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2016 E.C.
2016 E.C. · social · Q50 · Quantitative comparison
Quantity A: 20% of 80; Quantity B: 30% of 60.
A. Quantity B is greater than quantity A.
B. The relationship cannot be determined.
C. Quantity A is greater than quantity B.
D. The two quantities are equal.
Worked solutionUnofficial
Answer: A
Answer A: Quantity B is greater than quantity A.. The stem is: Quantity A: 20% of 80; Quantity B: 30% of 60. Letter A is the Abrari key for this Quantitative comparison. A=16, B=18; B>A.
Unofficial — solved by Abrari, not an official EAES key.
The water bill for a past month was Birr 200, consisting of a fixed charge of Birr 20 plus Birr 2 per cubic meter. How many cubic meters did the family consume?
A. 90
B. 180
C. 110
D. 100
Worked solutionUnofficial
Answer: A
Answer A: 90. The stem is: The water bill for a past month was Birr 200, consisting of a fixed charge of Birr 20 plus Birr 2 per cubic meter. How many cubic meters did the family consume? Letter A is the Abrari key for this Linear equations. (200-20)/2 = 90.
Unofficial — solved by Abrari, not an official EAES key.
Answer D: It has two solutions.. The stem is: Which of the following is true about x2+3x−4=0? Letter D is the Abrari key for this Quadratic equations. (x+4)(x-1)=0 => x=-4,1, two solutions.
Unofficial — solved by Abrari, not an official EAES key.
One mango sells for Birr 10 and one banana for Birr 5. If 30 fruits of mangos and bananas were purchased for Birr 200, how many were bananas?
A. 25
B. 15
C. 10
D. 20
Worked solutionUnofficial
Answer: D
Answer D: 20. The stem is: One mango sells for Birr 10 and one banana for Birr 5. If 30 fruits of mangos and bananas were purchased for Birr 200, how many were bananas? Letter D is the Abrari key for this Systems of equations. 10m+5b=200, m+b=30 => 5m=50 => m=10, b=20.
Unofficial — solved by Abrari, not an official EAES key.
If a tree casts a shadow 20 meters long and at the same time a pole of 3 meters casts a shadow 5 meters long, what is the height of the tree?
A. 8
B. 16
C. 4
D. 12
Worked solutionUnofficial
Answer: D
Answer D: 12. The stem is: If a tree casts a shadow 20 meters long and at the same time a pole of 3 meters casts a shadow 5 meters long, what is the height of the tree? Letter D is the Abrari key for this Similar triangles. h/20 = 3/5 => h=12.
Unofficial — solved by Abrari, not an official EAES key.
What is the height of a building if the angle of elevation of the top from a point 10 meters away from the ground floor is 60°?
A.3103
B. 5
C.103
D.53
Worked solutionUnofficial
Answer: C
Answer C: 103. The stem is: What is the height of a building if the angle of elevation of the top from a point 10 meters away from the ground floor is 60°? Letter C is the Abrari key for this Trigonometry. h = 10*tan60 = 10√3.
Unofficial — solved by Abrari, not an official EAES key.
Passage II: What is the matter with our reading is casualness, languor, preoccupation. We don't give the book a chance. We don't put ourselves at the disposal of the book. It is impossible to read properly without using all one's engine power. If we are not tired after reading, common sense is not in us. How one should grapple with a superior and not be out of breath? But even if we read with the whole force of our brain, and do nothing else, common sense is still not in us, while sublime conceit is. For we are assuming that, without further trouble, we can possess, co-ordinate, and assimilate all the ideas and sensations rapidly offered to us by a mind greater than our own. The assumption has only to be stated in order to appear in its monstrous absurdity. Hence, it follows that something remains to be done. This something is the act of reflection. Reading without subsequent reflection is ridiculous; it is equally a proof of folly and vanity. (Source: Warriner, J. E. et al, 1958.)
What is described as an absurd assumption about reading according to the passage?
A. Ideas can be instantly absorbed and organized.
B. Superior minds are easy to understand.
C. Reading does not require physical effort.
D. All books are equally valuable.
Worked solutionUnofficial
Answer: A
Answer A: Ideas can be instantly absorbed and organized.. The stem is: Passage II: What is the matter with our reading is casualness, languor, preoccupation. We don't give the book a chance. We don't put ourselves at the disposal of the book. It is impossible to read properly without using all one's engine power. If we are not tired after reading,… Letter A is the Abrari key for this reading-comprehension. The 'monstrous absurdity' is assuming we can possess, co-ordinate and assimilate all ideas rapidly without further trouble.
Unofficial — solved by Abrari, not an official EAES key.
Quantitative Reasoning. Which one of the following statements is true?
