question_id,source_question_id,form,pair,question,options_json,correct_answer,skill,subskill,difficulty,format,format_code,figure_path
P1,M1,P,1,"x is an integer.

Quantity A: \(3^{x+2}\)
Quantity B: \(9 \cdot 3^{x}\)","{""A"":""Quantity A is greater."",""B"":""Quantity B is greater."",""C"":""The two quantities are equal."",""D"":""The relationship cannot be determined from the information given.""}",C,Arithmetic,exponent rules,2,Quantitative Comparison,QC,
P2,M2,P,2,"(x + 7)^2 − (y − 2)^2 = 0
x + y = 3

Quantity A: \(x - y\)
Quantity B: \(0\)","{""A"":""Quantity A is greater."",""B"":""Quantity B is greater."",""C"":""The two quantities are equal."",""D"":""The relationship cannot be determined from the information given.""}",B,Algebra,difference of squares with a linear constraint,4,Quantitative Comparison,QC,
P3,M3,P,3,"x ≠ 1

Quantity A: \(\dfrac{x^2 - 3}{x - 1}\)
Quantity B: \(x + 3\)","{""A"":""Quantity A is greater."",""B"":""Quantity B is greater."",""C"":""The two quantities are equal."",""D"":""The relationship cannot be determined from the information given.""}",D,Algebra,rational expression vs a line,4,Quantitative Comparison,QC,
P4,M4,P,4,"Thirty cards are numbered with the integers from 1 to 30. If one card is selected at random, what is the probability that the integer on the card is a multiple of 3 or a multiple of 5 (or both)?","{""A"":""2/5"",""B"":""7/15"",""C"":""1/2"",""D"":""8/15"",""E"":""3/5""}",B,Data Analysis,probability with inclusion-exclusion,3,Multiple Choice (select one),MCQ,
P5,M5,P,5,"In the figure shown, EFGH is a square with sides of length 10, and RSTU is a square with sides of length 6. Point X lies on side FG and point Y lies on side ST. Triangle XGH has base GH and triangle YTU has base TU. If the ratio of the area of square EFGH to the area of square RSTU equals the ratio of the area of triangle XGH to the area of triangle YTU, what is the ratio of the length of XG to the length of YT? Give your answer as a fraction.",{},5/3,Geometry,area ratios of similar figures,3,Numeric Entry (type a value),NE,assessment_figures/quant/P5.svg
P6,M6,P,6,"The number x is 25 percent of the number y, and y is 40 percent of the number z. The number z is what percent greater than x?

(answer is a percent)",{},900,Arithmetic,"composed multiplicative percents, then reverse the base",4,Numeric Entry (type a value),NE,
P7,M7,P,7,"**REGIONAL POPULATION AND INTERNET USE, 2011**

TOTAL POPULATION 2011: 7,000 million — Asia 55%, Africa 16%, Europe 11%, Latin America/Caribbean 9%, North America 5%, Middle East 3%, Australia/Oceania 1%
TOTAL INTERNET USERS 2011: 2,100 million — Asia 38%, Europe 27%, North America 18%, Latin America/Caribbean 9%, Africa 4%, Middle East 3%, Australia/Oceania 1%

Which of the following is closest to the fraction of the 2011 population who were Internet users?","{""A"":""1/20"",""B"":""1/10"",""C"":""1/5"",""D"":""1/3"",""E"":""1/2""}",D,Data Analysis,fraction of a total (closest-to estimation),1,Multiple Choice (select one),MCQ,assessment_figures/quant/P7-P9.svg
P8,M8,P,8,"**REGIONAL POPULATION AND INTERNET USE, 2011**

TOTAL POPULATION 2011: 7,000 million — Asia 55%, Africa 16%, Europe 11%, Latin America/Caribbean 9%, North America 5%, Middle East 3%, Australia/Oceania 1%
TOTAL INTERNET USERS 2011: 2,100 million — Asia 38%, Europe 27%, North America 18%, Latin America/Caribbean 9%, Africa 4%, Middle East 3%, Australia/Oceania 1%

For which of the following regions was the 2011 number of Internet users greater than the 2011 population of the Middle East?

