A store raises the price of a jacket by 20%. A month later, it cuts the new price by 25%. The final price is what percent of the original price?
90% Multiply the two changes: 1.20 × 0.75 = 0.90. So the final price is 90% of the original. The 25% cut is taken from a bigger number than the 20% rise was, so the price ends up lower.
If n is a positive integer and n² is divisible by 72, what is the smallest possible value of n?
12 72 = 2³ × 3². For n² to contain 2³, n needs at least 2², because squaring doubles each exponent and 2¹ would only give 2². For n² to contain 3², n needs at least 3. So the smallest n is 2² × 3 = 12, and 12² = 144 = 2 × 72.
The average (arithmetic mean) of five numbers is 18. When one of the numbers is removed, the average of the remaining four numbers is 16. What number was removed?
26 Five numbers with an average of 18 add up to 5 × 18 = 90. Four numbers with an average of 16 add up to 4 × 16 = 64. The removed number is the difference: 90 − 64 = 26.
At a training program, the ratio of men to women is 3 to 5. After 12 more men join and no one leaves, the numbers of men and women are equal. How many people were in the program before the 12 men joined?
48 Write the groups as 3k men and 5k women. After 12 men join, 3k + 12 = 5k, so 2k = 12 and k = 6. That’s 18 men and 30 women, or 48 people before the new men arrived.
If 3x − 2y = 12 and x + y = 9, what is the value of x − y?
3 From x + y = 9, y = 9 − x. Substitute: 3x − 2(9 − x) = 12, so 5x − 18 = 12 and x = 6. Then y = 3, and x − y = 3.
Machine A can label a batch of bottles in 4 hours. Machine B can label the same batch in 12 hours. Working together at their own steady rates, how many hours will the two machines take to label one batch?
3 Add the rates, not the times. A does 1/4 of a batch per hour and B does 1/12. Together that’s 3/12 + 1/12 = 4/12 = 1/3 of a batch per hour, so one batch takes 3 hours.
A driver travels 120 miles to a client’s office at an average speed of 40 miles per hour and returns along the same route at an average speed of 60 miles per hour. What is the driver’s average speed, in miles per hour, for the whole round trip?
48 Average speed is total distance divided by total time. The trip out takes 120 ÷ 40 = 3 hours and the trip back takes 120 ÷ 60 = 2 hours. That’s 240 miles in 5 hours, or 48 miles per hour.
Last year the city installed brighter streetlights throughout the Elm district. In the 12 months that followed, reported nighttime burglaries in the district fell by 30%. City officials concluded that the new streetlights caused the drop.
Which of the following, if true, most strengthens the officials’ conclusion?
In nearby districts that did not get new streetlights, reported nighttime burglaries stayed about the same over the same 12 months. The officials say the lights caused the drop. If similar districts without new lights saw no change, that makes it less likely the drop came from something affecting the whole city, like a wider fall in crime. It’s a comparison group that points to the lights.
Bakery owner: Our sourdough loaves sell out by noon every day. So if we double the number of sourdough loaves we bake each morning, we’ll double our daily sourdough sales.
The owner’s argument depends on which of the following assumptions?
Enough customers would buy the extra sourdough loaves if they were available. Selling out shows demand is at least as high as the current supply. It doesn’t show demand is twice as high. For sales to double, there must be enough buyers for the extra loaves, so the argument needs this assumption.
Six months ago, Halden Software moved its staff to a four-day work week. Since then, output per employee has risen 10%. The company says the shorter week made its employees more productive.
Which of the following, if true, most seriously weakens the company’s claim?
In the same six months, Halden installed new tools that cut the time needed for its most common tasks by a third. The claim is that the shorter week caused the 10% rise. New tools that make the main tasks much faster are another strong explanation for the same rise. That makes it harder to give the credit to the four-day week.
At Larkin Corp, every employee who works in sales has completed the negotiation course. Some employees who have completed the negotiation course work in finance. No employee works in both sales and finance.
If the statements above are true, which of the following must also be true?
Some employees who have completed the negotiation course do not work in sales. Some course graduates work in finance. Nobody in finance works in sales. So those finance graduates are course graduates who don’t work in sales, which is exactly what this option says.
In the 1940s, the biologist Karl von Frisch argued that honeybees tell their nestmates where to find food by performing a “waggle dance.” A forager returning to the hive runs in a straight line while shaking her body, then circles back and repeats the run. The angle of the run, measured from straight up on the vertical comb, matches the angle between the food source and the sun. The length of the waggling part signals how far away the food is. Many scientists at first doubted that insects could pass on such abstract information, and some argued that bees found food mainly by smell. Later experiments, including some that used robotic bees, supported von Frisch’s view, although smell still plays a part. He shared the Nobel Prize in Physiology or Medicine in 1973.
