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SSAT Upper

SSAT Upper Quantitative II practice test

  • 25 questions
  • 30 minutes
  • A wrong answer costs 1/4 of a right one
  • Free

The Quantitative II section of the SSAT Upper practice test — 25 questions. Mark your answers, then press Finish at the bottom to see your score.

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Question 1

If h(x)=x2−2x, what is h(6)?

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Answer: C — 24

Substitute 6 for x: h(6)=62−2(6). This equals 36−12=24.

Question 2

Which of the following integers is divisible by 6 but not divisible by 9?

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Answer: C — 84

84 is even and has digit sum 12, so it is divisible by 6. Since 84÷9 is not an integer, 84 is not divisible by 9.

Question 3

A polygon has a perimeter of 900 centimeters. Six of its seven sides each measure 120 centimeters. What is the length of the seventh side?

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Answer: D — 180 cm

The six known sides total 6×120=720 centimeters. The remaining side is 900−720=180 centimeters long.

Question 4

Of 28 science reports, 21 were submitted before the deadline. What percent of the reports were submitted before the deadline?

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Answer: D — 75%

The fraction submitted early is 21/28=3/4. Since 3/4=75%, the answer is 75%.

Question 5

A machine fills 3 identical bottles every 8 seconds. At this rate, how many seconds will it take the machine to fill 45 bottles?

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Answer: D — 120

Since 45÷3=15, the machine needs 15 groups of 8 seconds. The time is 15×8=120 seconds.

Question 6

A list of numbers consists of four 12s, one 15, one 18, and one number x, where x<12. If the range of the list of numbers is 10, what is x?

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Answer: C — 8

Because x<12, the least value is x and the greatest value is 18. The range is 18−x=10, so x=8.

Question 7

If 4(3x−2)=52, what is x?

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Answer: B — 5

Dividing by 4 gives 3x−2=13. Then 3x=15, so x=5.

Question 8

Which of the following numbers is equal to 3−2?

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Answer: C — 19

A negative exponent gives the reciprocal: 3−2=132=19. It is not a negative number.

Question 9

Which graph shows a line that passes through (0,2) and falls 3 units for every 2 units it moves to the right?

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Answer: D

D is correct because its line passes through (0,2) and has slope −32. A treats a fall as a positive change; B reverses rise and run to obtain −23; C changes the sign of the given y-coordinate; E reverses the coordinates of the given point and passes through (2,0).

Question 10

A stone cube has edge length 6 inches. A cube with edge length 2 inches is cut from one corner. What is the volume of the stone that remains?

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Answer: D — 208 in3

The original cube has volume 63=216, and the removed cube has volume 23=8. The remaining volume is 216−8=208 in3.

Question 11

A lawn service charges a flat fee of $50 plus $18 for each hour of mowing. What is the least whole number of hours for which the total cost is at least $176?

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Answer: C — 7

Solve 50+18h≥176 to get 18h≥126, so h≥7. The least whole number of hours is 7.

Question 12

A factory produces 2.4×104 bolts per day. At that rate, which of the following is closest to the number of bolts produced in 365 days?

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Answer: B — 8.8×106

Estimate 2.4×104×365≈2.4×104×370=8.88×106, which is closest to 8.8×106.

Question 13

The number x is negative and satisfies ∣3x+4∣=∣x−8∣. What is the value of x?

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Answer: A — −6

The expressions inside the absolute values must be equal or opposites, giving x=−6 or x=1. Since x is negative, x=−6.

Question 14

Original tile4 inchesNew tile5 inches

A hallway mural is made from square tiles. Each original tile has side length 4 inches. The mural is remade with the same number of square tiles, but each new tile has side length 5 inches. By what percent is the area of the new mural greater than the area of the original mural?

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Answer: C — 5614%

Each original tile has area 42=16 square inches, and each new tile has area 52=25 square inches. The increase is 25−16=9 square inches for each original 16 square inches, so the percent increase is 916=5614%.

Question 15

A rectangle has perimeter 50 and area 150. What is the positive difference between the length and width of the rectangle?