Indicate **all** such regions.","{""A"":""Africa"",""B"":""Asia"",""C"":""Europe"",""D"":""Latin America/Caribbean"",""E"":""North America""}","B,C,E",Data Analysis,compare a part of one total to a part of another,2,Multiple Select (select one or more),MS,assessment_figures/quant/P7-P9.svg
P9,M9,P,9,"**REGIONAL POPULATION AND INTERNET USE, 2011**

TOTAL POPULATION 2011: 7,000 million — Asia 55%, Africa 16%, Europe 11%, Latin America/Caribbean 9%, North America 5%, Middle East 3%, Australia/Oceania 1%
TOTAL INTERNET USERS 2011: 2,100 million — Asia 38%, Europe 27%, North America 18%, Latin America/Caribbean 9%, Africa 4%, Middle East 3%, Australia/Oceania 1%

The number of Internet users in Asia and Europe combined in 2011 was closest to what percent of the 2011 population?","{""A"":""9.8%"",""B"":""13.3%"",""C"":""19.5%"",""D"":""44.6%"",""E"":""65.0%""}",C,Data Analysis,combined share as a percent of a different total,2,Multiple Choice (select one),MCQ,assessment_figures/quant/P7-P9.svg
P10,M10,P,10,"At 12:00 noon a hose began draining water from a tank at a constant rate of 100 ounces per minute. At 2:00 that afternoon, when water still remained in the tank, a second hose began draining as well, raising the constant rate to 250 ounces per minute. The tank was empty before 5:00 that afternoon. Which of the following could have been the amount of water, in ounces, in the tank at 12:00 noon?

Indicate **all** such amounts.","{""A"":""9,000"",""B"":""30,000"",""C"":""45,000"",""D"":""56,000"",""E"":""60,000""}","B,C,D",Arithmetic,piecewise constant rates with a deadline,3,Multiple Select (select one or more),MS,
P11,M11,P,11,"In the xy-plane, the equation of Line 1 is y = x. Line 2 is parallel to Line 1 and contains an x-intercept of 3.

Quantity A: the shortest distance between Line 1 and Line 2.
Quantity B: 2","{""A"":""Quantity A is greater."",""B"":""Quantity B is greater."",""C"":""The two quantities are equal."",""D"":""The relationship cannot be determined from the information given.""}",A,Geometry,shortest distance between parallel lines,5,Quantitative Comparison,QC,
P12,M12,P,12,A square is inscribed in a circle. The percent of the circle’s area that lies **outside** the square but **inside** the circle is closest to which of the following?,"{""A"":""30%"",""B"":""33%"",""C"":""36%"",""D"":""39%"",""E"":""40%""}",C,Geometry,area ratio of a circle and its inscribed polygon,5,Multiple Choice (select one),MCQ,
P13,M13,P,13,"x is a number greater than 0.

Quantity A: \(\dfrac{x}{x}\)
Quantity B: \(\dfrac{x}{3}\)","{""A"":""Quantity A is greater."",""B"":""Quantity B is greater."",""C"":""The two quantities are equal."",""D"":""The relationship cannot be determined from the information given.""}",D,Algebra,an identity vs a varying expression,2,Quantitative Comparison,QC,
P14,M14,P,14,"Quantity A:  the units digit of 7^83 + 3^54
Quantity B:  the units digit of 2^100 + 8^77","{""A"":""Quantity A is greater."",""B"":""Quantity B is greater."",""C"":""The two quantities are equal."",""D"":""The relationship cannot be determined from the information given.""}",B,Arithmetic,units digit of a sum of large powers (cyclicity),5,Quantitative Comparison,QC,
P15,M15,P,15,"x and y are nonzero numbers.

Quantity A: \(|x| + |y|\)
Quantity B: \(|x + y|\)","{""A"":""Quantity A is greater."",""B"":""Quantity B is greater."",""C"":""The two quantities are equal."",""D"":""The relationship cannot be determined from the information given.""}",D,Algebra,triangle inequality for absolute value,5,Quantitative Comparison,QC,
P16,M16,P,16,"For how many consecutive zeros does the integer equal to the product of all the integers from 1 through 60, inclusive, end? (That is, if N = 1 · 2 · 3 · … · 60, how many trailing zeros does N have?)",{},14,Arithmetic,trailing zeros of a large factorial,5,Numeric Entry (type a value),NE,
P17,M17,P,17,"A certain salesperson earns $3 for each hour worked plus a 10 percent commission on total sales. Last month the salesperson worked 250 hours and had total sales of $42,500. What percent of the amount earned last month was commission?","{""A"":""80.0%"",""B"":""82.0%"",""C"":""85.0%"",""D"":""88.0%"",""E"":""90.0%""}",C,Arithmetic,percent of a total made up of a part,1,Multiple Choice (select one),MCQ,
P18,M18,P,18,"The function f is defined for all real numbers x and satisfies

