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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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2016 E.C.

2016 E.C. · natural · Q43 · Quantitative reasoning - Inverse functions

If f(x)=102x+1f(x) = 10^{2x+1}, then which one of the following is equal to f−1(x)f^{-1}(x)?
  1. A. log(2x - 1)
  2. B. log⁡x+12\log \sqrt{x} + \frac{1}{2}
  3. C. log x + 12\frac{1}{2}
  4. D. log⁡x−12\log \sqrt{x} - \frac{1}{2}
Worked solutionUnofficial

Answer: D

Answer D: log⁡x−12\log \sqrt{x} - \frac{1}{2}. The stem is: If f(x)=102x+1f(x) = 10^{2x+1}, then which one of the following is equal to f−1(x)f^{-1}(x)? Letter D is the Abrari key for this Quantitative reasoning - Inverse functions. y=10^(2x+1) -> log y = 2x+1 -> x=(log y -1)/2 = (1/2)log y - 1/2 = log(sqrt(y)) - 1/2.

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

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2016 E.C. · natural · Q44 · Quantitative reasoning - Exponential functions

Which one of the following is NOT true about the graph of the function f(x)=(75)xf(x) = \left(\frac{7}{5}\right)^{x}? (accompanied by a graph image)

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

  1. A. It is an increasing function.
  2. B. Its y-intercept is 1.
  3. C. Its domain is the set of all real numbers.
  4. D. Its range is the set of all real numbers.
Worked solutionUnofficial

Answer: D

Answer D: Its range is the set of all real numbers.. The stem is: Which one of the following is NOT true about the graph of the function f(x)=(75)xf(x) = \left(\frac{7}{5}\right)^{x}? (accompanied by a graph image) Letter D is the Abrari key for this Quantitative reasoning - Exponential functions. Range of an exponential function is (0, infinity), not all reals, so D is the false (NOT true) statement. Image present but the mathematical answer is determinate. Flagged as image-dependent per instructions.

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

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2016 E.C. · natural · Q45 · Quantitative reasoning - Sequences

Which one of the following is the value of x in the sequence 23,34,56,89,x,188,...?
  1. A. 111
  2. B. 100
  3. C. 133
  4. D. 144
Worked solutionUnofficial

Answer: C

Answer C: 133. The stem is: Which one of the following is the value of x in the sequence 23,34,56,89,x,188,...? Letter C is the Abrari key for this Quantitative reasoning - Sequences. Differences 11,22,33,44,55: 89+44=133, 133+55=188. x=133.

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

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2016 E.C. · natural · Q46 · Quantitative reasoning - Sequences

What are the values of y and z in the sequence 1,−13,17,−115,131,−163,y,z,…1, -\frac{1}{3}, \frac{1}{7}, -\frac{1}{15}, \frac{1}{31}, -\frac{1}{63}, y, z, \dots?
  1. A. 1129\frac{1}{129} and −1227-\frac{1}{227}
  2. B. 1127\frac{1}{127} and −1255-\frac{1}{255}
  3. C. 1129\frac{1}{129} and −1255-\frac{1}{255}
  4. D. 1127\frac{1}{127} and −1227-\frac{1}{227}
Worked solutionUnofficial

Answer: B

Answer B: 1127\frac{1}{127} and −1255-\frac{1}{255}. The stem is: What are the values of y and z in the sequence 1,−13,17,−115,131,−163,y,z,…1, -\frac{1}{3}, \frac{1}{7}, -\frac{1}{15}, \frac{1}{31}, -\frac{1}{63}, y, z, \dots? Letter B is the Abrari key for this Quantitative reasoning - Sequences. Denominators 2^n - 1: 1,3,7,15,31,63,127,255 with alternating signs; y=1/127, z=-1/255.

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

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2016 E.C. · natural · Q47 · Quantitative reasoning - Statistics (comparison)

Data: c, a, b, e, f, c, d where 0 < a < b < c < d < e < f. Compare Quantity P (mode of the data) and Quantity Q (median of the data). Which relationship holds?
  1. A. Quantity P is greater than Quantity Q.
  2. B. Quantity P is less than Quantity Q.
  3. C. Quantity P and Quantity Q are equal.
  4. D. The relationship cannot be determined.
Worked solutionUnofficial

Answer: C

Answer C: Quantity P and Quantity Q are equal.. The stem is: Data: c, a, b, e, f, c, d where 0 < a < b < c < d < e < f. Compare Quantity P (mode of the data) and Quantity Q (median of the data). Which relationship holds? Letter C is the Abrari key for this Quantitative reasoning - Statistics (comparison). Mode = c (appears twice). Ordered data: a,b,c,c,d,e,f (7 values); median = 4th = c. So P=Q=c, equal. Flagged: question stem oddly phrased ('which is NOT true').

