900 Practice Questions for the Upper Level SSAT & ISEE

Because the question asks for an approximation, you can round each value to the nearest whole number before adding. However, there is some risk here because some of the answers are fairly close together.

4. D

Carefully proceed through the multiplication to obtain 0.75.

Because all of the answers contain the same digits, all you need to do is determine the decimal value. Multiplying 0.025 by 30 (a factor of 10) will move the decimal one place to the right.

5. E

As Z > 3, 5Z + 7 > 5(3) + 7 or 22. Only choice (E) is greater than 27.

6. E

Distribute the exponent to the numerator and the denominator, and maintain the negative sign as cubing a negative number generates a negative number.

7. B

To determine how many small boxes fit into the larger box, divide the volumes of the boxes. As the smaller cube has side length of 4, its volume is 4³ or 64. As the larger cube has a base perimeter of 32, it has side lengths of or 8, and a volume of 8³ or 512. Divide 512 by 64: 8.

8. D

Because there are not separate operations inside the parentheses, the parentheses do not matter. Under PEMDAS, addition and subtraction are co-equal, and you solve left to right.

9. B

First, set up the four consecutive integers, where x represents the least of the integers: x, x + 1, x + 2, and x + 3. Write an equation for the requirement: (x + 3) = x – 3. Add 3 to both sides and multiply both sides by 3: 3x + 18 = x. Subtract x and 18 from both sides: 2x = –18. Divide both sides by 2: x = –9. As the question asks for the greatest of the integers, add 3 to –9.

Test the answers, starting with choice (C). If 0 is the greatest of the integers, then –3 is the least. Test the requirement: 0 ≠ (–3) – 3. It may not be obvious whether you need a larger or smaller number, so pick a direction. When you test choice (B), the requirement will be satisfied: –6 = (–9) – 3 = –6.

10. B

As there are six sides to a hexagon and each side is reduced by 3, the total reduction will be 18. 42 – 18 = 24.

You can plug in for each of the 6 sides, making sure that the sides add up to 42. To keep things simple, pick the same number: 7. If each side is reduced by 3, the new sides will be 4, resulting in a perimeter of 24.

11. E

Add the numbers together for the denominator: 1,600. Of those 1,600, 200 chose Documentary: .

12. D

Set up a proportion: . Cross multiply and divide both sides by 320: x = 75.

Translate English into Math, using a variable (y) for what, multiplication (×) for of, and equals (=) for is: 240 = × 320. Multiply both sides by 240 and divide both sides by 320: x = 75.

13. C

First, convert meters to inches to obtain an apples-to-apples comparison: 1.5 × 39 = 58.5. Subtract 58.5 from 84: 25.5.

14. E

There is not enough information about where Carol and Mike work because there is no information about the direction from the coffee shop in which they work. They can work 20 blocks from each other, 140 blocks from each other, or anything in between.

15. C

Deal with one term at a time, starting with the coefficients. A negative exponent is the reciprocal of a positive exponent. Thus, 3^–2 is the same as . As the denominator already contains 9, the simplified denominator must contain 81. As a appears only in the numerator and has a positive exponent, nothing needs to be changed. As b has a negative exponent, the term becomes . As c appears only in the denominator and has a positive exponent, nothing needs to be changed. As d has a negative exponent, the term becomes = d⁶.

16. D

The 8 represents 800, the first 5 represents 50, and the second 5 represents 5. These three values are added together (800 + 50 + 5 = 855). When the original number is divided by 5, each of the three values is divided by 5.

17. D

First, set up a proportion to find the number: . Cross multiply and divide both sides by 40: x = 600. Now, set up a proportion to find the requested value: . Cross multiply and divide by 60: y = 360.

You can use logic. If 40% of a number is 240, 60% of the number will be greater than 240 but not by a factor of 10. Eliminate choices (A), (B), and (E). An increase from 40% of 240 to 60% of 240 is certainly going to add more than 20. Eliminate choice (C).

