SQAI - ÀMBIT DE SERVEIS CAMPUS UNIVERSITARI

6. ÀMBIT DE SERVEIS CAMPUS UNIVERSITARI

6.4. SQAI

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LESSON 1 MATH

SCRATCH PAPER 1

Question 4

Four containers of ﬂour are on the table:

The ﬁrst contains 1

3 of a pound, the second contains 1

6 of a pound, the third contains 1 9 of a pound, and the fourth contains 1

18 of a pound. If each container can hold one pound of flour, how many additional pounds of flour are required to fill all four containers?

Machine Units Made per Hour Percentage of Defective Units

A 2,800 12%

B 1,500 7%

C 750 6%

What is the ratio of the number of defective units created in an hour by machine A to the number of defective units created in an hour by machine B?

Question 6

In the equation above, if n is an integer, which of the following could be a possible value of x ?

Indicate all such values.

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LESSON 1 MATH

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LESSON 1 MATH

SCRATCH PAPER 1

PLUGGING IN

to 1, then which of the following is equal to g

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LESSON 1 MATH

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LESSON 1 MATH

SCRATCH PAPER 1

1. A

B d =

C n =

D l =

E

2. A

B f =

C g =

D E

R E SP ONSE

1. Recognize the opportunity: PLUG IN!

2. Set up your scratch paper.

3. Assign an easy number (e.g. 2, 5, 10, 100) to one variable.

4. Work through the problem.

5. Find the answer to the question. That’s your target number. Circle it.

6. Check all answer choices.

Question 3

If a factory produces 1,500 light bulbs in one minute, how many light bulbs will it produce in t seconds?

1,500t 25t the reciprocal of

A group of 10 people decides to share equally in an apartment that costs r dollars to rent each month.

If x people drop out of the group, how much more, in dollars, must each remaining person pay?

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LESSON 1 MATH

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LESSON 1 MATH

SCRATCH PAPER 1

Check your work. For every problem, you should have terms labeled, a target number circled, and all answer choices checked.

Quant Comps

Question 6

y ≠ 0

Quantity A Quantity B

–10y –y

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

TR IG G E R

Trigger: _______________________________________________________________

Need a weird number? Try FROZEN:

F – Fractions R – Repeats O – One Z – Zero E – Extremes N – Negative

Question 7

x > y > 0

Quantity A Quantity B

6x 7y

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the

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LESSON 1 MATH

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LESSON 1 MATH

SCRATCH PAPER 1

6. A a b c d B y =

y = y =

7. A a b c d B x = y = x = y = x = y =

R E SP ONSE

1. Recognize the Opportunity: PLUG IN!

2. Draw your set-up.

3. Plug in an easy number (according to the problem’s rules).

4. Cross off answer choices.

5. Repeat using FROZEN.

Question 8

3 < x < 6 < y < 10

Quantity A Quantity B

The greatest possible 7 value of y – x

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Question 9

a, b, and c are consecutive even integers such that a < b < c.

Quantity A Quantity B

a + c 2b + 2

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Question 10

a ≠ 0

Quantity A Quantity B

|a – 1| |a| – 1

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

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LESSON 1 MATH

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LESSON 1 MATH

SCRATCH PAPER 1

Must Be

Question 11

If a, b, and c are odd integers, which of the following must also be odd?

(a + b)c ac + b

(a + b) – (b + c) abc

(b – a) + (c – b)

TR IG G E R

Trigger: _______________________________________________________________

Question 12

If p and q are integers, such that p < 0 < q, which of the following must be true?

Indicate all such statements.

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^2p< 2q

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p²< q²

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p + q = 0

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LESSON 1 MATH

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LESSON 1 MATH

SCRATCH PAPER 1

A B C D E 11.

a = a = a =

b = b = b =

c = c = c =

R E SP ONSE

1. Recognize the Opportunity: PLUG IN!

2. Draw your set-up.

3. Plug in an easy number (according to the problem’s rules).

4. Cross off answer choices.

5. Repeat using FROZEN.

DRILL

Question 1 of 7

Bill is twice as old as Heidi and six years younger than Mel. If Heidi is h years old, how old is Mel in

Question 2 of 7

Quantity A Quantity B

6 + x 6 – x

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Question 3 of 7

0 < x < 10 0 < y < 1

Quantity A Quantity B

x – y 9

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

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LESSON 1 MATH

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LESSON 1 MATH

SCRATCH PAPER 1

Question 4 of 7

Eleven years ago, Lauren was half as old as Mike will be in 4 years. If Mike is m years old now, how

Question 5 of 7

P < Q

Quantity A Quantity B

Q – P Q P–

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Question 6 of 7

If the sum of three consecutive odd integers is k, then, in terms of k, what is the greatest of the three integers?

