Data Sufficiency

A certain plumber charges $\$92$ for each job completed in $4$ hours or less and $\$23$ per hour for each job completed in more than $4$ hours. If it took the plumber a total of $7$ hours to complete two separate jobs, what was the total amount charged by the plumber for the two jobs? (1) The plumber charged $\$92$ for one of the two jobs. (2) The plumber charged $\$138$ for one of the two jobs.

In the figure above, what is the area of region PQRST ? (1) PQ = RS (2) PT = QT

If $x$ and $y$ are positive numbers, is $$\frac{x+1}{y+1}>\frac{x}{y}?$$ (1) $x>1$ (2) $x<y$

In the figure above, PQRT is a rectangle. What is the length of segment PQ ? (1) The area of region PQRS is 39 and TS = 6. (2) The area of region PQRT is 30 and QR = 10.

If a school district paid a total of $\$35$ per desk for $x$ desks and a total of $\$30$ per table for $y$ tables, what was the total amount that the district paid for these desks and tables? (1) The total amount the district paid for the $y$ tables was $\$900$. (2) $x=90$, and the total amount the district paid for the $x$ desks was $3.5$ times the total amount the district paid for the $y$ tables.

In the figure above, the vertices of ΔOPQ and ΔQRS have coordinates as indicated. Do ΔOPQ and ΔQRS have equal areas? (1) b = 2a (2) d = 2c

Three children inherited a total of $X$ dollars. If the oldest child inherited $\$7,000$ more than the youngest child, and the youngest child inherited $\$9,000$ less than the middle child, what is the value of $X$? (1) The middle child inherited $\$27,000$. (2) The youngest child and the middle child together inherited a total of $\$45,000$.

In the figure above, what is the value of z? (1) x = y = 1 (2) w = 2

If a building has $6,000$ square meters of floor space, how many offices are in the building? (1) Exactly $\frac{1}{4}$ of the floor space is not used for offices. (2) There are exactly $20$ executive offices, and each of these occupies $3$ times as much floor space as the average for all of the remaining offices.

Is rw = 0? (1) −6 < r < 5 (2) 6 < w < 10 Source: [OG 2016]

For which type of investment, J or K, is the annual rate of return greater? (1) Type J returns $\$115$ per $\$1,000$ invested for any one-year period, and Type K returns $\$300$ per $\$2,500$ invested for any one-year period. (2) The annual rate of return for an investment of Type K is $12\%$.

Every object in a box is either a sphere or a cube, and every object in the box is either red or green. How many objects are in the box? (1) There are six cubes and 5 green objects in the box. (2) There are two red spheres in the box.

If Car X followed Car Y across a certain bridge that is $\frac{1}{2}$ mile long, how many seconds did it take Car X to travel across the bridge? (1) Car X drove onto the bridge exactly $3$ seconds after Car Y drove onto the bridge and drove off the bridge exactly $2$ seconds after Car Y drove off the bridge. (2) Car Y traveled across the bridge at a constant speed of $30$ miles per hour.

A noncompressible ball in the shape of a sphere is to be passed through a square opening in a board. What is the perimeter of the opening? (1) The radius of the ball is equal to 2 inches. (2) The square opening is the smallest square opening through which the ball will fit.

Will Candidate A win the most votes of any of the competing candidates in the upcoming election? (1) An opinion poll, Poll P, indicates that $60\%$ of respondents prefer Candidate A over other candidates competing in the upcoming election. (2) An election-forecasting opinion poll is a method to estimate election outcomes based on a sample that is representative of the population of all of those legally entitled to vote.

In the figure shown, is ℓ 1 ∥ ℓ 2 ? (1) r = s (2) t = u

The government of Nation X makes policy decisions intended to advance the public interest, such as policy decisions aiming to promote employment, economic flourishing, and environmental protection. A policy decision can involve a significant trade-off, i.e., it can entail foreseeably giving up part or all of one valued outcome in the pursuit of another valued outcome. Does a policy decision by Nation X to permit extensive clearcutting of forests provide a valued outcome at the expense of another valued outcome? (1) Extensive clearcutting of forests is permitted in Nation X because it provides immediate economic gains by enabling businesses such as farming and lumbering to flourish and provide employment. (2) Extensive clearcutting of forests is permitted in Nation X even though it reduces forests' absorption of carbon dioxide, and this indirectly contributes to global warming, resulting in adverse climate changes that are certain to be very costly for Nation X to manage.

Is n equal to zero? (1) The product of n and some nonzero number is 0. (2) The sum of n and 0 is 0.

Is Sarah's mathematics test score higher than the class average? (1) Sarah scored $90\%$ on her mathematics test, answering $45$ out of $50$ questions correctly. (2) Sarah's high percentage score indicates that she performed exceptionally well, with only a few questions answered incorrectly.

If r and s are positive integers, is r + s even? (1) r is even. (2) s is even.