18. E

Let x represent the width of the rectangle, and write an equation to solve for x based on the given perimeter: x + x + 4x + 4x = 50. Combine like terms and divide both sides by 10: x = 5. Thus, the width is 5, and the length is 20. The area is 100.

19. C

Questions seeking the area of a weird shaded region generally require you to subtract the area of one normal shape from the area of another normal shape. In this case, subtract the area of the triangle from the area of the quarter circle. The area of a quarter circle is πr², but we need to find the radius from the circumference. As C = 2πr = 12π, the radius is 6. Now find the area of the quarter circle: π(6)² = 9π. As the triangle is a right triangle, the radii are also the base and height. The area of a triangle is bh = (6)(6) = 18. Choice (C) reflects the difference between the two areas.

You can estimate that the area is a small fraction of the area of the circle. Using the circumference, find that the radius is 6. So, the area is 36π = approximately 108. (100π = approximately 300.) Choices (A) and (D) are negative, so you can eliminate them. Choice (B) is about 18, while choice (C) is about 9. Given that one quarter of the circle is about 27, choice (B) is too large.

20. E

As there are 10 cents in one dime, there are 10a cents in a dimes. As there are 25 cents in one quarter, there are 25b cents in b quarters. There are 6 cents in six pennies.

Plug in for a and b such as a = 2 and b = 3. As there are 10 cents in one dime, there are 20 cents in two dimes. As there are 25 cents in one quarter, there are 75 cents in three quarters. Add these, along with 6 cents for the six pennies, for 101 cents. Only choice (E) matches these results when the selected numbers are tested.

21. C

Set up a proportion to solve for 3k, cross multiply, and divide by 210: , 1,200 = 210k, and k = or . The next proportion calls for 6k, which is . Follow the same procedure: , 1,200 = 100x, and x = 12.

If you cut a percent in half and double the number, the result will be the same.

22. C

Each term decreases by : ; . Subtract from −, and the missing number is –2.

23. B

If 350 people have smart phones and 150 people have tablets, that would mean there are 500 people. However, there are only 400 people, which means 100 of those people were counted twice.

It is useful to use the following formula in these types of questions: G₁ + G₂ + N – B = T. This stands for Group 1 + Group 2 + Neither – Both = Total. Here, as there is no N, the completed formula is 350 + 150 – B = 400. Solve for B: 100.

24. B

Begin with choices (A), (B), and (C), as they are easier to compare. Because y > 1, 2y > y, so 2y + 2 > y + 2. Likewise, 2 > –2, so 2y + 2 > 2y – 2. So far, choice (C) is the largest. Now address choice (D). As y > and 2y > y, 2y > . Choice (B) is still greatest. Finally, simplify choice (E): = 1 + . As y > 1 and y > , y + y (or 2y) > 1 + . Choice (B) is greatest.

Plug in a value for y, such as y = 2. Test each answer. Choice (B) is largest when y = 2.

25. E

The sum of the external angles of any triangle, including an equilateral triangle, is always 360°.

Draw an equilateral triangle and write in 60° at each vertex. Extend a line at each vertex to create an exterior angle. As there are 180° in a line, each exterior angle is 120°. Therefore, the sum is 360°.

1. C

While choices (C) and (E) are both possibilities, the one-sided nature of the passage suggests a political advertisement more than a newspaper article.

2. A

The passage states, “Since the early 1900s, the temperature of the air and sea at Earth’s surface has increased approximately 0.8°C (1.8°F), and roughly 66% of that increase has taken place in the last 30 years.”

3. E

The passage is about global warming and its possible causes and effects.

4. D

The passage states, “Since the early 1900s, the temperate of the air and sea at Earth’s surface has increased approximately 0.8°C (1.8°F), and roughly 66% of that increase has taken place in the last 30 years.”

5. B

The passage provides a brief introduction to the history of the Alvin Ailey American Dance Theater.

6. C

“Influences” earlier in the sentence leads to “aspects” as the answer.

