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SAT · EUEE topic

Quantitative reasoning: every EUEE question 2015–2018 E.C. (144 questions), solved

144 questions · 2015 ×39 · 2016 ×42 · 2017 ×43 · 2018 ×20

Number, algebra, geometry and data items from EUEE SAT papers. SAT has no MoE textbook, so there are no page references.

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2017 E.C.

2017 E.C. · social · Q37 · Quantitative - Radicals comparison

Which one of the following is the largest number?
  1. A. 23\sqrt[3]{2}
  2. B. 56\sqrt[6]{5}
  3. C. 34\sqrt[4]{3}
  4. D. 1112\sqrt[12]{11}
Worked solutionUnofficial

Answer: C

Answer C: 34\sqrt[4]{3}. The stem is: Which one of the following is the largest number? Letter C is the Abrari key for this Quantitative - Radicals comparison.

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q38 · Quantitative - Quadratic max

A ball is shot into the air from the top of the building. The height in meter is given by h(t)=kt−t2+30h(t)=kt-t^2+30, where tt is the time taken in second. What is the possible value of kk if the maximum value of height from the ground is 34?
  1. A. 4
  2. B. 2\sqrt{2}
  3. C. 2
  4. D. 5
Worked solutionUnofficial

Answer: A

Answer A: 4. The stem is: A ball is shot into the air from the top of the building. The height in meter is given by h(t)=kt−t2+30h(t)=kt-t^2+30, where tt is the time taken in second. What is the possible value of kk if the maximum value of height from the ground is 34? Letter A is the Abrari key for this Quantitative - Quadratic max.

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q39 · Quantitative - Functions evaluation

If f(x)=sin⁡πx+ex2+∣x∣+x3f(x)=\sin \pi x + e^{x^2} + |x| + x^3 and g(x)=cos⁡πx+ln⁡(x+1)+xg(x)=\cos \pi x + \ln(x+1) + x, then what is the value of f(1)−2g(0)f(1)-2g(0)?
  1. A. ln⁡2\ln 2
  2. B. ee
  3. C. e+2e+2
  4. D. 0
Worked solutionUnofficial

Answer: C

Answer C: e+2e+2. The stem is: If f(x)=sin⁡πx+ex2+∣x∣+x3f(x)=\sin \pi x + e^{x^2} + |x| + x^3 and g(x)=cos⁡πx+ln⁡(x+1)+xg(x)=\cos \pi x + \ln(x+1) + x, then what is the value of f(1)−2g(0)f(1)-2g(0)? Letter C is the Abrari key for this Quantitative - Functions evaluation. Site key marked D (0), but computing: f(1)=sin(pi)+e^1+1+1=e+2; g(0)=cos0+ln1+0=1, so f(1)-2g(0)=e+2-2=e. Neither cleanly matches; several commenters say C (e+2). Likely site error. Verify.

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q40 · Quantitative - Domain of function

Which one of the following is the domain of g(x)=ln⁡(1−x)+ln⁡xg(x)=\ln(1-x)+\ln x?
  1. A. R∖{−1,0}\mathbb{R} \setminus \{-1,0\}
  2. B. (0,∞)(0, \infty)
  3. C. (1,∞)(1, \infty)
  4. D. (0,1)(0,1)
Worked solutionUnofficial

Answer: D

Answer D: (0,1)(0,1). The stem is: Which one of the following is the domain of g(x)=ln⁡(1−x)+ln⁡xg(x)=\ln(1-x)+\ln x? Letter D is the Abrari key for this Quantitative - Domain of function.

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q41 · Quantitative - Exponents

If −x+2y=4-x + 2y = 4, then what is the value of 25y5x\frac{25^y}{5^x}?
  1. A. 625
  2. B. 125
  3. C. 25
  4. D. 5
Worked solutionUnofficial

Answer: A

Answer A: 625. The stem is: If −x+2y=4-x + 2y = 4, then what is the value of 25y5x\frac{25^y}{5^x}? Letter A is the Abrari key for this Quantitative - Exponents.

