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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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2015 E.C.

2015 E.C. · social · Q41 · data-interpretation/set

How many of the students are neither female nor are between (18-20) years old? (Male=560; 18-20 = 60%)
  1. A. 336
  2. B. 224
  3. C. 200
  4. D. 120
Worked solutionUnofficial

Answer: B

Answer B: 224. The stem is: How many of the students are neither female nor are between (18-20) years old? (Male=560; 18-20 = 60%) Letter B is the Abrari key for this data-interpretation/set. Neither female nor 18-20 = males not in 18-20 = 560 x 40% = 224 (assumes proportional age split).

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

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2015 E.C. · social · Q42 · percentage

The profit of a certain Company this year is 102% of last year's profit. If the total profit of this year is 2,040,102 Birr, what was last year's profit?
  1. A. 2,080,104 Birr
  2. B. 4,080,204 Birr
  3. C. 2,000,100 Birr
  4. D. 2,040,102 Birr
Worked solutionUnofficial

Answer: C

Answer C: 2,000,100 Birr. The stem is: The profit of a certain Company this year is 102% of last year's profit. If the total profit of this year is 2,040,102 Birr, what was last year's profit? Letter C is the Abrari key for this percentage. 2,040,102 / 1.02 = 2,000,100.

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

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2015 E.C. · social · Q43 · exponential-model

The population of a certain colony of insects will double in size every year. The population at the beginning was estimated to be 3,150. If p represents the population after n years, then which one of the following equation represents the model of the population after n years?
  1. A. p(n)=2(3,150)np(n) = 2(3,150)^n
  2. B. p(n)=3,150(2)np(n) = 3,150(2)^n
  3. C. p(n)=3,150(2)n−1p(n) = 3,150(2)^{n-1}
  4. D. p(n)=2(3,150)n−1p(n) = 2(3,150)^{n-1}
Worked solutionUnofficial

Answer: B

Answer B: p(n)=3,150(2)np(n) = 3,150(2)^n. The stem is: The population of a certain colony of insects will double in size every year. The population at the beginning was estimated to be 3,150. If p represents the population after n years, then which one of the following equation represents the model of the population after n years? Letter B is the Abrari key for this exponential-model.

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

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2015 E.C. · social · Q46 · algebra/inequality

Suppose xx and yy are positive real numbers and Q1(x,y)=(x+y)3Q_1(x,y) = (x+y)^3 and Q2(x,y)=x3+y3Q_2(x,y) = x^3 + y^3, then which one of the following is true about Q1Q_1 and Q2Q_2?
  1. A. Q1Q_1 is less than Q2Q_2.
  2. B. Q1Q_1 is greater than Q2Q_2.
  3. C. Q1Q_1 is equal to Q2Q_2.
  4. D. The relationship cannot be determined from the information given.
Worked solutionUnofficial

Answer: B

Answer B: Q1Q_1 is greater than Q2Q_2.. The stem is: Suppose xx and yy are positive real numbers and Q1(x,y)=(x+y)3Q_1(x,y) = (x+y)^3 and Q2(x,y)=x3+y3Q_2(x,y) = x^3 + y^3, then which one of the following is true about Q1Q_1 and Q2Q_2? Letter B is the Abrari key for this algebra/inequality. (x+y)^3 = x^3+y^3+3xy(x+y) > x^3+y^3 for positive x,y.

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

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2015 E.C. · social · Q47 · arithmetic-sequence

Suppose 3, 7, 11, 15, 19, 23, ... are the first six terms of an arithmetic sequence, then which one of the following is the 15th term of the sequence?
  1. A. 60
  2. B. 66
  3. C. 59
  4. D. 52
Worked solutionUnofficial

Answer: C

Answer C: 59. The stem is: Suppose 3, 7, 11, 15, 19, 23, ... are the first six terms of an arithmetic sequence, then which one of the following is the 15th term of the sequence? Letter C is the Abrari key for this arithmetic-sequence. a1=3, d=4; a15 = 3 + 14*4 = 59.