f(x) + 2 · f(1 − x) = 3x

for every real number x. What is the value of f(2)?",{},-4,Algebra,solve a functional equation by substituting the reflected argument,5,Numeric Entry (type a value),NE,
P19,M19,P,19,Which of the following lists has the greatest standard deviation?,"{""A"":""12, 24, 36, 48, 60"",""B"":""12, 36, 36, 36, 60"",""C"":""12, 30, 36, 42, 60"",""D"":""12, 12, 36, 60, 60"",""E"":""24, 24, 36, 48, 48""}",D,Data Analysis,comparing spread / standard deviation,3,Multiple Choice (select one),MCQ,
P20,M20,P,20,"The numbers x and y are positive integers, and 1/x + 1/y = 1/6. Which of the following could be the value of x + y?

Indicate **all** such values.","{""A"":""20"",""B"":""24"",""C"":""26"",""D"":""27"",""E"":""49""}","B,D,E",Algebra,reciprocal Diophantine equation; which sum is attainable,5,Multiple Select (select one or more),MS,
P21,M21,P,21,"The numbers a and b are positive real numbers with a + b = 10. Which of the following could be the value of a² + b²?

Indicate **all** such values.","{""A"":""48"",""B"":""50"",""C"":""68"",""D"":""99"",""E"":""100""}","B,C,D",Algebra,a symmetric constraint bounds an asymmetric expression (AM–GM),5,Multiple Select (select one or more),MS,
P22,M22,P,22,"Lines p and q intersect to form four 90-degree angles. The points (−6, 1) and (2, 17) are on line p. The points (−10, 3) and (−2, t) are on line q. What is the value of t ?","{""A"":""−13"",""B"":""−9"",""C"":""−1"",""D"":""7"",""E"":""19""}",C,Geometry,coordinate geometry (perpendicular lines),4,Multiple Choice (select one),MCQ,
P23,M23,P,23,"A history department gave a placement exam to its 80 students. The 60 first-year students scored a mean of fewer than 70 points, and the 20 transfer students scored a mean of exactly 90 points.

Quantity A: The mean placement-exam score of all 80 students
Quantity B: 75","{""A"":""Quantity A is greater."",""B"":""Quantity B is greater."",""C"":""The two quantities are equal."",""D"":""The relationship cannot be determined from the information given.""}",B,Data Analysis,weighted average,4,Quantitative Comparison,QC,
P24,M24,P,24,"A coach must select a team of 6 swimmers from a squad of 11 to attend a championship meet. If Marta must be on the team, how many different teams are possible?","{""A"":""210"",""B"":""252"",""C"":""330"",""D"":""462"",""E"":""924""}",B,Data Analysis,combinations,4,Multiple Choice (select one),MCQ,
P25,M25,P,25,"The integer r is even and the integer s is odd. Which of the following expressions must be an even integer?

Select **all** the expressions that must be even integers.","{""A"":""r² + s² + 1"",""B"":""3r² + 5s + 9"",""C"":""6r + s² + 2"",""D"":""rs + 7s + r""}","A,B",Arithmetic,parity (odd/even structure),4,Multiple Select (select one or more),MS,
P26,M26,P,26,"For a certain circle, the area of the circle, in square centimeters, is more than 35π greater than the circumference of the circle, in centimeters. Which of the following could be the radius of the circle, in centimeters?

Indicate **all** such values.","{""A"":""4"",""B"":""6"",""C"":""8"",""D"":""10"",""E"":""12""}","C,D,E",Geometry,circle area and circumference bounds,4,Multiple Select (select one or more),MS,
P27,M27,P,27,"g is the tens digit of 73,436².
h is the tens digit of 81,265².
What is the value of g^(1/h) ?","{""A"":""1"",""B"":""2"",""C"":""3"",""D"":""4"",""E"":""9""}",C,Arithmetic,digits of powers,5,Multiple Choice (select one),MCQ,
Q1,N1,Q,1,"Quantity A:  8^10
Quantity B:  4^15","{""A"":""Quantity A is greater."",""B"":""Quantity B is greater."",""C"":""The two quantities are equal."",""D"":""The relationship cannot be determined from the information given.""}",C,Arithmetic,exponent rules,2,Quantitative Comparison,QC,
Q2,N2,Q,2,"p^2 − q^2 = 0
p − q = 6