A. Every non-negative integer is a natural number.
B. Every integer number can be numerator of a rational number.
C. The sum of two irrational numbers is irrational number.
D. The intersection of the set of integers and the set of irrational numbers is non-empty set.
Worked solutionUnofficial
Answer: B
Answer B: Every integer number can be numerator of a rational number.. The stem is: Quantitative Reasoning. Which one of the following statements is true? Letter B is the Abrari key for this number-systems. Any integer n = n/1 is rational, so it can be a numerator. A is debatable (0), C false (e.g. sqrt2 + (-sqrt2)=0), D false (integers and irrationals are disjoint).
Unofficial — solved by Abrari, not an official EAES key.
A ball is shot into the air from the top of a building. The height in meters is given by h(t)=kt−t2+30, where t is the time in seconds. What is the possible value of k if the maximum height from the ground is 34?
A. 4
B.2
C. 2
D. 5
Worked solutionUnofficial
Answer: A
Answer A: 4. The stem is: A ball is shot into the air from the top of a building. The height in meters is given by h(t)=kt−t2+30, where t is the time in seconds. What is the possible value of k if the maximum height from the ground is 34? Letter A is the Abrari key for this quadratic-functions. Vertex value: max = 30 + k^2/4 = 34, so k^2/4 = 4, k^2 = 16, k = 4.
Unofficial — solved by Abrari, not an official EAES key.
If f(x)=sinπx+ex2+∣x∣+x3 and g(x)=cosπx+ln(x+1)+x, then what is the value of f(1)−2g(0)?
A.ln2
B.e
C.e+2
D. 0
Worked solutionUnofficial
Answer: C
Answer C: e+2. The stem is: If f(x)=sinπx+ex2+∣x∣+x3 and g(x)=cosπx+ln(x+1)+x, then what is the value of f(1)−2g(0)? Letter C is the Abrari key for this functions. f(1)=sin(pi)+e^1+|1|+1 = 0+e+1+1 = e+2. g(0)=cos0+ln1+0 = 1+0+0 = 1, so 2g(0)=2. f(1)-2g(0) = (e+2)-2 = e. That gives (B) e. But recomputing: e+2-2 = e. So answer is e = (B). Wait: several commenters say C (e+2). If g(0) were miscomputed as 0 the result is e+2. The site marks (D) 0, which is wrong. My computation gives (B) e. Flagged: I disagree with the site's (D); correct value f(1)-2g(0)=e, i.e. option B. Selecting B is more defensible than C; setting suggested_answer to B.
Unofficial — solved by Abrari, not an official EAES key.
Answer A: 625. The stem is: If −x+2y=4, then what is the value of 5x25y? Letter A is the Abrari key for this exponents. 25^y/5^x = 5^{2y}/5^x = 5^{2y-x} = 5^4 = 625 (since 2y - x = 4).
Unofficial — solved by Abrari, not an official EAES key.
A woman burns 416 calories in an hour of exercise. She burns 10 calories per minute swimming in the water and 6 calories per minute pedaling on a stationary bike. How many minutes of the hour does she spend exercising in the water?
A. 14
B. 56
C. 46
D. 60
Worked solutionUnofficial
Answer: A
Answer A: 14. The stem is: A woman burns 416 calories in an hour of exercise. She burns 10 calories per minute swimming in the water and 6 calories per minute pedaling on a stationary bike. How many minutes of the hour does she spend exercising in the water? Letter A is the Abrari key for this word-problem. Let w = minutes swimming. 10w + 6(60-w) = 416 -> 4w + 360 = 416 -> 4w = 56 -> w = 14.
Unofficial — solved by Abrari, not an official EAES key.
A daily profit earned by a T-shirt factory is modeled by p(x)=−x2+1,400x−80,000, where p is the profit and x is the price for each T-shirt sold. What range of prices will yield a profit of at least Birr 400,000?
A.x≥800
B.600≤x≤800
C.x≤600
D.x≤600 or x≥800
Worked solutionUnofficial
Answer: B
Answer B: 600≤x≤800. The stem is: A daily profit earned by a T-shirt factory is modeled by p(x)=−x2+1,400x−80,000, where p is the profit and x is the price for each T-shirt sold. What range of prices will yield a profit of at least Birr 400,000? Letter B is the Abrari key for this quadratic-inequality. x^2+1400x-80000 >= 400000 -> x^2 -1400x +480000 <= 0 -> (x-600)(x-800) <= 0 -> 600 <= x <= 800.
Unofficial — solved by Abrari, not an official EAES key.
What is the value of z in the sequence 1,2,4,8,10,20,22,z,…?