7. B

The author has a positive attitude towards the topic.

8. B

The passage states, “When the opportunity to perform on Broadway came along, Ailey moved to New York and sought a new dance studio. Unable to find one like the Horton Dance Company, he started his own group, and the Alvin Ailey American Dance Theater was born.”

9. A

The passage states, “Ailey was particularly proud that his company was multi-racial, and that hiring decisions were always made based solely on a dancer’s talent—not his race.”

10. C

The passage states, “Pro- and anti-suffragists had descended upon Nashville in swarms.”

11. C

The passage states, “We had lobbied for weeks, firmly against the idea of allowing women to vote, with still others in the opposite corner.”

12. D

The passages states “As the proceedings began, words from my mother’s letter rang in my head: ‘Hurrah, and vote for suffrage! Don’t keep them in doubt.’ When asked for my vote on the matter, my response was so quick, the looks of surprise on my fellow legislators’ faces could not be disguised. With that single utterance, a half-century of activism by the likes of Susan B. Anthony and Alice Paul came to an end. The next day, I shared: “I know that a mother’s advice is always safest for her boy to follow.”

13. A

The passage states, “I walked into the Tennessee state legislature, gripping my mother’s letter and wearing my anti-suffrage red rose boutonniere.”

14. C

The passage tells the story of the day the narrator changed his vote from opposing the 19^th Amendment to favoring it.

15. C

The passage states, “Florence Nightingale was born into a rich, well-connected British family, and if her parents had had their way, she would have married a rich gentleman and settled into a conventional upper-class woman’s life. Alas, at 17 she had several encounters that she felt were calls from God, compelling her to serve others; by 24 she renounced her parents’ wishes and undertook the task of educating herself to become a nurse.”

16. D

The passage states, “Nutrition was paltry and supplies were extremely limited, which Nightingale believed directly influenced the death rate.”

17. C

The passage states, “Florence Nightingale was born into a rich, well-connected British family, and if her parents had had their way, she would have married a rich gentleman and settled into a conventional upper-class woman’s life.”

18. E

The passage states, “After two years in Crimea, Nightingale returned to England and established the Nightingale Training School for nurses at St. Thomas’ Hospital.”

19. B

The passage states, “Alas, at 17 she had several encounters that she felt were calls from God, compelling her to serve others; by 24 she renounced her parents’ wishes and undertook the task of educating herself to become a nurse.”

20. D

The passage states, “During the Crimean War, Florence Nightingale and a team of 38 volunteer nurses—whom she had trained herself—were sent to the Ottoman Empire, near modern day Istanbul.”

21. B

The passage focuses primarily on discoveries of chimpanzee behaviors that were similar to behaviors of humans.

22. C

The passage states, “At that time, there was not much known about chimpanzees, and scientists hoped that studying these animals would lead to insights about human evolution.”

23. C

The passage states, “Jane made a major discovery just a few months after she first arrived in Gombe, when she observed a chimp feeding on a baby pig. Until then, scientists had believed that chimpanzees were vegetarians; further studies showed the chimps frequently hunting smaller animals.”

24. C

The passage states, “More than fifty years ago, Jane Goodall arrived in Tanganyika (now Tanzania), East Africa, where she planned to study chimpanzees in what would become Gombe Stream National Park.”

25. D

The passage states, “An even more significant discovery occurred just weeks after she first saw chimps eating meat: she watched two chimps strip the leaves off twigs in order to fashion tools they used to dig termites out of a termite mound. This was revolutionary because up until this time anthropologists considered tool-making a distinctly human characteristic.”

26. D

The passage primarily focuses on the various causes of the Draft Riots.

27. C

The passage states, “By the time all was said and done, 119 people perished—most of them rioters, but some were black New Yorkers who fell prey to racists who used them as scapegoats for perceived injustices.”

28. A

The passage states, “By the time all was said and done, 119 people perished—most of them rioters, but some were black New Yorkers who fell prey to racists who used them as scapegoats for perceived injustices.”