Quantity A: \(q\)
Quantity B: \(-2\)","{""A"":""Quantity A is greater."",""B"":""Quantity B is greater."",""C"":""The two quantities are equal."",""D"":""The relationship cannot be determined from the information given.""}",B,Algebra,difference of squares with a linear constraint,4,Quantitative Comparison,QC,
Q3,N3,Q,3,"x ≠ −1

Quantity A: \(\dfrac{x^2 - 4}{x + 1}\)
Quantity B: \(x - 1\)","{""A"":""Quantity A is greater."",""B"":""Quantity B is greater."",""C"":""The two quantities are equal."",""D"":""The relationship cannot be determined from the information given.""}",D,Algebra,rational expression vs a line,4,Quantitative Comparison,QC,
Q4,N4,Q,4,"Of the 40 employees at an office, 18 are enrolled in the dental plan, 25 are enrolled in the vision plan, and 9 are enrolled in both plans. If one of the 40 employees is selected at random, what is the probability that the employee is enrolled in neither plan?","{""A"":""3/20"",""B"":""9/40"",""C"":""3/8"",""D"":""17/40"",""E"":""17/20""}",A,Data Analysis,probability with inclusion-exclusion,3,Multiple Choice (select one),MCQ,
Q5,N5,Q,5,"In the figure shown, circle C has radius 9 and circle D has radius 6. A sector of circle C with central angle x° has the same area as a sector of circle D with central angle y°. What is the value of x/y? Give your answer as a fraction.",{},4/9,Geometry,area ratios of similar figures,3,Numeric Entry (type a value),NE,assessment_figures/quant/Q5.svg
Q6,N6,Q,6,"A bottle holds 20 percent as much as a jug, and a jug holds 40 percent as much as a barrel. The barrel holds what percent more than the bottle?

(answer is a percent)",{},1150,Arithmetic,"composed multiplicative percents, then reverse the base",4,Numeric Entry (type a value),NE,
Q7,N7,Q,7,"**A MUSIC-STREAMING SERVICE: SUBSCRIBERS AND CONCERT-TICKET SALES BY GENRE**

The service classifies each of its 8,000 thousand subscribers by a single favorite genre, and separately reports the 2,000 thousand concert tickets it sold, by genre. Each column below is a percent distribution that totals 100%.

| Genre | Percent of subscribers (total 8,000 thousand) | Percent of concert tickets (total 2,000 thousand) |
|---|---|---|
| Pop | 34% | 30% |
| Rock | 24% | 28% |
| Hip-hop | 16% | 19% |
| Country | 12% | 12% |
| Jazz | 8% | 4% |
| Classical | 6% | 7% |

Rock was the favorite genre of approximately what fraction of the service's subscribers?","{""A"":""1/8"",""B"":""1/6"",""C"":""1/4"",""D"":""3/8"",""E"":""5/8""}",C,Data Analysis,fraction of a total (closest-to estimation),1,Multiple Choice (select one),MCQ,assessment_figures/quant/Q7-Q9.svg
Q8,N8,Q,8,"**A MUSIC-STREAMING SERVICE: SUBSCRIBERS AND CONCERT-TICKET SALES BY GENRE**

The service classifies each of its 8,000 thousand subscribers by a single favorite genre, and separately reports the 2,000 thousand concert tickets it sold, by genre. Each column below is a percent distribution that totals 100%.

| Genre | Percent of subscribers (total 8,000 thousand) | Percent of concert tickets (total 2,000 thousand) |
|---|---|---|
| Pop | 34% | 30% |
| Rock | 24% | 28% |
| Hip-hop | 16% | 19% |
| Country | 12% | 12% |
| Jazz | 8% | 4% |
| Classical | 6% | 7% |

For which of the following genres was the number of subscribers more than 4 times the number of concert tickets the service sold for that genre?