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

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2015 E.C. · social · Q48 · geometric-sequence

Which one of the following is the sequence defined recursively by G8=384G_8 = 384 and Gn=2G(n−1)G_n = 2G_{(n-1)}?
  1. A. 2, 4, 8, 16, 32 ...
  2. B. 7, 14, 28, 56, 112 ...
  3. C. 9, 18, 36, 72, 144 ...
  4. D. 3, 6, 12, 24, 48 ...
Worked solutionUnofficial

Answer: D

Answer D: 3, 6, 12, 24, 48 .... The stem is: Which one of the following is the sequence defined recursively by G8=384G_8 = 384 and Gn=2G(n−1)G_n = 2G_{(n-1)}? Letter D is the Abrari key for this geometric-sequence. G1 = 384/2^7 = 3, so 3,6,12,24,48.

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

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2015 E.C. · social · Q50 · geometric-series

Which one of the following is the sum of the first six terms of the sequence (5(2)n)n=1∞(5(2)^n)_{n=1}^{\infty}?
  1. A. 80
  2. B. 160
  3. C. 155
  4. D. 630
Worked solutionUnofficial

Answer: D

Answer D: 630. The stem is: Which one of the following is the sum of the first six terms of the sequence (5(2)n)n=1∞(5(2)^n)_{n=1}^{\infty}? Letter D is the Abrari key for this geometric-series. 10+20+40+80+160+320 = 630.

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

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2015 E.C. · social · Q51 · linear-systems

Given the system of linear equations 2x+3y=112x + 3y = 11 and 3x+2y=93x + 2y = 9, if xx and yy satisfy the system, what is the value of y−xy - x?
  1. A. 2
  2. B. 3
  3. C. -2
  4. D. -3
Worked solutionUnofficial

Answer: A

Answer A: 2. The stem is: Given the system of linear equations 2x+3y=112x + 3y = 11 and 3x+2y=93x + 2y = 9, if xx and yy satisfy the system, what is the value of y−xy - x? Letter A is the Abrari key for this linear-systems. x=1, y=3, so y-x=2.

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

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2015 E.C. · social · Q52 · counting/permutations

A person wants to have a four digit password with the first digit greater than 5. How many different passwords the person can create using the digits 0 to 9?
  1. A. 2,560
  2. B. 4,000
  3. C. 10,000
  4. D. 5,040
Worked solutionUnofficial

Answer: B

Answer B: 4,000. The stem is: A person wants to have a four digit password with the first digit greater than 5. How many different passwords the person can create using the digits 0 to 9? Letter B is the Abrari key for this counting/permutations. First digit in {6,7,8,9} = 4 choices; remaining 3 digits 10 each: 4*10*10*10 = 4000.

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

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2015 E.C. · social · Q53 · probability

A fair 12-sided die, with faces numbered 1 to 12, is to be rolled once. What is the probability of rolling a number that is not 4, 6, and 11?
  1. A. 14\frac{1}{4}
  2. B. 1112\frac{11}{12}
  3. C. 112\frac{1}{12}
  4. D. 34\frac{3}{4}
Worked solutionUnofficial

Answer: D

Answer D: 34\frac{3}{4}. The stem is: A fair 12-sided die, with faces numbered 1 to 12, is to be rolled once. What is the probability of rolling a number that is not 4, 6, and 11? Letter D is the Abrari key for this probability. 9 favorable of 12 = 3/4.

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

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2015 E.C. · social · Q54 · percentage

A container contains 48 liters of water. If 5% of the water in the container is used, how much water is left in the container?
  1. A. 46.4
  2. B. 45.4
  3. C. 45.6
  4. D. 46.6
Worked solutionUnofficial

Answer: C

Answer C: 45.6. The stem is: A container contains 48 liters of water. If 5% of the water in the container is used, how much water is left in the container? Letter C is the Abrari key for this percentage. 48 * 0.95 = 45.6.

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

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2015 E.C. · social · Q55 · algebra/geometry

The length of a rectangle is 3 units more than its width. If the width is increased by 4 units and the length is decreased by 2 units then its area will increase by 10 square units. What will be the length of the rectangle?
  1. A. 6 units
  2. B. 4 units
  3. C. 7 units
  4. D. 3 units
Worked solutionUnofficial

Answer: A

Answer A: 6 units. The stem is: The length of a rectangle is 3 units more than its width. If the width is increased by 4 units and the length is decreased by 2 units then its area will increase by 10 square units. What will be the length of the rectangle? Letter A is the Abrari key for this algebra/geometry. (w+4)(w+1)=w(w+3)+10 -> w=3, length=6.