29. E

The passage states, “Only recently had the U.S. Congress passed a law that required all men between the ages of 20 and 45 to register to be drafted into military service.”

30. A

As the passage later mentioned acts of violence against black people, “conflict” is the answer.

31. B

The passage is about the president’s call for public health laws, following a devastating disease that affected commerce.

32. B

The passage states, “While with reverence and resignation we contemplate the dispensations of Divine Providence in the alarming and destructive pestilence with which several of our cities and towns have been visited, there is cause for gratitude and mutual congratulations that the malady has disappeared and that we are again permitted to assemble in safety at the seat of Government for the discharge of our important duties.”

33. D

The passage states, “But when we reflect that this fatal disorder has within a few years made repeated ravages in some of our principal sea ports, and with increased malignancy, and when we consider the magnitude of the evils arising from the interruption of public and private business, whereby the national interests are deeply affected, I think it my duty to invite the Legislature of the Union to examine the expediency of establishing suitable regulations in aid of the health laws of the respective States.”

34. B

The passage states, “[T]here seems to be a necessity that Congress, who alone can regulate trade, should frame a system which, while it may tend to preserve the general health, may be compatible with the interests of commerce and the safety of the revenue.”

35. E

As the passage focuses on a devastating disease, “afflicted” is the answer.

36. C

The passage describes part of a journey and the excitement shared by the author and his friends.

37. D

The author is one of the passengers in the stage coach and provides a first-person point of view.

38. E

Most of the imagery relates to the terrain: “Just here the land was rolling—a grand sweep of regular elevations and depressions as far as the eye could reach—like the stately heave and swell of the ocean’s bosom after a storm. And everywhere were cornfields, accenting with squares of deeper green, this limitless expanse of grassy land. But presently this sea upon dry ground was to lose its ‘rolling’ character and stretch away for seven hundred miles as level as a floor!”

39. A

The passage states, “We jumped into the stage, the driver cracked his whip, and we bowled away and left “the States” behind us.… There was a freshness and breeziness, too, and an exhilarating sense of emancipation from all sorts of cares and responsibilities, that almost made us feel that the years we had spent in the close, hot city, toiling and slaving, had been wasted and thrown away.… We jumped out and stretched our legs every time the coach stopped, and so the night found us still vivacious and unfatigued.”

40. B

The tone is positive and expressive of excitement for the journey.

1. A

Habitual means routine.

2. B

To investigate is to study something.

3. C

To consider is to ponder something.

4. D

To meander is to wander or roam about.

5. C

To answer is to reply to someone.

6. E

To stumble is to trip.

7. A

Singular means unusual or out of the ordinary.

Some words have less commonly known definitions, called secondary definitions. Unusual is a secondary definition of singular.

8. E

Articulate means well-spoken.

9. B

Cumbersome means bulky or hard to carry.

10. D

To glean is to collect or garner.

11. A

To be patriotic is to be devoted.

12. E

Tedious means boring.

13. A

To be logical is to be rational.

14. C

Gratitude means appreciation.

15. E

Foolhardy means unwise.

16. B

Devious means tricky.

17. A

To capitulate is to give up.

18. A

To corrode is to crumble.

19. C

To consume is to eat.

20. C

A mnemonic is a type of reminder.

21. B

Pedestrian means ordinary.

Some words have less commonly known definitions, called secondary definitions. Ordinary is a secondary definition of pedestrian.

22. A

Furtive means secret.

23. D

Copious means plentiful.

24. E

Avarice means greed.

25. D

Misgiving means doubt.

26. A

Temperate means calm or restrained.

27. C

Stoic means impassive, especially in the face of pain or misfortune.

28. D

Acrid means sharp, especially as in an odor.

29. E

Obstinate means stubborn.

30. A

A tempest is a storm.

You may have heard the phrase a tempest in a teapot, which refers to a small problem that has been exaggerated. After all, how bad can a storm in a teapot really be?

31. C

Sweet is a pleasant flavor. Pretty is a pleasant sight.