A. 24
B. 44
C. 40
D. 32
Worked solutionUnofficial
Answer: B
Answer B: 44. The stem is: What is the value of z in the sequence 1,2,4,8,10,20,22,z,…? Letter B is the Abrari key for this number-series. Pattern alternates: +1 then x2. 1(+1)2(x2)4? Actually: 1,2 (x2); 2,4 (x2); 4,8 (x2); 8,10 (+2)? Reinterpret as x2 then +2: 1x2=2, 2x2=4, 4x2=8, 8+2=10, 10x2=20, 20+2=22, 22x2=44. So z=44.
Unofficial — solved by Abrari, not an official EAES key.
What is the possible value of the missing term x in the sequence −1,0,1,2,−1.8,1,26,−1,x,1,242,−1,728,1,…?
A. 36
B. 54
C. 34
D. 80
Worked solutionUnofficial
Answer: D
Answer D: 80. The stem is: What is the possible value of the missing term x in the sequence −1,0,1,2,−1.8,1,26,−1,x,1,242,−1,728,1,…? Letter D is the Abrari key for this number-series. The interleaved subsequence at the x-position appears to follow 3^n - 1: 2, 8, 26, 80, 242, 728 (i.e. 3^1-1=2, 3^2-1=8, 3^3-1=26, 3^4-1=80, 3^5-1=242, 3^6-1=728). So x=80. The printed sequence has a garbled term ('-1.8') so flagged; site answer D=80 is consistent with the 3^n-1 pattern.
Unofficial — solved by Abrari, not an official EAES key.
Consider the lengths of the sides of a triangle x,y,z. Compare Quantity P and Quantity Q. Quantity P: 3x+y−z Quantity Q: 4x
A. Quantity P is greater than Quantity Q.
B. Quantity P is less than Quantity Q.
C. The two quantities are equal.
D. The two quantities cannot be compared.
Worked solutionUnofficial
Answer: D
Answer D: The two quantities cannot be compared.. The stem is: Consider the lengths of the sides of a triangle x,y,z. Compare Quantity P and Quantity Q. Quantity P: 3x+y−z Quantity Q: 4x Letter D is the Abrari key for this quantitative-comparison. P - Q = (3x+y-z) - 4x = y - z - x. By the triangle inequality x + z > y, so y - z - x < 0, meaning P < Q. That would make (B). However with y as the largest side y < x+z always, so y-z-x is strictly negative -> P<Q (B). The source gives no answer. Best-reasoned answer is (B) Quantity P is less than Quantity Q; flagged because the site left it unsolved and it hinges on triangle-inequality interpretation.
Unofficial — solved by Abrari, not an official EAES key.
A corporation pays ten employees a total of Birr 100,000 every month. Six out of ten employees receive less than Birr 10,000 per month. Compare Quantity P and Quantity Q. Quantity P: The average of the monthly payment of the corporation Quantity Q: The median of the monthly payment of the corporation
A. Quantity P is less than Quantity Q.
B. Quantity P is greater than Quantity Q.
C. The two quantities are equal.
D. The two quantities cannot be compared.
Worked solutionUnofficial
Answer: B
Answer B: Quantity P is greater than Quantity Q.. The stem is: A corporation pays ten employees a total of Birr 100,000 every month. Six out of ten employees receive less than Birr 10,000 per month. Compare Quantity P and Quantity Q. Quantity P: The average of the monthly payment of the corporation Quantity Q: The median of the monthly paym… Letter B is the Abrari key for this statistics. Average = 100000/10 = 10000. Since 6 of 10 employees earn less than 10000, the median (average of 5th and 6th values) lies among the lower earners and is below 10000, so P (mean) > Q (median).
Unofficial — solved by Abrari, not an official EAES key.
An engineer is putting black and white colored ceramics on a square floor of area 36 m2. Each ceramic has area 1 m2. The engineer places the black ones along both diagonals and the rest is covered by white colored ceramics. In what ratio is black to white ceramic used?
A. 1:2
B. 1:6
C. 4:5
D. 1:5
Worked solutionUnofficial
Answer: A
Answer A: 1:2. The stem is: An engineer is putting black and white colored ceramics on a square floor of area 36 m2. Each ceramic has area 1 m2. The engineer places the black ones along both diagonals and the rest is covered by white colored ceramics. In what ratio is black to white cer… Letter A is the Abrari key for this geometry. 6x6 grid = 36 tiles. On a grid of even side, the two diagonals cover 2*6 = 12 tiles with no shared center tile, so black = 12, white = 24, ratio 12:24 = 1:2. Site answer A=1:2.
Unofficial — solved by Abrari, not an official EAES key.
A person makes a glass of juice and used half of the glass with avocado, one third of the remaining half with mangoes, and the rest is filled by banana. What is the ratio of bananas to avocadoes in the glass? [Note: source stem is garbled/truncated.]