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

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2015 E.C. · social · Q56 · linear-systems

Which one of the following is the solution set of the following system of linear equations: 2x+3y=12x + 3y = 1 and x−4y=6x - 4y = 6?
  1. A. {(−1,1)}\{(-1, 1)\}
  2. B. {(−2,−1)}\{(-2, -1)\}
  3. C. {(2,−1)}\{(2, -1)\}
  4. D. {(−2,1)}\{(-2, 1)\}
Worked solutionUnofficial

Answer: C

Answer C: {(2,−1)}\{(2, -1)\}. The stem is: Which one of the following is the solution set of the following system of linear equations: 2x+3y=12x + 3y = 1 and x−4y=6x - 4y = 6? Letter C is the Abrari key for this linear-systems. x=2, y=-1.

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

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2015 E.C. · social · Q60 · similar-triangles

Suppose △ABC∼△DEF\triangle ABC \sim \triangle DEF and DFDF is two third of ACAC. If DE=12mDE=12m, then how much is ABAB?
  1. A. 8m
  2. B. 24m
  3. C. 6m
  4. D. 18m
Worked solutionUnofficial

Answer: D

Answer D: 18m. The stem is: Suppose △ABC∼△DEF\triangle ABC \sim \triangle DEF and DFDF is two third of ACAC. If DE=12mDE=12m, then how much is ABAB? Letter D is the Abrari key for this similar-triangles. Ratio DEF:ABC = 2/3, so DE = (2/3)AB -> AB = 12 * 3/2 = 18m.

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

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2016 E.C.

2016 E.C. · natural · Q24 · Reading comprehension - Passage II (Air pollution)

How can an air pollution-free environment be created for the new generation?
  1. A. By planting trees every year
  2. B. By restricting private use of car
  3. C. By devising rules and regulations
  4. D. Tackling the causes of air pollution from the source
Worked solutionUnofficial

Answer: D

Answer D: Tackling the causes of air pollution from the source. The stem is: How can an air pollution-free environment be created for the new generation? Letter D is the Abrari key for this Reading comprehension - Passage II (Air pollution). Passage: 'By collectively addressing the root causes of air pollution...'

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

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2016 E.C. · natural · Q33 · Quantitative reasoning - Inequalities

How many numbers in the set {-8,-5,-4,-1,0,2,5,7,8} satisfy |5-3x| < 11?
  1. A. 4
  2. B. 3
  3. C. 5
  4. D. 6
Worked solutionUnofficial

Answer: A

Answer A: 4. The stem is: How many numbers in the set {-8,-5,-4,-1,0,2,5,7,8} satisfy |5-3x| < 11? Letter A is the Abrari key for this Quantitative reasoning - Inequalities. |5-3x|<11 gives -2<x<16/3(~5.33); members {-1,0,2,5} = 4.

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

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2016 E.C. · natural · Q34 · Quantitative reasoning - Radicals

What is the rationalizing factor of the denominator of 334\frac{3}{^3\sqrt{4}}?
  1. A. 2\sqrt{2}
  2. B. 32^3\sqrt{2}
  3. C. 323\sqrt{2}
  4. D. 2
Worked solutionUnofficial

Answer: B

Answer B: 32^3\sqrt{2}. The stem is: What is the rationalizing factor of the denominator of 334\frac{3}{^3\sqrt{4}}? Letter B is the Abrari key for this Quantitative reasoning - Radicals. cbrt(4)=2^(2/3); multiply by cbrt(2)=2^(1/3) to get 2. Rationalizing factor is cube root of 2.

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

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2016 E.C. · natural · Q35 · Quantitative reasoning - GCF/LCM

The GCF and LCM of two numbers are 12 and 336. If one number is 84, find the other number.
  1. A. 36
  2. B. 48
  3. C. 72
  4. D. 96
Worked solutionUnofficial

Answer: B

Answer B: 48. The stem is: The GCF and LCM of two numbers are 12 and 336. If one number is 84, find the other number. Letter B is the Abrari key for this Quantitative reasoning - GCF/LCM. GCF*LCM = product: 12*336 = 4032; 4032/84 = 48.

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

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2016 E.C. · natural · Q36 · Quantitative reasoning - Linear equations

If 3x−2=3−5x3x-2=3-5x, then which one of the following is equal to 7-4x?
  1. A. 92\frac{9}{2}
  2. B. −92-\frac{9}{2}
  3. C. 132\frac{13}{2}
  4. D. 192\frac{19}{2}
Worked solutionUnofficial

Answer: A

Answer A: 92\frac{9}{2}. The stem is: If 3x−2=3−5x3x-2=3-5x, then which one of the following is equal to 7-4x? Letter A is the Abrari key for this Quantitative reasoning - Linear equations. 8x=5, x=5/8; 7-4(5/8)=7-5/2=9/2.