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

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2016 E.C. · natural · Q48 · Quantitative reasoning - Triangle inequality (comparison)

Let x, y, z be the lengths of the sides of a triangle. Compare Quantity P (x + y + 3) and Quantity Q (z + 3). Which one is NOT true?
  1. A. Quantity P is greater than Quantity Q.
  2. B. Quantity P is less than Quantity Q.
  3. C. Quantity P and Quantity Q are equal.
  4. D. The relationship cannot be determined.
Worked solutionUnofficial

Answer: A

Answer A: Quantity P is greater than Quantity Q.. The stem is: Let x, y, z be the lengths of the sides of a triangle. Compare Quantity P (x + y + 3) and Quantity Q (z + 3). Which one is NOT true? Letter A is the Abrari key for this Quantitative reasoning - Triangle inequality (comparison). By triangle inequality x+y>z, so x+y+3>z+3, i.e., P>Q is TRUE. The question asks which is NOT true; A states P>Q which IS true, so this appears contradictory. Likely intended answer: P is greater (A) as the correct comparison. Question stem 'NOT true' conflicts; flagged.

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

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2016 E.C. · natural · Q49 · Quantitative reasoning - Permutations

How many different four-letter words which start with the vowel can be formed from the word MATH if the letters cannot be used more than once?
  1. A. 8
  2. B. 24
  3. C. 6
  4. D. 18
Worked solutionUnofficial

Answer: C

Answer C: 6. The stem is: How many different four-letter words which start with the vowel can be formed from the word MATH if the letters cannot be used more than once? Letter C is the Abrari key for this Quantitative reasoning - Permutations. MATH has one vowel (A); fix A first, arrange remaining 3 letters = 3! = 6.

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

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2016 E.C. · natural · Q50 · Quantitative reasoning - Probability

A bag contains 15 balls numbered 1 through 15. What is the probability of selecting a number that is odd or a multiple of 4?
  1. A. 15\frac{1}{5}
  2. B. 13\frac{1}{3}
  3. C. 815\frac{8}{15}
  4. D. 1115\frac{11}{15}
Worked solutionUnofficial

Answer: D

Answer D: 1115\frac{11}{15}. The stem is: A bag contains 15 balls numbered 1 through 15. What is the probability of selecting a number that is odd or a multiple of 4? Letter D is the Abrari key for this Quantitative reasoning - Probability. Odd {1,3,5,7,9,11,13,15}=8; multiples of 4 {4,8,12}=3; disjoint; 11/15.

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

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2016 E.C. · natural · Q51 · Quantitative reasoning - Geometry (polygons)

Which one of the following can NOT be the degree measure of each interior angle of a regular polygon?
  1. A. 120°
  2. B. 140°
  3. C. 135°
  4. D. 105°
Worked solutionUnofficial

Answer: D

Answer D: 105°. The stem is: Which one of the following can NOT be the degree measure of each interior angle of a regular polygon? Letter D is the Abrari key for this Quantitative reasoning - Geometry (polygons). Interior angle 180-360/n. 120->n=6, 140->n=9, 135->n=8, 105->n=4.8 (not integer). So 105 impossible.

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

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2016 E.C. · natural · Q52 · Quantitative reasoning - Geometry (triangles)

Let ΔABC be an isosceles triangle with ∠C=90°\angle C = 90°. If the length of side AC‾\overline{AC} is 4 cm, then what is the length of side AB in centimeters?
  1. A. 4
  2. B. 424\sqrt{2}
  3. C. 222\sqrt{2}
  4. D. 8
Worked solutionUnofficial

Answer: B

Answer B: 424\sqrt{2}. The stem is: Let ΔABC be an isosceles triangle with ∠C=90°\angle C = 90°. If the length of side AC‾\overline{AC} is 4 cm, then what is the length of side AB in centimeters? Letter B is the Abrari key for this Quantitative reasoning - Geometry (triangles). Isosceles right triangle with legs AC=BC=4; hypotenuse AB=4√2.

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

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2016 E.C. · natural · Q53 · Quantitative reasoning - Data interpretation

Using the school-income table (Tuition/Term/Donations/Grants/Misc for P,Q,R,S,T), which school has the lowest income from donations and term fees (combined)?
  1. A. Q
  2. B. S
  3. C. T
  4. D. R
Worked solutionUnofficial

Answer: A

Answer A: Q. The stem is: Using the school-income table (Tuition/Term/Donations/Grants/Misc for P,Q,R,S,T), which school has the lowest income from donations and term fees (combined)? Letter A is the Abrari key for this Quantitative reasoning - Data interpretation. Donations+Term: P=54+24=78, Q=21+12=33, R=60+45=105, S=51+24=75, T=60+30=90. Lowest is Q=33.