32. A

Bread is made from wheat. Gasoline is made from oil.

33. E

A pen is used for writing. A mop is used for cleaning.

34. B

To be insistent is to be tenacious. To be concerned is to be worried.

If you don’t know the meaning of tenacious, work backwards. Concerned is not by definition related to any word except worried. Select choice (B).

35. D

Mohair is a fiber that comes from a goat. Angora is a fiber that comes from a rabbit.

If you don’t know the meaning of mohair, work backwards. Thread and cap, wool and sweater, and down (type of feather) and pillow, and cage and mouse are not by definition related, so you can select choice (D).

36. A

A miner provides raw materials for a jeweler. A fisher provides raw materials for a chef.

37. D

To table is to delay. To color is to distort.

The answers indicate that table is being used as a verb. If you don’t know the secondary meaning of table, work backwards. Yell and whisper are opposites. Could a word mean the opposite of delay? Sure, so keep choice (A). Cover and prevent, grow and shift, and improve and escalate are not by definition related, so you can eliminate choices (B), (C), and (E). You may not know that the secondary meaning of color means distort, in which case you might eliminate choice (D) and select choice (A). If you think that color might mean distort, could a word mean the same as delay? Of course, so keep choice (D) as well. You should always guess when you are down to two.

38. E

Acumen means shrewdness. Flamboyance means showiness.

If you don’t know the meaning of flamboyance, you need to leave this question blank. If you don’t know the meaning of acumen or shrewdness or both but do know the word flamboyance, work backwards. Flamboyance is not by definition related to any word except showiness. Select choice (E).

39. E

A scale measures weight. A circumferentor measures angles.

If you don’t know the meaning of circumferentor, use process of elimination. The easier answers to eliminate are choices (A) and (E) because a speedometer does not measure sound and a thermometer does not measure energy. If you know that a pipette measures volume or a tachometer measures rotation (or both), you can also eliminate choices (B) or (C) or both. Always guess when you are down to two.

40. A

To be precocious is to be quite developed. To be insolent is to be quite impolite.

If you don’t know the meaning of precocious, work backwards. If you know that insolent means to be quite impolite, keep choice (A) because a word can mean quite developed. If you don’t know the word insolent, keep choice (A) because you should never eliminate a word you don’t know. Neither lengthy and round nor teary and sad are by definition related, so you can eliminate choices (B) and (D). Scared is a lesser version of terrified. Could there be a word that is a lesser version of developed? Sure, so keep choice (C). Happy is a lesser version of joyful. While there could be a word that is a lesser version of developed, choices (C) and (E) have the same defining sentence and therefore cancel themselves out. Eliminate both answers and select choice (A).

41. C

A car is used for transportation. An oven is used for cooking.

42. A

Artwork is shown by display. A sword is shown by brandish (to wield or display).

If you don’t know the meaning of brandish, use process of elimination. None of the pairs in choices (B), (C), (D), and (E) are by definition related, so select choice (A).

43. E

A camera is used by a filmmaker. A ladle is used by a cook.

44. C

A fiasco is a big problem. A lamentation is a big complaint.

If you don’t know the meaning of fiasco, work backwards. Mistake and error are the same, and something can be the same as a problem, so keep choice (A). Puzzle and question are not by definition related, so eliminate choice (B). If you know lamentation, keep choice (C) because a lamentation is a big complaint, and something can be a big problem. If you don’t know lamentation, keep choice (C) because you should never eliminate words you don’t know. Arguably, a correction is used for improvement. Can something be used for a problem in the same manner? Probably not, so eliminate choice (D). An amalgamation is a collection. If you know amalgamation, you can eliminate choices (A) and (E), as they share a defining sentence and cancel each other out. This leaves choice (C). If you do not know amalgamation, keep choice (E) because you should never eliminate a word you don’t know.

45. B

Rules are set by parents. Laws are set by governments.

46. D

Callow means immature. Rushed means hurried.

