That is the reason

1

is not prime: it has only one factor. Option B is tempting because most primes are odd, but

2

is prime and even, so "odd" cannot belong in the definition.

Gaaffii 2

The GCF of two numbers is 9 and their LCM is 54. If one of the numbers is 18. What is the other number?

A.36
B.54
C.27
D.72

Deebii fi ibsa ilaalaa

Deebii: C 27

Maaliif

For any two whole numbers, GCF times LCM equals the product of the numbers. So the missing number is

\frac{9 \times 54}{18} = \frac{486}{18} = 27

. Check it: the greatest common factor of

18

and

27

is

9

, and their least common multiple is

54

. Option B,

54

, is tempting because that number already appears in the question, but

54

is the LCM, not the second number.

Gaaffii 3

If x = 0.424424442... and y = 0.242242224... then the fraction form of x + y is equal to

A.6/10
B.3/4
C.2/3
D.4/5

Deebii fi ibsa ilaalaa

Deebii: C 2/3

Maaliif

Neither decimal repeats, but their digits pair up. Wherever

x

has a

4

,

y

has a

2

, and wherever

x

has a

2

,

y

has a

4

. Every digit of the sum is therefore

6

, so

x + y = 0.6666\ldots

, and

0.\overline{6} = \frac{2}{3}

. Option A,

\frac{6}{10}

, is what you get by stopping after one digit, but the sixes carry on forever.

Gaaffii 4

For any real numbers a, b and c. Which one of the following is true?

A.If a < b then a² < b²
B.If a < b then ac < bc
C.If a² < b² then b < a
D.If a < b and b < c then c > a

Deebii fi ibsa ilaalaa

Deebii: D If a < b and b < c then c > a

Maaliif

Option D is the transitive property of order: if

a < b

and

b < c

, then

a < c

, which is the same as saying

c > a

. It holds for every choice of real numbers. Option B looks safe, but multiplying an inequality by a negative number flips it:

2 < 3

while

2(-1) > 3(-1)

.

Gaaffii 6

Let a and b be positive integers and p and q are real numbers. Which of the following is true?

A.(a+b)ᵖ = aᵖ + bᵖ
B.(a)⁻ᵖ / (b)⁻ᵠ = bᵠ / aᵖ
C.(a)⁻ᵖ / (b)⁻ᵠ = bᵠ / αᵖ
D.aᵖ / (a)⁻ᵠ = (a)ᵖ⁻ᵠ

Deebii fi ibsa ilaalaa

Deebii: B (a)⁻ᵖ / (b)⁻ᵠ = bᵠ / aᵖ

Maaliif

A negative exponent moves a factor across the fraction bar:

a^{-p} = \frac{1}{a^{p}}

, and

\frac{1}{b^{-q}} = b^{q}

. Putting the two together,

\frac{a^{-p}}{b^{-q}} = \frac{b^{q}}{a^{p}}

, which is option B. Option C states the same rule but writes

\alpha^{p}

underneath, and

\alpha

is not one of the letters the question defined. Option D fails because

\frac{a^{p}}{a^{-q}} = a^{p+q}

.

Gaaffii 7

Which one of the following is the rationalizing factor to rationalize the denominator of 7/(3+√5)?

A.(√3+√5)/(√3+√5)
B.(√3-5)/(√3-5)
C.(√3-√5)/(√3-√5)
D.(3-√5)/(3-√5)

Deebii fi ibsa ilaalaa

Deebii: D (3-√5)/(3-√5)

Maaliif

To clear a denominator of the form

3 + \sqrt5

you multiply by its conjugate

3 - \sqrt5

, because

(3+\sqrt5)(3-\sqrt5) = 9 - 5 = 4

, a whole number. Writing the factor as

\frac{3-\sqrt5}{3-\sqrt5}

keeps the value of the fraction unchanged, so option D is the rationalizing factor. Option C, with

\sqrt3

, is tempting, but the denominator holds a plain

3

, and that product would leave surds behind.

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Gaaffilee 42 kuusaa kana keessa jiran hunda akka waraqaa qormaataa maxxanfameetti, furtuu deebii ibsa 42 waliin immoo akka faayilii lammaffaatti. Maxxansaa yookiin daataa malee dubbisaa.

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Qormaata galuumsa kutaa 12ffaa Herregaa, bara 2017 A.L.I (2025), maxxansa 1

Gaaffilee qormaata kanaa yaalaa

Which one of the following defines prime number?

The GCF of two numbers is 9 and their LCM is 54. If one of the numbers is 18. What is the other number?

If x = 0.424424442... and y = 0.242242224... then the fraction form of x + y is equal to

For any real numbers a, b and c. Which one of the following is true?

Let a and b be positive integers and p and q are real numbers. Which of the following is true?

Which one of the following is the rationalizing factor to rationalize the denominator of 7/(3+√5)?

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Qormaata kana taa'uu dura Herregaa qayyabadhu