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

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2016 E.C. · natural · Q54 · Quantitative reasoning - Data interpretation

Which school has the lowest percentage of income from term fees out of its total income?
  1. A. R
  2. B. S
  3. C. Q
  4. D. P
Worked solutionUnofficial

Answer: C

Answer C: Q. The stem is: Which school has the lowest percentage of income from term fees out of its total income? Letter C is the Abrari key for this Quantitative reasoning - Data interpretation. Totals P=270,Q=150,R=450,S=210,T=280. Term%: P=8.9%, Q=8.0%, R=10%, S=11.4%, T=10.7%. Lowest is Q (8.0%) = option C.

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

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2016 E.C. · natural · Q55 · Quantitative reasoning - Data interpretation (average)

What is the average of the income from tuition fees of the five schools?
  1. A. 100
  2. B. 90
  3. C. 210
  4. D. 120
Worked solutionUnofficial

Answer: D

Answer D: 120. The stem is: What is the average of the income from tuition fees of the five schools? Letter D is the Abrari key for this Quantitative reasoning - Data interpretation (average). Tuition: 120+60+210+90+120=600; 600/5=120.

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

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2016 E.C. · natural · Q56 · Quantitative reasoning - Data interpretation

Which school has the highest percentage of income from grants out of its total income?
  1. A. Q
  2. B. P
  3. C. T
  4. D. S
Worked solutionUnofficial

Answer: A

Answer A: Q. The stem is: Which school has the highest percentage of income from grants out of its total income? Letter A is the Abrari key for this Quantitative reasoning - Data interpretation. Totals P=270,Q=150,R=450,S=210,T=280. Grants%: P=60/270=22.2%, Q=54/150=36%, R=120/450=26.7%, S=42/210=20%, T=55/280=19.6%. Highest is Q=36%.

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

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2016 E.C. · natural · Q57 · Quantitative reasoning - Data interpretation (ratio)

Which school has the lowest ratio of miscellaneous to term fees?
  1. A. Q
  2. B. S
  3. C. R
  4. D. T
Worked solutionUnofficial

Answer: B

Answer B: S. The stem is: Which school has the lowest ratio of miscellaneous to term fees? Letter B is the Abrari key for this Quantitative reasoning - Data interpretation (ratio). Misc/Term: P=12/24=0.5, Q=3/12=0.25, R=15/45=0.333, S=3/24=0.125, T=15/30=0.5. Lowest is S=0.125.

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

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2016 E.C. · social · Q39 · Sequences

What is a possible value of t in the sequence 100, 98, 94, 86, t, 38, ...?
  1. A. 78
  2. B. 70
  3. C. 82
  4. D. 54
Worked solutionUnofficial

Answer: B

Answer B: 70. The stem is: What is a possible value of t in the sequence 100, 98, 94, 86, t, 38, ...? Letter B is the Abrari key for this Sequences. Differences -2,-4,-8,-16,-32: 86-16=70, then 70-32=38. t=70.

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

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2016 E.C. · social · Q40 · Recursive sequences

Let {a_n} be a sequence with a1=3, a2=2 and for each n>=2, an+1=nan−1−ana_{n+1} = na_{n-1} - a_n. Which one of the following is equal to a6a_6?
  1. A. 14
  2. B. 56
  3. C. -14
  4. D. -4
Worked solutionUnofficial

Answer: C

Answer C: -14. The stem is: Let {a_n} be a sequence with a1=3, a2=2 and for each n>=2, an+1=nan−1−ana_{n+1} = na_{n-1} - a_n. Which one of the following is equal to a6a_6? Letter C is the Abrari key for this Recursive sequences. a3=2*3-2=4; a4=3*2-4=2; a5=4*4-2=14; a6=5*2-14=-4. Gives D(-4). Recompute: a_{n+1}=n*a_{n-1}-a_n. a3(n=2)=2*a1-a2=6-2=4; a4(n=3)=3*a2-a3=6-4=2; a5(n=4)=4*a3-a4=16-2=14; a6(n=5)=5*a4-a5=10-14=-4 => D.

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

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2016 E.C. · social · Q41 · Permutations

How many different arrangements of the digits of the number '234523' are there?
  1. A. 180
  2. B. 720
  3. C. 360
  4. D. 256
Worked solutionUnofficial

Answer: A

Answer A: 180. The stem is: How many different arrangements of the digits of the number '234523' are there? Letter A is the Abrari key for this Permutations. Digits 2,3,4,5,2,3: 6!/(2!2!)=720/4=180.