The passage is mainly concerned with
describing a theory of how bees share the location of food and how it gained support Most of the passage explains how the waggle dance works. The rest describes the early doubts and the later evidence that backed von Frisch. Together, that’s a theory and how it came to be accepted.
In the 1940s, the biologist Karl von Frisch argued that honeybees tell their nestmates where to find food by performing a “waggle dance.” A forager returning to the hive runs in a straight line while shaking her body, then circles back and repeats the run. The angle of the run, measured from straight up on the vertical comb, matches the angle between the food source and the sun. The length of the waggling part signals how far away the food is. Many scientists at first doubted that insects could pass on such abstract information, and some argued that bees found food mainly by smell. Later experiments, including some that used robotic bees, supported von Frisch’s view, although smell still plays a part. He shared the Nobel Prize in Physiology or Medicine in 1973.
According to the passage, the angle of a forager’s straight run indicates
the direction of the food source in relation to the sun The passage says the angle of the run “matches the angle between the food source and the sun.” That’s direction. Distance is shown by the length of the waggle, a different part of the dance.
When Corvane, a regional grocery chain, launched a loyalty card, its managers expected the main benefit to be more repeat visits. Repeat visits did rise slightly, but the larger payoff came from data. By tracking which products card holders bought together, Corvane rearranged its stores and cut its stock of slow-selling items, which reduced food waste by nearly a fifth. Some analysts warn that gains like these may not last. Once rival chains offer similar cards, they say, shoppers may carry several cards and feel loyal to none.
Which of the following can most reasonably be inferred from the passage?
The card’s main value to Corvane turned out to be different from what its managers had expected. Managers expected repeat visits to be the main benefit. The passage says repeat visits rose only slightly and that “the larger payoff came from data.” So the main value was different from what they expected.
What is the value of x?
(1) 2x + 3y = 12
(2) y = 2
Choose the answer that describes whether the statements give enough information.
Both statements together are enough, but neither one alone is. Statement (1) is one equation with two unknowns, so x could be many values. Statement (2) says nothing about x. Together, 2x + 3(2) = 12 gives 2x = 6, so x = 3. Both are needed.
If n is an integer, is n even?
(1) n² is even.
(2) n + 3 is odd.
Choose the answer that describes whether the statements give enough information.
Each statement alone is enough. If n² is even, n must be even, because an odd number times an odd number is always odd. If n + 3 is odd, n must be even, because odd minus odd is even. Each statement answers the question by itself.
A store sold 120 shirts in March. Every shirt was either blue or white. How many blue shirts did the store sell in March?
(1) The store sold 30 more white shirts than blue shirts in March.
(2) The store sold more white shirts than blue shirts in March.
Choose the answer that describes whether the statements give enough information.
Statement (1) alone is enough, but statement (2) alone is not. With (1), blue = b and white = b + 30, so 2b + 30 = 120 and b = 45. That’s one answer, so (1) is enough. Statement (2) only says white beat blue, which fits 45 blue, 50 blue, 10 blue and many others.
The table shows a company’s sales, in thousands of units, by region.
Region | 2024 | 2025
North | 200 | 230
South | 150 | 180
East | 320 | 368
West | 80 | 100
Central | 250 | 275
Which region had the greatest percent increase in sales from 2024 to 2025?
West Divide each increase by the 2024 figure. North 30/200 = 15%, South 30/150 = 20%, East 48/320 = 15%, West 20/80 = 25%, Central 25/250 = 10%. West has the greatest percent increase.
Read the two sources, then answer the question.
Source 1, email from the team manager: “Our budget for the team planning day is $6,000, and we can’t go over it. Everyone who comes will need lunch and a travel allowance.”
Source 2, venue quote: “Room hire: $1,800 flat fee for the day. Lunch: $55 per person. Travel allowance (paid by your company): $90 per person, as agreed.”
What is the greatest number of people who can attend without going over the budget?
28 After the $1,800 room fee, $4,200 is left. Each person costs $55 + $90 = $145. 4,200 ÷ 145 ≈ 28.97, so 28 people fit: 28 × $145 = $4,060, for a total of $5,860. A 29th person would bring the total to $6,005.
A bar chart shows a company’s monthly website visits, in thousands: January 40, February 45, March 54, April 64.
Between which two consecutive months was the percent increase in visits greatest?
February to March January to February: 5/40 = 12.5%. February to March: 9/45 = 20%. March to April: 10/54 ≈ 18.5%. The greatest percent increase is February to March, even though March to April added more visits.
United States · Admission test