ALES — Academic Staff and Graduate Education Entrance Examination (Turkey)

If x and y are positive integers such that 3x + 5y = 47, what is the maximum possible value of x + y?

• A11
• B13
• C15
• D17

A train traveling at a constant speed of 72 km/h crosses a 400-meter long tunnel in 30 seconds. What is the length of the train in meters?

• A150 meters
• B200 meters
• C250 meters
• D300 meters

In a right triangle ABC, angle B is 90 degrees, AB = 6 cm, and BC = 8 cm. A semicircle is drawn with diameter AC. What is the area of the semicircle in square centimeters?

• A12.5π
• B25π
• C50π
• D100π

A merchant buys an item for ₺400 and marks up the price by 40%. During a promotional sale, the merchant offers a 25% discount on the marked price. What is the final selling price of the item?

• A₺420
• B₺440
• C₺460
• D₺480

Worker A can complete a project in 12 days, while Worker B can complete the same project in 18 days. If Worker A works alone for 4 days and then Worker B joins A to finish the remaining work together, how many total days does it take to complete the project?

• A7.2 days
• B8.8 days
• C9.6 days
• D10.4 days

What is the sum of all integer values of x that satisfy the inequality |2x - 7| <= 9?

• A28
• B31
• C35
• D40

The arithmetic mean of 5 distinct positive integers is 24. If the largest integer is 50, what is the smallest possible value for the second largest integer?

• A16
• B18
• C19
• D21

A bag contains 4 red balls, 5 blue balls, and 3 green balls. If two balls are drawn at random without replacement, what is the probability that both drawn balls are of the same color?

• A19/66
• B23/66
• C29/66
• D31/66

How many 3-digit positive integers can be formed using the digits {1, 2, 3, 4, 5, 6} without repetition such that the resulting number is divisible by 5?

• A20
• B25
• C30
• D36

If 2^(x+1) + 2^(x+3) = 160, what is the value of x?

• A3
• B4
• C5
• D6

The ratio of a father's age to his son's age is currently 7:2. In 15 years, the ratio of their ages will become 2:1. What is the current age of the father?

• A35
• B42
• C49
• D56

A solution contains 30% alcohol by volume. How many liters of pure water must be added to 40 liters of this solution to reduce the alcohol concentration to 20%?

• A10 liters
• B15 liters
• C20 liters
• D25 liters

What is the area of a circle inscribed in an equilateral triangle with a side length of 6 cm?

• A3π cm²
• B6π cm²
• C9π cm²
• D12π cm²

The polynomial P(x) = x^3 - 4x^2 + kx - 6 leaves a remainder of 4 when divided by (x - 2). What is the value of k?

• A5
• B7
• C9
• D11

In a group of 50 students, 30 study Mathematics, 25 study Physics, and 10 study both subjects. How many students in the group study neither Mathematics nor Physics?

• A5
• B7
• C10
• D12

Five people (A, B, C, D, E) stand in a straight line. If A and B must always stand next to each other, in how many different ways can the 5 people be arranged?

• A24
• B48
• C72
• D96

If log_2(x) + log_2(x - 3) = 2, what is the real value of x?

• A1
• B4
• C5
• D7

A rectangle has a perimeter of 36 cm. What is the maximum possible area of this rectangle in square centimeters?

• A64
• B72
• C81
• D90

Read the paragraph: 'The first public libraries were not built to spread reading. They were built because private collectors died and their heirs wanted the tax relief that a donation brought. Only decades later, once the buildings existed and stood empty for most of the week, did municipalities begin inventing reasons to fill them.' What does the paragraph imply about the purpose of early public libraries?

• ATheir eventual educational role followed from their existence rather than motivating it.
• BHeirs of private collectors were personally committed to public literacy.
• CMunicipalities opposed the donation of private collections on financial grounds.
• DEarly libraries were used intensively from the day they opened.

The average score of 12 students in a test was 75. When 3 new students joined, the average score of all 15 students increased to 78. What was the average score of the 3 new students?

• A84
• B87
• C90
• D93

What is the unit digit of 7^2026?

• A1
• B3
• C7
• D9

A clock shows 03:15. What is the acute angle between the hour hand and the minute hand?

• A0°
• B7.5°
• C12.5°
• D15°

In how many ways can a committee of 4 members be selected from 6 men and 5 women such that the committee contains at least 2 women?

• A185
• B205
• C215
• D245

If (a + b)^2 = 100 and a*b = 21, what is the value of a^2 + b^2?

• A58
• B62
• C79
• D84

A car travels from City X to City Y at 60 km/h and returns from City Y to City X at 90 km/h along the same route. What is the average speed of the car for the entire round trip?

• A72 km/h
• B75 km/h
• C78 km/h
• D80 km/h

Which sentence disrupts the flow of the paragraph? (I) Salvage archaeology exists to record sites that construction is about to destroy. (II) Because the developer, not a research council, pays for the dig, the budget is set by the building schedule rather than by the questions the site raises. (III) Excavators must therefore decide in advance which layers they will not have time to record. (IV) Museum galleries increasingly use low-lux lighting to slow pigment fading on displayed textiles. (V) The published record of such a site is consequently shaped as much by the contractor's calendar as by the archaeology itself.

• ASentence II
• BSentence III
• CSentence IV
• DSentence V

Complete the paragraph: 'A dictionary that recorded only the words its editors approved of would be useless within a generation. Usage moves, and the words that shift fastest are exactly the ones speakers most need explained. ________' Which sentence best completes the paragraph?