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

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2016 E.C. · social · Q43 · Probability

If two six faced fair dice are rolled, what is the probability of getting a pair of numbers whose sum is either 6 or 12?
  1. A. 536\frac{5}{36}
  2. B. 29\frac{2}{9}
  3. C. 16\frac{1}{6}
  4. D. 736\frac{7}{36}
Worked solutionUnofficial

Answer: C

Answer C: 16\frac{1}{6}. The stem is: If two six faced fair dice are rolled, what is the probability of getting a pair of numbers whose sum is either 6 or 12? Letter C is the Abrari key for this Probability. Sum 6: 5 ways; sum 12: 1 way; total 6/36=1/6.

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

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2016 E.C. · social · Q44 · Modular arithmetic

If today is Monday, then what is the day after 57 days starting from today?
  1. A. Wednesday
  2. B. Sunday
  3. C. Monday
  4. D. Tuesday
Worked solutionUnofficial

Answer: D

Answer D: Tuesday. The stem is: If today is Monday, then what is the day after 57 days starting from today? Letter D is the Abrari key for this Modular arithmetic. 57 mod 7 = 1; Monday+57 days = Tuesday (D). ('day after 57 days' interpretation).

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

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2016 E.C. · social · Q45 · Probability

A box contains 4 black, 5 white and 3 red balls. If a ball is drawn at random, what is the probability that the ball is neither black nor red?
  1. A. 512\frac{5}{12}
  2. B. 23\frac{2}{3}
  3. C. 712\frac{7}{12}
  4. D. 34\frac{3}{4}
Worked solutionUnofficial

Answer: A

Answer A: 512\frac{5}{12}. The stem is: A box contains 4 black, 5 white and 3 red balls. If a ball is drawn at random, what is the probability that the ball is neither black nor red? Letter A is the Abrari key for this Probability. White = 5/12.

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

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2016 E.C. · social · Q46 · Simple interest

A person deposited money at simple interest 12% per year. After three years, received total Birr 163,200. Which was the initial amount?
  1. A. 140,000
  2. B. 120,000
  3. C. 100,000
  4. D. 280,000
Worked solutionUnofficial

Answer: B

Answer B: 120,000. The stem is: A person deposited money at simple interest 12% per year. After three years, received total Birr 163,200. Which was the initial amount? Letter B is the Abrari key for this Simple interest. P(1+0.12*3)=1.36P=163200 => P=120,000.

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

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2016 E.C. · social · Q47 · Geometric series

What is the value of k, if ∑n=1∞5nk=14\sum_{n=1}^{\infty} 5^{nk} = \frac{1}{4}?
  1. A. 2
  2. B. -2
  3. C. 1
  4. D. -1
Worked solutionUnofficial

Answer: D

Answer D: -1. The stem is: What is the value of k, if ∑n=1∞5nk=14\sum_{n=1}^{\infty} 5^{nk} = \frac{1}{4}? Letter D is the Abrari key for this Geometric series. r=5^k, sum=r/(1-r)=1/4 => 4r=1-r => r=1/5=5^-1 => k=-1.

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

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2016 E.C. · social · Q48 · Ratio

A person wants to divide Birr 4,600 for his three children in the ratio 1/2, 1/3, 1/4. What are the shares from smallest to largest?
  1. A. 1,200, 1,400 and 2,000
  2. B. 800, 1,600 and 2,200
  3. C. 1,200, 1,600 and 1,800
  4. D. 1,000, 1,600 and 2,000
Worked solutionUnofficial

Answer: C

Answer C: 1,200, 1,600 and 1,800. The stem is: A person wants to divide Birr 4,600 for his three children in the ratio 1/2, 1/3, 1/4. What are the shares from smallest to largest? Letter C is the Abrari key for this Ratio. Ratio 1/2:1/3:1/4 = 6:4:3, total 13 parts, 4600/13=353.8 (non-integer). Options don't sum consistently; C sums to 4600 (1200+1600+1800). Answer uncertain due to non-integer division.

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

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2016 E.C. · social · Q49 · Quantitative comparison

Let x and y be real numbers such that x > y. Quantity A: x2+y2x^2 + y^2; Quantity B: 2xy.
  1. A. Quantity B is greater than quantity A.
  2. B. The relationship cannot be determined.
  3. C. Quantity A is greater than quantity B.
  4. D. The two quantities are equal.
Worked solutionUnofficial

Answer: C

Answer C: Quantity A is greater than quantity B.. The stem is: Let x and y be real numbers such that x > y. Quantity A: x2+y2x^2 + y^2; Quantity B: 2xy. Letter C is the Abrari key for this Quantitative comparison. x^2+y^2-2xy=(x-y)^2>0 since x>y.

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

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