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q42 · Quantitative - Word problem

A farmer has ten cows. Every day, he receives the same amount of milk in liters from each cow. One day he received half the daily amount from four cows, three-fourth from three cows, and no milk from three cows. In total, he didn't receive ninety-two liters of milk on that day. How many liters of milk did he receive on that particular day?
  1. A. 16
  2. B. 92
  3. C. 68
  4. D. 160
Worked solutionUnofficial

Answer: C

Answer C: 68. The stem is: A farmer has ten cows. Every day, he receives the same amount of milk in liters from each cow. One day he received half the daily amount from four cows, three-fourth from three cows, and no milk from three cows. In total, he didn't receive ninety-two liters of milk on that day.… Letter C is the Abrari key for this Quantitative - Word problem.

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q43 · Quantitative - Word problem

A woman burns 416 calories in an hour exercise. She burns 10 calories/min swimming and 6 calories/min on the bike. How many minutes of the hour does she spend exercising in the water?
  1. A. 14
  2. B. 56
  3. C. 46
  4. D. 60
Worked solutionUnofficial

Answer: A

Answer A: 14. The stem is: A woman burns 416 calories in an hour exercise. She burns 10 calories/min swimming and 6 calories/min on the bike. How many minutes of the hour does she spend exercising in the water? Letter A is the Abrari key for this Quantitative - Word problem.

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q44 · Quantitative - Quadratic inequality

A daily profit is p(x)=−x2+1,400x−80,000p(x) = -x^2 + 1{,}400x - 80{,}000. What range of prices will yield a profit of at least Birr 400,000?
  1. A. x≥800x \geq 800
  2. B. 600≤x≤800600 \leq x \leq 800
  3. C. x≤600x \leq 600
  4. D. x≤600x \leq 600 or x≥800x \geq 800
Worked solutionUnofficial

Answer: B

Answer B: 600≤x≤800600 \leq x \leq 800. The stem is: A daily profit is p(x)=−x2+1,400x−80,000p(x) = -x^2 + 1{,}400x - 80{,}000. What range of prices will yield a profit of at least Birr 400,000? Letter B is the Abrari key for this Quantitative - Quadratic inequality.

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q45 · Quantitative - Function domain/range

Which one of the following is true about the function f(x)=x25f(x) = x^{\frac{2}{5}}?
  1. A. The range of ff is {y∈R∣y≥0}\{ y \in \mathbb{R} \mid y \geq 0 \}
  2. B. The domain of ff is {x∈R∣x≥0}\{ x \in \mathbb{R} \mid x \geq 0 \}
  3. C. The domain of ff is {x∈R∣x≤0}\{ x \in \mathbb{R} \mid x \leq 0 \}
  4. D. The range of ff is {y∣y∈R}\{ y \mid y \in \mathbb{R} \}
Worked solutionUnofficial

Answer: A

Answer A: The range of ff is {y∈R∣y≥0}\{ y \in \mathbb{R} \mid y \geq 0 \}. The stem is: Which one of the following is true about the function f(x)=x25f(x) = x^{\frac{2}{5}}? Letter A is the Abrari key for this Quantitative - Function domain/range.

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q46 · Quantitative - Sequence

What is the value of zz in the sequence 1,2,4,8,10,20,22,z,…1, 2, 4, 8, 10, 20, 22, z, \dots?
  1. A. 24
  2. B. 44
  3. C. 40
  4. D. 32
Worked solutionUnofficial

Answer: B

Answer B: 44. The stem is: What is the value of zz in the sequence 1,2,4,8,10,20,22,z,…1, 2, 4, 8, 10, 20, 22, z, \dots? Letter B is the Abrari key for this Quantitative - Sequence. Pattern +1,x2 alternating: 22x2=44 (B).

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q47 · Quantitative - Sequence

What is the possible value of the missing term xx in the sequence −1,0,1,2,−1.8,1,26,−1,x,1,242,−1,728,1,…-1, 0, 1, 2, -1.8, 1, 26, -1, x, 1, 242, -1, 728, 1, \dots?
  1. A. 36
  2. B. 54
  3. C. 34
  4. D. 80
Worked solutionUnofficial

Answer: D

Answer D: 80. The stem is: What is the possible value of the missing term xx in the sequence −1,0,1,2,−1.8,1,26,−1,x,1,242,−1,728,1,…-1, 0, 1, 2, -1.8, 1, 26, -1, x, 1, 242, -1, 728, 1, \dots? Letter D is the Abrari key for this Quantitative - Sequence. Powers of 3 minus 1: 3^n-1 pattern (2,26,80,242,728). x=3^4-1=80 (D).