• ALexicographers must therefore describe how words are actually used, not prescribe how the…
• BEditors should accordingly restrict new entries to terms that appear in formal written pr…
• CDictionaries have been compiled in one form or another since antiquity.
• DMost speakers consult a dictionary only when they are uncertain about spelling.

Read the paragraph: 'It is often said that the printing press democratised knowledge. In the first century after Gutenberg, however, the great majority of printed sheets were indulgences, calendars and official proclamations — documents produced for institutions that already held power. The press lowered the cost of reproducing text; it did not by itself change who decided which texts were worth reproducing.' What is the author's main point?

• AThe printing press had little measurable effect on the cost of producing books.
• BIndulgences and calendars were the most historically significant documents of the period.
• CCheaper reproduction did not in itself redistribute control over what got published.
• DKnowledge became genuinely democratic within a century of Gutenberg's invention.

A container in the shape of a right circular cylinder has a base radius of 4 cm and a height of 10 cm. What is the total surface area of the cylinder in square centimeters?

• A80π
• B96π
• C112π
• D128π

Five researchers (Ali, Burak, Ceren, Deniz, Emre) each present on one day from Monday to Friday, one presentation per day. Burak presents on Friday. Ali presents on Wednesday. Deniz presents on the day immediately before Emre. On which day does Ceren present?

• AMonday
• BTuesday
• CThursday
• DIt cannot be determined from the information given.

What is the remainder when 2^50 is divided by 7?

• A1
• B2
• C4
• D5

Which option is closest in meaning to the sentence: 'Far from resolving the dispute, the arbitrator's report gave each side fresh grounds for complaint.'?

• AThe arbitrator's report settled the dispute, although both sides continued to complain.
• BRather than ending the dispute, the report supplied both sides with new reasons to object.
• CThe arbitrator deliberately worded the report so as to provoke both sides.
• DNeither side had any real grounds for complaint before the report was issued.

Four positive numbers a, b, c, d form a geometric progression. If a = 3 and d = 24, what is the sum of b and c?

• A14
• B18
• C21
• D24

Read the paragraph: 'Reviewers of the new bridge design keep asking whether it is beautiful. That is the wrong question, and asking it lets the engineers off lightly. A bridge that is admired but closes for repair every third winter has failed at the only task it was given. Ask instead what it will cost to keep open in 2075, and the design conversation changes entirely.' What is the author's primary purpose in this paragraph?

• ATo argue that aesthetic judgement should be replaced by lifetime-maintenance cost as the…
• BTo demonstrate that the new bridge design is structurally unsound
• CTo praise engineers for prioritising durability over appearance
• DTo explain the technical methods used to forecast repair schedules

Put the sentences in the order that forms a coherent paragraph: (1) The result is that the same word can be spelled three ways in a single volume without any of them being an error. (2) Early printers set type from manuscripts written in whatever hand the copyist preferred. (3) Standard orthography arrived only when publishing houses grew large enough to impose in-house style rules on their compositors. (4) Faced with an unfamiliar spelling, a compositor simply set what he saw, or what he thought he saw.

• A(2)-(4)-(1)-(3)
• B(1)-(2)-(4)-(3)
• C(3)-(2)-(4)-(1)
• D(2)-(1)-(3)-(4)

A shopkeeper sells two items for ₺600 each. On one item, the shopkeeper gains 20%, and on the other, loses 20%. What is the net profit or loss on the entire transaction?

• ANo profit, no loss
• B₺50 loss
• C₺50 gain
• D₺100 loss

What is the sum of the roots of the quadratic equation 2x^2 - 8x + 5 = 0?

• A2
• B4
• C5/2
• D8

If x/y = 3/4 and y/z = 5/6, what is the ratio x/z?

• A3/5
• B5/8
• C9/10
• D10/9

Three alarm clocks ring at intervals of 12 minutes, 15 minutes, and 20 minutes respectively. If they ring together at 08:00 AM, at what time will they next ring together?

• A08:45 AM
• B09:00 AM
• C09:15 AM
• D09:30 AM

What is the domain of the function f(x) = sqrt(16 - x^2)?

• A[-4, 4]
• B(-4, 4)
• C[0, 4]
• D(-infinity, 4]

If 5^x = 10, what is the value of 5^(2x + 1)?

• A100
• B250
• C500
• D1000

Read the paragraph: 'Every seed bank keeps two collections. The working collection is opened, sampled and regrown, and it slowly drifts as the varieties best suited to the storage facility's own climate come to dominate. The base collection is sealed and never touched, which preserves the original genetics but leaves curators unable to confirm that the seeds are still alive.' What can be inferred about seed-bank curation?

• ABase collections are regrown more often than working collections.
• BVerifying that stored seeds remain viable is incompatible with keeping them genetically u…
• CWorking collections lose viability faster than base collections do.
• DSeed banks in cold climates preserve genetic diversity better than those in warm climates.

If x and y are positive real numbers satisfying x^2 + y^2 = 25 and xy = 12, what is the value of x + y?

• A5
• B6
• C7
• D8

A tank is filled by Pipe A in 6 hours and Pipe B in 8 hours. Pipe C can empty the full tank in 12 hours. If all three pipes are opened simultaneously when the tank is empty, how long will it take to fill the tank?

• A4.8 hours
• B5.2 hours
• C6.0 hours
• D7.2 hours

A box contains 5 red cards numbered 1 to 5 and 5 blue cards numbered 1 to 5. If one card is drawn at random, what is the probability that it is either red or has an even number?

• A0.5
• B0.6
• C0.7
• D0.8

The median of 7 consecutive odd integers is 21. What is the value of the largest of these integers?

• A23
• B25
• C27
• D29