If you don’t know the meaning of callow, work backwards. None of the pairs in choices (A), (B), (C), and (E) are by definition related. Select choice (D).

47. E

Loquacious is very talkative. Fascinating is very interesting.

If you don’t know the meaning of loquacious, work backwards. Neither implicating (accusing) and congratulating nor socialized and mesmerized are by definition related, so you can eliminate choices (A) and (C). If you don’t know implicating, though, keep choice (A) because you should never eliminate a word you don’t know. To be articulate (clear) is to be understandable. Could loquacious mean talkative? Sure, so keep choice (B). Presumptive means highly probable. Can talkative mean highly loquacious? Possibly, so keep choice (D). Fascinating is very interesting. Can loquacious mean very talkative? Sure, so keep choice (E). Depending on how many words you don’t know, you may need to skip this question.

48. A

A buckle fastens a belt. A lace fastens a shoe.

49. B

A pack is made up of more than one wolf. A garden is made up of more than one flower.

50. D

A good actor must be talented. A good weightlifter is expected to be strong.

51. C

Agony is the opposite of pleasure. Interference is the opposite of cooperation.

52. B

To connive is to scheme. To grow is to flourish.

If you don’t know the meaning of connive, work backwards None of the pairs in choices (A), (C), (D), and (E) are by definition related. Select choice (B).

53. C

A page is one part of a website. A photograph is one part of a compendium.

If you don’t know the meaning of compendium, use process of elimination. None of the pairs in choices (A), (B), (D), and (E) are by definition related. Select choice (C).

54. A

Dubious means doubtful. Idiosyncratic means peculiar.

If you don’t know the meaning of dubious, work backwards. None of the pairs in choices (B), (C), (D), and (E) are by definition related. Select choice (A).

55. E

Qualm is the opposite of confidence. Compliment is the opposite of criticism.

If you don’t know the meaning of qualm, work backwards. Yank is the same as pull. Can something be the same as confidence? Sure, so keep choice (A). Box is the same as carton, so now eliminate choices (A) and (B), which have the same defining relationship and cancel each other out. Manager and owner are not by defining related, so eliminate choice (C). Joy is a stronger version of pleasure. Can something be a stronger version of confidence? Yes, so keep choice (D). Compliment is the opposite of criticism. Can something be the opposite of confidence? Yes, so keep choice (E). You should always guess when you are down to two.

56. B

A breeze is a very light version of a hurricane. A swirl is a very light version of a maelstrom.

If you don’t know the meaning of maelstrom, use process of elimination. Warmth is not a very light version of coldness, day is not a very light version of week, downpour is not a very light version of drizzle, and gold is not a very light version of silver, so eliminate (A), (C), (D), and (E).

57. B

Debilitate is the opposite of strengthen. Neglect is the opposite of cultivate.

If you don’t know the meaning of debilitate, work backwards. Eradicate is the same as destroy. Could a word be the same as strengthen? Sure, so keep choice (A). Neglect is the opposite of cultivate. Could a word be the opposite of strengthen? Yes, so keep choice (B). Bend and snap are not by definition related, so eliminate choice (C). Decorate is the same as adorn, which means that you can eliminate choices (A) and (D), which share a defining sentence and cancel each other out. Simulate is the same as pretend and likewise cancels out. If you don’t know one or more of eradicate, cultivate, adorn, and simulate, keep the answer or answers because you should never eliminate a word you don’t know. Depending on how many answers you cannot eliminate, you may need to skip this question.

58. E

A glare is a facial expression that precedes a yell. A pucker is a facial expression that precedes a kiss.

59. A

Dishonest is a bad type of speaking. Noxious is a bad type of gas.

If you don’t know the meaning of noxious, use process of elimination. Muggy is not a bad type of summer, furry is not a bad type of cat, cloudy is not a bad type of mountain, and healthy is not a bad type of look, so eliminate choices (B), (C), (D), and (E).

60. E

Subtle is much less clear than obvious. Possible is much less likely than probable.