Indicate **all** such genres.","{""A"":""Pop"",""B"":""Rock"",""C"":""Country"",""D"":""Jazz"",""E"":""Classical""}","A,D",Data Analysis,compare a part of one total to a part of another,2,Multiple Select (select one or more),MS,assessment_figures/quant/Q7-Q9.svg
Q9,N9,Q,9,"**A MUSIC-STREAMING SERVICE: SUBSCRIBERS AND CONCERT-TICKET SALES BY GENRE**

The service classifies each of its 8,000 thousand subscribers by a single favorite genre, and separately reports the 2,000 thousand concert tickets it sold, by genre. Each column below is a percent distribution that totals 100%.

| Genre | Percent of subscribers (total 8,000 thousand) | Percent of concert tickets (total 2,000 thousand) |
|---|---|---|
| Pop | 34% | 30% |
| Rock | 24% | 28% |
| Hip-hop | 16% | 19% |
| Country | 12% | 12% |
| Jazz | 8% | 4% |
| Classical | 6% | 7% |

The number of concert tickets the service sold for Pop and Rock combined was closest to what percent of the total number of subscribers?","{""A"":""7.2%"",""B"":""14.5%"",""C"":""29.0%"",""D"":""58.0%"",""E"":""72.5%""}",B,Data Analysis,combined share as a percent of a different total,2,Multiple Choice (select one),MCQ,assessment_figures/quant/Q7-Q9.svg
Q10,N10,Q,10,"Peter and Sheila decide to work together to gather 400 logs for a bonfire. Peter starts gathering logs at a constant rate of 20 logs per hour at 10:00 a.m. and Sheila begins gathering 30 logs per hour at 1:00 p.m. If Peter and Sheila decide to stop for dinner some time between 5:00 p.m. and 7:00 p.m., how many more hours might they need to gather logs together at their constant gathering rates after finishing dinner before having their bonfire?

Indicate **all** such amounts.","{""A"":""0"",""B"":""1"",""C"":""2"",""D"":""3"",""E"":""4"",""F"":""5""}","B,C",Arithmetic,piecewise constant rates with a deadline,3,Multiple Select (select one or more),MS,
Q11,N11,Q,11,"In the xy-plane, the equation of Line 1 is y = -x. Line 2 is a parallel line that contains a y-intercept of 4.

Quantity A: \(2\sqrt{3}\)
Quantity B: the shortest distance between Line 1 and Line 2.","{""A"":""Quantity A is greater."",""B"":""Quantity B is greater."",""C"":""The two quantities are equal."",""D"":""The relationship cannot be determined from the information given.""}",A,Geometry,shortest distance between parallel lines,5,Quantitative Comparison,QC,
Q12,N12,Q,12,An equilateral triangle is inscribed in a circle. The percent of the circle’s area that lies **outside** the triangle but **inside** the circle is closest to which of the following?,"{""A"":""55%"",""B"":""60%"",""C"":""65%"",""D"":""70%"",""E"":""75%""}",B,Geometry,area ratio of a circle and its inscribed polygon,5,Multiple Choice (select one),MCQ,
Q13,N13,Q,13,"m is a number greater than 0.

Quantity A: \(\dfrac{\sqrt{m^2}}{m}\)
Quantity B: \(m^2\)","{""A"":""Quantity A is greater."",""B"":""Quantity B is greater."",""C"":""The two quantities are equal."",""D"":""The relationship cannot be determined from the information given.""}",D,Algebra,an identity vs a varying expression,2,Quantitative Comparison,QC,
Q14,N14,Q,14,"Quantity A:  the units digit of 9^64 + 4^53 + 5^30
Quantity B:  the units digit of 3^47 + 7^38","{""A"":""Quantity A is greater."",""B"":""Quantity B is greater."",""C"":""The two quantities are equal."",""D"":""The relationship cannot be determined from the information given.""}",B,Arithmetic,units digit of a sum of large powers (cyclicity),5,Quantitative Comparison,QC,
Q15,N15,Q,15,"x and y are nonzero numbers.

Quantity A: \(|x| + |y|\)
Quantity B: \(|x - y|\)","{""A"":""Quantity A is greater."",""B"":""Quantity B is greater."",""C"":""The two quantities are equal."",""D"":""The relationship cannot be determined from the information given.""}",D,Algebra,triangle inequality for absolute value,5,Quantitative Comparison,QC,
Q16,N16,Q,16,Let M = 90! (the product of the integers from 1 to 90). What is the largest integer k such that 10^k divides M evenly?,{},21,Arithmetic,trailing zeros of a large factorial,5,Numeric Entry (type a value),NE,
Q17,N17,Q,17,"An electrician charges a $60 service-call fee plus $45 per hour of work. For a job that took 4 hours, the hourly charges were what percent of the total charge for the job?","{""A"":""25.0%"",""B"":""64.0%"",""C"":""75.0%"",""D"":""78.0%"",""E"":""84.0%""}",C,Arithmetic,percent of a total made up of a part,1,Multiple Choice (select one),MCQ,
Q18,N18,Q,18,"The function g is defined for all real numbers x and satisfies