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

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2016 E.C. · natural · Q37 · Quantitative reasoning - Age word problem

A father is 32 and his son is 8 now. In how many years will the father be three times as old as his son?
  1. A. 6
  2. B. 3
  3. C. 4
  4. D. 5
Worked solutionUnofficial

Answer: C

Answer C: 4. The stem is: A father is 32 and his son is 8 now. In how many years will the father be three times as old as his son? Letter C is the Abrari key for this Quantitative reasoning - Age word problem. 32+t=3(8+t) -> 8=2t -> t=4.

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

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2016 E.C. · natural · Q38 · Quantitative reasoning - Systems of equations

For what value(s) of k does the system {2x+3y=1, kx+6y=-3} have a unique solution?
  1. A. k = 4
  2. B. k = -4
  3. C. k ≠ -4
  4. D. k ≠ 4
Worked solutionUnofficial

Answer: D

Answer D: k ≠ 4. The stem is: For what value(s) of k does the system {2x+3y=1, kx+6y=-3} have a unique solution? Letter D is the Abrari key for this Quantitative reasoning - Systems of equations. Unique when 2/k != 3/6, i.e., k != 4.

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

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2016 E.C. · natural · Q39 · Quantitative reasoning - Word problem

The difference of two numbers is 10, and 3 times the larger plus 2 times the smaller is 55. Find the larger number.
  1. A. 6
  2. B. 14
  3. C. 5
  4. D. 15
Worked solutionUnofficial

Answer: D

Answer D: 15. The stem is: The difference of two numbers is 10, and 3 times the larger plus 2 times the smaller is 55. Find the larger number. Letter D is the Abrari key for this Quantitative reasoning - Word problem. L-S=10, 3L+2S=55 -> 5L=75 -> L=15.

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

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2016 E.C. · natural · Q40 · Quantitative reasoning - Quadratic equations

One root of 2x2+1=h−5x2x^2 + 1 = h - 5x (h constant) is four times the other. What are the roots?
  1. A. −12-\frac{1}{2} and -2
  2. B. −2-2 and -8
  3. C. 12\frac{1}{2} and 2
  4. D. 2 and 8
Worked solutionUnofficial

Answer: A

Answer A: −12-\frac{1}{2} and -2. The stem is: One root of 2x2+1=h−5x2x^2 + 1 = h - 5x (h constant) is four times the other. What are the roots? Letter A is the Abrari key for this Quantitative reasoning - Quadratic equations. 2x^2+5x+(1-h)=0; sum of roots r+4r=5r=-5/2 -> r=-1/2; roots -1/2 and -2.

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

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2016 E.C. · natural · Q41 · Quantitative reasoning - Percentage

What percent of 16 is 12?
  1. A. 25%
  2. B. 70%
  3. C. 75%
  4. D. 50%
Worked solutionUnofficial

Answer: C

Answer C: 75%. The stem is: What percent of 16 is 12? Letter C is the Abrari key for this Quantitative reasoning - Percentage. 12/16 = 0.75 = 75%.

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

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2016 E.C. · natural · Q42 · Quantitative reasoning - Rational equations

If 3x2+13x+6=x2x+2−3\frac{3x^2 + 1}{3x + 6} = \frac{x^2}{x + 2} - 3, then what is the value of 19x+1\frac{1}{9x + 1}?
  1. A. −118-\frac{1}{18}
  2. B. −15-\frac{1}{5}
  3. C. 118\frac{1}{18}
  4. D. 120\frac{1}{20}
Worked solutionUnofficial

Answer: A

Answer A: −118-\frac{1}{18}. The stem is: If 3x2+13x+6=x2x+2−3\frac{3x^2 + 1}{3x + 6} = \frac{x^2}{x + 2} - 3, then what is the value of 19x+1\frac{1}{9x + 1}? Letter A is the Abrari key for this Quantitative reasoning - Rational equations. Multiply by 3(x+2): 3x^2+1 = 3x^2-9x-18 -> 1=-9x-18 -> 9x=-19 -> 9x+1=-18; 1/(9x+1)=-1/18 (A). Option A=-1/18.

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

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