1. C

Divide 17 by 4: 4 . As 4 boxes will not quite be enough, she needs to buy 5 boxes.

Test the answers starting with choice (C). At 4 staplers per box, there would be 20 staplers, which is more than enough. Test choice (B) to see if that answer works. Now there are only 16 staplers, one too few, so the answer must be (C).

2. B

Convert 39 to a decimal and subtract, taking care to borrow as needed.

First subtract 39 from 100: 61. Now subtract the from 61.

3. C

First, convert yards to feet, for an apples-to-apples comparison. 8 × 3 = × 3 = 26. Now divide 36 by 2: 13.

4. C

Substitute the values given and solve: 10(4) + (5)² = 40 + 25 = 65.

5. B

Begin with the first 15 bouquets and multiply by $12: $180. For the four additional bouquets, the rate is $16: 4 × $16 = $64. Add the dollar amounts.

6. D

Convert the fractions to decimals: 4.75, 3.25, and 4.75. Add the numbers, making sure to carry the 1 as needed.

First add the whole numbers: 4 + 3 + 4 = 11. Now add the first two fractions: = 1. The two sums so far yield 12. Finally, add the final fraction.

7. D

Let a and b represent the length of the two female hamsters, and set up the average equation: = 4.1. Multiply both sides by 2: a + b = 8.2. Next, let c, d, e, f, g, and h represent the length of the six male hamsters and set up the average equation: = 5.3. Multiply both sides by 6: c + d + e + f + g + h = 31.8. Now, set up the average equation for all six hamsters and substitute the values you have determined: = = = 5.

A good way to think of average is Total = Average × Number (TAN). Here, the number of female hamsters is 2, and the average is 4.1. Thus, the total length of the hamsters is 4.1 × 2 = 8.2. Likewise, the number of male hamsters is 6, and the average is 5.3. Thus, the total length of these hamsters is 5.3 × 6 = 31.8. Finally, the total length of all the hamsters is 40, and the number of hamsters is 8, so the average length is 5.

8. D

Turn the improper fraction − into a mixed number using long division and finding the remainder: 4 goes into 15 evenly 3 times, with a remainder of 3, so the mixed number is −3 .

9. D

According to the chart, the number of suburban people who selected dalmatians is about 80 – 15 = 65. Reduce .

10. A

First, determine what percentage of suburban people selected bulldogs, about 15% (20% – 5%). You can see that 5% of urban people selected bulldogs. You can multiply these percents by the total (20,000) and subtract the values, or subtract the percents and multiply the difference by the total. Either way, the result is 2,000.

11. D

The sum of a series of n evenly spaced numbers where S₁ is the first number and S_n is the last number is given by the expression n. In this case, you are told that there are 26 evenly spaced numbers, and that the first number is 20 cents. You need to figure out the last number. The pattern shows that the day (1, 2, 3, etc.) is multiplied by 20 cents, so on the 26^th day, the value is $5.20. Plug these values into the formula (using dollars or cents): 26 = 70.20.

You can write out the donations and add them up, but this may be time consuming and result in a careless error.

12. C

Translate each element: five times a number is 5x, two times a different number is 2y, is less than or equal to is ≤, and 44 is 44.

13. D

Set up an equation: 2s + 4s = 24. Combine like terms and divide by 6: s = 4. Plug 4 into 4s: 16.

Test the answers, starting with choice (C). If 4s = 8, then s = 2, and 2s = 4. As 4 + 8 is less than 24, eliminate choice (C) as well as choices (A) and (B). Try choice (D). If 4s = 16, then s = 4, and 2s = 8. As 8 + 16 = 24, choice (D) is correct.

14. B

Follow PEMDAS. First, raise –5 to the second power: 25. Now, multiply the result by –2: –50.

15. E

Of the 24 squares, 18 are shaded: , which is 75%.

16. D

Start by writing the average equation: = 80. Then multiply both sides by 2: P + Q = 160. Check the answers. None of choices (A), (B), and (C) match the equation you wrote. Manipulate choice (D) to see if it matches, by adding P and 80 to both sides. It does.