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q48 · Quantitative - Calendar

How many days are there from the first day of March to the last day of May?
  1. A. 92
  2. B. 89
  3. C. 90
  4. D. 91
Worked solutionUnofficial

Answer: A

Answer A: 92. The stem is: How many days are there from the first day of March to the last day of May? Letter A is the Abrari key for this Quantitative - Calendar. March 31 + April 30 + May 31 = 92 (A).

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q49 · Quantitative - Comparison (triangle inequality)

Consider the lengths of the sides of a triangle x,y,zx, y, z. Compare Quantity P = 3x+y−z3x + y - z with Quantity Q = 4x4x.
  1. A. Quantity P is greater than Quantity Q.
  2. B. Quantity P is less than Quantity Q.
  3. C. The two quantities are equal.
  4. D. The two quantities cannot be compared.
Worked solutionUnofficial

Answer: B

Answer B: Quantity P is less than Quantity Q.. The stem is: Consider the lengths of the sides of a triangle x,y,zx, y, z. Compare Quantity P = 3x+y−z3x + y - z with Quantity Q = 4x4x. Letter B is the Abrari key for this Quantitative - Comparison (triangle inequality). No site answer key. By triangle inequality y - z < x, so 3x + y - z < 4x, i.e. P < Q (B). Verify.

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q50 · Quantitative - Comparison (mean vs median)

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 = average monthly payment with Quantity Q = median monthly payment.
  1. A. Quantity P is less than Quantity Q.
  2. B. Quantity P is greater than Quantity Q.
  3. C. The two quantities are equal.
  4. 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 = average monthly payment with Quantity Q = median monthly payment. Letter B is the Abrari key for this Quantitative - Comparison (mean vs median).

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q51 · Quantitative - Geometry/ratio

An engineer is putting black and white ceramics on a square floor of area 36m236\text{m}^2. Each ceramic has area 1m21\text{m}^2. Black ones are placed along both diagonals; the rest are white. In what ratio is black to white ceramic used?
  1. A. 1:2
  2. B. 1:6
  3. C. 4:5
  4. D. 1:5
Worked solutionUnofficial

Answer: A

Answer A: 1:2. The stem is: An engineer is putting black and white ceramics on a square floor of area 36m236\text{m}^2. Each ceramic has area 1m21\text{m}^2. Black ones are placed along both diagonals; the rest are white. In what ratio is black to white ceramic used? Letter A is the Abrari key for this Quantitative - Geometry/ratio. 6x6 grid, both diagonals (even side, no overlap) = 12 black, 24 white -> 12:24 = 1:2 (A).

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q52 · Quantitative - Fractions/ratio

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?
  1. A. 1:2
  2. B. 1:6
  3. C. 2:3
  4. 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? Letter C is the Abrari key for this Quantitative - Fractions/ratio. Avocado=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 (C).

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q53 · Quantitative - Work/rate

Two pipes A and B are used to fill a water tank. Pipe A can fill the tank in 3 hours, and pipe B in 6 hours. How long will it take in hours to fill the tank if both pipes are opened at the same time?
  1. A. 4
  2. B. 5
  3. C. 2
  4. D. 9
Worked solutionUnofficial

Answer: C

Answer C: 2. The stem is: Two pipes A and B are used to fill a water tank. Pipe A can fill the tank in 3 hours, and pipe B in 6 hours. How long will it take in hours to fill the tank if both pipes are opened at the same time? Letter C is the Abrari key for this Quantitative - Work/rate.

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q54 · Quantitative - Work/rate

The old and new machines fill 35 and 50 bottles per hour respectively; a total of 590 bottles are filled every day. One day the old machine broke after working for 4 hours. How long in hours for the new machine to fill the remaining bottles that day?
  1. A. 5
  2. B. 8
  3. C. 7
  4. D. 13
Worked solutionUnofficial

Answer: A

Answer A: 5. The stem is: The old and new machines fill 35 and 50 bottles per hour respectively; a total of 590 bottles are filled every day. One day the old machine broke after working for 4 hours. How long in hours for the new machine to fill the remaining bottles that day? Letter A is the Abrari key for this Quantitative - Work/rate. Old fills 4*35=140; remaining 590-140=450; new at 50/hr -> 9 hours (not 5). Site key marks A(5); computation ambiguous. Verify.

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q55 · Quantitative - Geometry (count triangles)

How many triangles are there in the diagram?