A. 1:2
B. 1:6
C. 2:3
D. 1:3
Worked solutionUnofficial
Answer: C
Answer C: 2:3. The stem is: A person makes a glass of juice and used half of the glass with avocado, one third of the remaining half with mangoes, and the rest is filled by banana. What is the ratio of bananas to avocadoes in the glass? [Note: source stem is garbled/truncated.] Letter C is the Abrari key for this ratio. Avocado = 1/2. Remaining = 1/2; mango = 1/3 of 1/2 = 1/6; banana = 1/2 - 1/6 = 1/3. Banana:Avocado = (1/3):(1/2) = 2:3. Site answer C. Flagged because the source stem text is garbled/incomplete.
Unofficial — solved by Abrari, not an official EAES key.
This item uses a figure in the original paper (not redrawn here).
A. 14
B. 18
C. 12
D. 16
Worked solutionUnofficial
Answer: D
Answer D: 16. The stem is: How many triangles are there in the diagram? Letter D is the Abrari key for this counting-figures. Requires counting triangles in a figure I cannot see. A commenter suggests D (16). Image-dependent; flagged.
Unofficial — solved by Abrari, not an official EAES key.
If a spherical soccer ball has a volume of 36π cm3, then which one of the following is the surface area of the ball in square centimeters?
A.12π
B.316π
C.332π
D.36π
Worked solutionUnofficial
Answer: D
Answer D: 36π. The stem is: If a spherical soccer ball has a volume of 36π cm3, then which one of the following is the surface area of the ball in square centimeters? Letter D is the Abrari key for this geometry. V = (4/3)pi r^3 = 36pi -> r^3 = 27 -> r = 3. Surface area = 4 pi r^2 = 4 pi * 9 = 36 pi.
Unofficial — solved by Abrari, not an official EAES key.
Points A, B and C are located on a circle with center O and radius 2 units long. If A, B and C are joined to form an equilateral triangle, then what is the area of triangle ABC in square units?
A.3
B. 3
C.33
D. 1
Worked solutionUnofficial
Answer: C
Answer C: 33. The stem is: Points A, B and C are located on a circle with center O and radius 2 units long. If A, B and C are joined to form an equilateral triangle, then what is the area of triangle ABC in square units? Letter C is the Abrari key for this geometry. For an equilateral triangle inscribed in a circle of radius R, area = (3*sqrt(3)/4) R^2 = (3sqrt3/4)*4 = 3sqrt3.
Unofficial — solved by Abrari, not an official EAES key.
Use the following information: a bar graph shows the data of a student's study pattern recorded for 32 days. How many days did the student study less than 8 hours?
This item uses a figure in the original paper (not redrawn here).
A. 6
B. 18
C. 12
D. 24
Worked solutionUnofficial
Answer: D
Answer D: 24. The stem is: Use the following information: a bar graph shows the data of a student's study pattern recorded for 32 days. How many days did the student study less than 8 hours? Letter D is the Abrari key for this data-interpretation. Requires reading bar-graph values I cannot see (32-day study pattern). A commenter suggests D (24). Image-dependent; flagged.
Unofficial — solved by Abrari, not an official EAES key.
Use the bar graph (student's study pattern over 32 days). How many days did the student study more than the average amount of the study?
This item uses a figure in the original paper (not redrawn here).
A. 8
B. 5
C. 15
D. 17
Worked solutionUnofficial
Answer: C
Answer C: 15. The stem is: Use the bar graph (student's study pattern over 32 days). How many days did the student study more than the average amount of the study? Letter C is the Abrari key for this data-interpretation. Requires reading the bar graph I cannot see. A commenter suggests C (15). Image-dependent; flagged.
Unofficial — solved by Abrari, not an official EAES key.
2017 E.C. · social · Q36 · Quantitative - Number systems
Which one of the following statements is true?
A. Every non-negative integer is a natural number.
B. Every integer number can be numerator of a rational number.
C. The sum of two irrational numbers is irrational number.
D. The intersection of the set of integers and the set of irrational numbers is non-empty set.
Worked solutionUnofficial
Answer: B
Answer B: Every integer number can be numerator of a rational number.. The stem is: Which one of the following statements is true? Letter B is the Abrari key for this Quantitative - Number systems.
Unofficial — solved by Abrari, not an official EAES key.
No. Every keyed letter on this page is unofficial — solved by Abrari from the past paper, then checked against the textbook when a stored quote exists. Abrari never calls an answer an official EAES or MoE key.
Is Abrari affiliated with the Ministry of Education or EAES?
Abrari is an independent study aid and is not affiliated with, endorsed by, or an official product of the Ethiopian Ministry of Education (MoE) or EAES.
Can I download the textbook PDF?
No. Abrari does not offer textbook downloads. Mapped units open in the on-site reader only.
How do I practice these questions timed?
Use the practice links on this page or go to https://abrari.app/#try. The web try-out and the Abrari app use the same unofficial question bank.