Plug in numbers for P and Q, following the restrictions given, such as P = 60 and Q = 100. Only choice (D) is valid when you plug P and Q into the answer choices.

17. C

Let x represent the number of baseball cards Alice has. When she gives away 40% of those cards, she has 60% left or 0.6x. She then gives away 40% of 0.6x, which is (0.4)(0.6x) or 0.24x. Thus, she has 0.6x – 0.24x left, or 0.36x. That is 36% of the original amount.

As the original amount is not given, plug in a number, such as 100. If she gives Luke 40% of her collection, she gives away 40 baseball cards, leaving Alice with 60 baseball cards. If she gives Luke 40% of the 60 cards she has left, she gives away 24 of her cards, leaving Alice with 36 baseball cards, As she started with 100, 36 represents 36%.

18. E

Multiply $72.75 by 0.55 to get $40.0125. Choice (E) is closest in value.

Because the question invites you to make an approximation, divide $72.75 by 2 to get $36.375. Because the new price of the ticket is more than half of the original, any answer with a lesser value is wrong, leaving only choice (E).

19. E

The only like terms involve the fifth-degree exponent and the numbers without variables: 6x⁵ – 4x⁵ = 2x⁵, and 8 – 12 = 4. For the remaining elements, be careful about signs: distribute the negative sign to obtain x⁴, –2x³ remains as is, and distribute the negative sign to obtain –3x². Put the elements in descending order of power: 2x⁵ + x⁴ – 2x³ – 3x² – 4.

20. D

The base of the rectangle is give as b. If the height of the rectangle is 4 less than the base, then the height is b – 4. As perimeter is the sum of the sides, or 2(b + h), the perimeter of the rectangle is 2(b + b – 4) = 2(2b – 4) = 4b – 8.

Plug in a value for b, such as b = 10. As the height is 4 less than the base, the base is 6. The perimeter (all sides added) is 32. Only choice (D) yields 32 when 10 is plugged in.

21. D

Combine like terms, starting with the coefficient: . Next address k, remembering that when you divide common bases, you subtract the exponents: k². The s elements cancel out. Finally, address u, again applying the divide/subtract rule: u. Thus, the remaining elements are .

22. D

Trace your pencil along the lines to find out which cannot be drawn without lifting the pencil or re-tracing. If visual perception is not your strong suit, skip this question without guessing.

23. E

The average of evenly-spaced numbers is also the median of those numbers. Thus, the median here is 12. As the numbers are even, the next number after 12 is 14, followed by 16.

24. A

If p + q is divisible by 13, then (A) must also be divisible by 13 because you can factor out a 3: 3(p+ q). It must be the case that 3 times a number divisible by 13 is also divisible by 13.

Plug in numbers for p and q, ideally avoiding numbers that individually are divisible by 13. A good pair would be p = 6 and q = 7. Test these numbers in the answer choices to see which will be divisible by 13. Only choice (A) works.

25. A

This question requires you to guess and check. Begin with the units digit. Q can be 0 or 5, as 0 + 0 = 0, and 5 + 5 = 10. Proceed to the tens digit. There is no number that when added to itself will yield an odd number. Thus, we need to carry a 1 from the sum of the units digit. We now know that Q is 5. Now, N can be 3 or 8, as 3 + 3 + 1 = 7, and 8 + 8 + 1 = 17. Finally go to the hundreds digit. M + P can be any combination that adds up to 6 if N = 3. M + P can be any combination that adds up to 5 if N = 8, and the 1 was carried. So, the two sets of numbers are (1) Q = 5, N = 3, and M + P = 6, and (2) Q = 5, N = 8, and M + P = 5. Thus, the two possible sums of digits are 14 and 18. Only 18 is an answer.

SSAT Practice Test: Answers and Explanations

ANSWER KEY

Writing Sample

Section 1

Section 2

Section 3

Section 4