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Answer: B — 5

The side lengths must add to 25 and multiply to 150, so they are 10 and 15. Their positive difference is 5.

Question 16

Six rowing-club members pay annual dues averaging 90 dollars. After a seventh member joins and pays d dollars, the average becomes 92 dollars. What is d?

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Answer: D — 104

The original total is 6×90=540. The new total is 7×92=644, so d=644−540=104.

Question 17

Spinner A has 4 equal sections labeled 1,2,3, and 4. Spinner B has 3 equal sections labeled 2,3, and 4. Both are spun once. What is the probability that the product of the two labels is a multiple of 4?

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Answer: D — 712

There are 4⋅3=12 ordered outcomes. The favorable pairs are (1,4),(2,2),(2,4),(3,4),(4,2),(4,3), and (4,4), so the probability is 712.

Question 18

A rectangle has diagonal length 25 and perimeter 70. What is the area of the rectangle?

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Answer: C — 300

Let the side lengths be l and w. The perimeter gives l+w=35, and the diagonal gives l2+w2=252=625. Since (l+w)2=l2+w2+2lw, we have 352=625+2lw. Thus 1225=625+2lw, so lw=300.

Question 19

How many milliliters of a 60% acid solution must be mixed with 30 milliliters of a 20% acid solution to produce a mixture that is 40% acid?

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Answer: C — 30

Let x be the mL of 60% solution: 0.6x+0.2⋅30=0.4(x+30). Then 0.6x+6=0.4x+12, so 0.2x=6 and x=30.

Question 20

Maya can paint a room alone in 10 hours, and Luis can paint the same room alone in 15 hours. Working together at those rates, how many hours will they need to paint the room?

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Answer: B — 6

Combined rate is 110+115=16 of the job per hour, so the job takes 6 hours.

Question 21

Six numbers have a mean of 18. When the smallest and largest numbers are removed, the mean of the remaining four numbers is 17. If the largest number is 20 greater than the smallest number, what is the largest number?

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Answer: D — 30

The sum of all six numbers is 6⋅18=108. The sum of the four remaining numbers is 4⋅17=68, so the smallest and largest numbers have sum 40. If the largest is 20 greater than the smallest, the two numbers are 10 and 30. Therefore the largest number is 30.

Question 22

A positive number is increased by p% and then the result is decreased by 40%. The final value is 9% less than the original number. What is p?

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Answer: C — 5123

After the increase and decrease, the multiplier is (1+p100)(0.60). The final value is 0.91 of the original, so 0.60(1+p100)=0.91. Thus 1+p100=9160 and p=5123.

Question 23

How many positive integers less than 200 are multiples of 6 but are not multiples of 9 or 10?

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Answer: D — 18

There are 33 multiples of 6 below 200. Of these, 11 are multiples of 18 and 6 are multiples of 30; the 2 multiples of 90 were subtracted twice. Thus the count is 33−11−6+2=18.

Question 24

A geometric design consists of parallelogram ABCD, with vertices named in order, where AB=14 and AD=12. Point E is the midpoint of AB, and point F lies on AD with AF=4. Segments CE and BF intersect at X. Triangle BXC is shaded. What is the area of the shaded triangle?

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Answer: E — It cannot be determined from the information given.

E is correct because triangle BXC occupies 314 of the parallelogram, making its area 3h, where the perpendicular height h is not specified; A assumes ∠DAB=30∘, giving h=6; B assumes ∠DAB=45∘, giving h=62; C assumes ∠DAB=60∘, giving h=63; D assumes the parallelogram is a rectangle, giving h=12.

Question 25

A jar originally contains red and blue beads only. If 3 red beads are added, half the beads in the jar are red. If instead 3 blue beads are added to the original jar, one-third of the beads in the jar are red. How many beads were originally in the jar?

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Answer: B — 15

From adding red beads, r+3r+b+3=12, so b=r+3. From adding blue beads, rr+b+3=13, so 2r=b+3. Substituting gives 2r=r+6, so r=6, b=9, and the original total is 15.

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