This item uses a figure in the original paper (not redrawn here).

  1. A. 14
  2. B. 18
  3. C. 12
  4. 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 Quantitative - Geometry (count triangles). Requires the figure; commenters suggest 16 (D). Verify with image.

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q56 · Quantitative - Sphere

If a spherical soccer ball has a volume of 36π cm336\pi \text{ cm}^3, then which one of the following is the surface area of the ball in square centimeter?
  1. A. 12π12\pi
  2. B. 16π3\frac{16\pi}{3}
  3. C. 32π3\frac{32\pi}{3}
  4. D. 36π36\pi
Worked solutionUnofficial

Answer: D

Answer D: 36π36\pi. The stem is: If a spherical soccer ball has a volume of 36π cm336\pi \text{ cm}^3, then which one of the following is the surface area of the ball in square centimeter? Letter D is the Abrari key for this Quantitative - Sphere. V=36pi -> (4/3)pi r^3=36pi -> r^3=27 -> r=3; SA=4pi r^2=36pi (D).

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q57 · Quantitative - Circle/equilateral triangle

Points A, B and C are located on a circle with center O and radius 2 units long. If A, B and C form an equilateral triangle, then what is the area of triangle ABC in square units?
  1. A. 3\sqrt{3}
  2. B. 3
  3. C. 333\sqrt{3}
  4. D. 1
Worked solutionUnofficial

Answer: C

Answer C: 333\sqrt{3}. 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 form an equilateral triangle, then what is the area of triangle ABC in square units? Letter C is the Abrari key for this Quantitative - Circle/equilateral triangle. Side = r*sqrt(3)=2sqrt(3); area=(sqrt3/4)*(2sqrt3)^2=(sqrt3/4)*12=3sqrt3 (C).

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q58 · Quantitative - Bar graph interpretation

How many days did the student study less than 8 hours?

This item uses a figure in the original paper (not redrawn here).

  1. A. 6
  2. B. 18
  3. C. 12
  4. D. 24
Worked solutionUnofficial

Answer: D

Answer D: 24. The stem is: How many days did the student study less than 8 hours? Letter D is the Abrari key for this Quantitative - Bar graph interpretation. Requires the bar graph; a commenter suggests D (24). Verify with image.

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q59 · Quantitative - Bar graph interpretation

Which time in hours is the median amount of the study?

This item uses a figure in the original paper (not redrawn here).

  1. A. 2
  2. B. 6
  3. C. 4
  4. D. 8
Worked solutionUnofficial

Answer: D

Answer D: 8. The stem is: Which time in hours is the median amount of the study? Letter D is the Abrari key for this Quantitative - Bar graph interpretation. Requires the bar graph; a commenter suggests D (8). Verify with image.

Unofficial — solved by Abrari, not an official EAES key.

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2017 E.C. · social · Q60 · Quantitative - Bar graph interpretation

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).

  1. A. 8
  2. B. 5
  3. C. 15
  4. D. 17
Worked solutionUnofficial

Answer: C

Answer C: 15. The stem is: How many days did the student study more than the average amount of the study? Letter C is the Abrari key for this Quantitative - Bar graph interpretation. Requires the bar graph; a commenter suggests C (15). Verify with image.

Unofficial — solved by Abrari, not an official EAES key.

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2018 E.C.

2018 E.C. · social · Q36 · Quantitative - Arithmetic

Section Two: Quantitative Reasoning (Questions 36-60)
Directions: This section contains 25 quantitative reasoning items which consist of percentage, probability, mathematical logical analytical reasoning, comparison of algebra, quadratic equation, exponentials, rational, linear equations, ratios, Solve each of the problems given in questions 36 - 60 according to their specific two quantities, geometry and trigonometry, and data interpretation using table. instructions and select the correct answer from the given four alternatives. Then, blacken the letter of your choice on the separate answer sheet provided.

A shop sells a shoe at a price of Birr 1225 with a 30% discount notice. How much was the original price of the shoe in Birr?
  1. A. 1592.50
  2. B. 3675
  3. C. 1750
  4. D. 1432.50
Worked solutionUnofficial

No keyed letter is published for this item. No keyed letter is published for this 2018 E.C. social item (Quantitative - Arithmetic). The bank has no key we trust (often an unkeyed 2018 item, a missing figure, or confidence none). Try the options yourself, then practise the same subject timed in the app.

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