3 · g(x) + g(3 − x) = 4x + 2

for every real number x. What is the value of g(6)?",{},11,Algebra,solve a functional equation by substituting the reflected argument,5,Numeric Entry (type a value),NE,
Q19,N19,Q,19,"If set T is comprised of the first five positive multiples of 6, which of the following sets of integers would have a standard deviation greater than that of set T?","{""A"":""−20, −10, 0, 10, 20"",""B"":""2, 4, 6, 8, 10"",""C"":""25, 30, 35, 40, 45"",""D"":""106, 107, 108, 109, 110"",""E"":""1,006, 1,012, 1,018, 1,024, 1,030""}",A,Data Analysis,comparing spread / standard deviation,3,Multiple Choice (select one),MCQ,
Q20,N20,Q,20,"If m and n are integers such that m + n = (1/4)(mn) and 0 < m < n, which of the following CANNOT be the value of n − m?

Indicate **all** such values.","{""A"":""0"",""B"":""2"",""C"":""6"",""D"":""8"",""E"":""15""}","A,B,D",Algebra,reciprocal Diophantine equation; which sum is attainable,5,Multiple Select (select one or more),MS,
Q21,N21,Q,21,"The numbers a and b are positive real numbers with a + b = 12. Which of the following could be the value of the product ab?

Indicate **all** such values.","{""A"":""16"",""B"":""27"",""C"":""32"",""D"":""36"",""E"":""42""}","A,B,C,D",Algebra,a symmetric constraint bounds an asymmetric expression (AM–GM),5,Multiple Select (select one or more),MS,
Q22,N22,Q,22,"In the xy-plane, line j passes through the points (1, 2) and (9, 6). Line k is perpendicular to line j and passes through the point (6, 8). What is the y-coordinate of the point where line k crosses the y-axis?","{""A"":""−4"",""B"":""5"",""C"":""11"",""D"":""20"",""E"":""26""}",D,Geometry,coordinate geometry (perpendicular lines),4,Multiple Choice (select one),MCQ,
Q23,N23,Q,23,"On a single day a shop recorded 80 purchases. The 60 purchases made at the in-store counter averaged more than $50 each, while the 20 purchases made through the shop's mobile app averaged exactly $30 each.

Quantity A: The mean value of all 80 purchases that day
Quantity B: $45","{""A"":""Quantity A is greater."",""B"":""Quantity B is greater."",""C"":""The two quantities are equal."",""D"":""The relationship cannot be determined from the information given.""}",A,Data Analysis,weighted average,4,Quantitative Comparison,QC,
Q24,N24,Q,24,"A 4-person committee is to be formed from a department of 9 employees. If the department's 2 senior members must both be on the committee, how many different committees are possible?","{""A"":""21"",""B"":""35"",""C"":""42"",""D"":""84"",""E"":""126""}",A,Data Analysis,combinations,4,Multiple Choice (select one),MCQ,
Q25,N25,Q,25,"The integer m is odd and the integer n is even. Which of the following expressions must be an odd integer?

Select **all** the expressions that must be odd integers.","{""A"":""2mn + n + 5"",""B"":""(m + n)²"",""C"":""mn + 3n"",""D"":""m²n + m"",""E"":""4m + n² + 6""}","A,B,D",Arithmetic,parity (odd/even structure),4,Multiple Select (select one or more),MS,
Q26,N26,Q,26,"For a certain circle, the area of the circle, in square inches, is less than the circumference of the circle, in inches, increased by 24π. Which of the following could be the radius of the circle, in inches?

Indicate **all** such values.","{""A"":""1"",""B"":""3"",""C"":""5"",""D"":""9"",""E"":""11""}","A,B,C",Geometry,circle area and circumference bounds,4,Multiple Select (select one or more),MS,
Q27,N27,Q,27,"u is the units digit of 2^26.
v is the units digit of 12^9.
What is the value of u^(1/v) ?","{""A"":""2"",""B"":""4"",""C"":""6"",""D"":""8"",""E"":""9""}",A,Arithmetic,digits of powers,5,Multiple Choice (select one),MCQ,