Question 7 of 7

Item F costs three times as much as item G, and item H costs $4 more than one-third the price of item G.

Quantity A Quantity B

The cost of item F The cost of item H

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

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LESSON 1 MATH

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LESSON 1 MATH

SCRATCH PAPER 1

T R IG GE R

Variables in the answer choices

R E SP ONSE

1. List A,B,C,D,E on scratch paper.

2. Replace variable with number.

3. Work the problem.

4. Identify and circle target number.

5. Check all answer choices.

T R IG GE R

Quant Comp with variables

R E SP ONSE

1. Draw set-up.

2. Plug in an easy number.

3. Eliminate two answer choices.

4. Repeat using FROZEN.

TR IG G E R

“Must be”

R E SP ONSE

1. Draw set-up.

2. Plug in an easy number.

3. Eliminate answer choices.

4. Repeat using FROZEN.

Lesson 2 Math

2 EXPONENTS & ROOTS

Question 1

12 20

3 5

× =

9 25 3 21 5 20 1 3 5 3 3 5 5

TR IG G E R

Trigger: _______________________________________________________________

Question 2 x x x x

5 3

4 2

+ + =

–4x² –x² 2x x x²

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LESSON 2 MATH

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LESSON 2 MATH

SCRATCH PAPER

2 R E SP ONSE

Find and cancel common factors.

Convert large bases to their prime factors.

2

^{Question 3}

Quantity A Quantity B

4 4

12 11

− 48

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Question 4

12⁶ = 3^a2^b. What is the value of a + b ?

Question 5

Which of the following statements must be true?

Indicate all such statements.

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( x)³ = x⁻¹

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(x²) = ( x)²

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x^-2 < x²

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LESSON 2 MATH

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LESSON 2 MATH

SCRATCH PAPER

2 2 HIDDEN PLUG INS

Question 1

Sarah pays 1

8 of her monthly income for food, 1

8 for utilities, 1

8 for student loans, and 4

5 of the remainder for rent. If at the end of each month Sarah puts 1

2 of her remaining income into a CD account, what portion of Sarah’s monthly income does she put into the account?

In a certain apartment building, 40 percent of the units have one bedroom, and the remaining units have two bedrooms. If 20 percent of the one-bedrooms and 10 percent of the two-one-bedrooms are vacant, what percent of the units in the building are vacant?

10% 14% 15% 30% 40%

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LESSON 2 MATH

SCRATCH PAPER SCRATCH PAPER

2 R E SP ONSE

Plug In for the unknown value or amount.

2 PITA

Question 1

Vicken, Roger, and Adam went to buy a $90 radio. If Roger agrees to pay twice as much as Adam, and Vicken agrees to pay three times as much as Roger, how much must Roger pay?

$10 $20 $30 $45 $65

TR IG G E R

Trigger: _______________________________________________________________

Question 2

Mike bought a used car and had it repainted. If the cost of the paint job was one-ﬁfth of the purchase price of the car, and if the cost of the car and the paint job combined was $4,800, then what was the purchase price of the car?

$800 $960 $3,840 $4,000 $4,250

Question 3

Gerald is three times as old as his cousin Lucy and 14 years older than his parrot Polly. In 4 years Lucy

will be half as old as Polly will be then. How old is Gerald?

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LESSON 2 MATH

SCRATCH PAPER SCRATCH PAPER

2

1. R A V

A 10 B 20 C 30 D 45 E 65

R E SP ONSE

1. Recognize the Opportunity: Plug In the Answers (PITA)!

2. List answer choices on your scratch paper.

3. Label the ﬁrst column.

4. Plug In (C).

5. Work the problem in bite-sized pieces, making a new column for each new step.

6. POE.

2 Plugging In Drill

Question 1 of 5

One-half the members of a team are juniors, one-third are sophomores, and the remainder are seniors.

Quantity A Quantity B

The number of juniors on the team

The number of seniors on the team

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Question 2 of 5

If –1 < x < 0, which of the following has the

Question 3 of 5

In a high school pep band that consists of forty students, the number of seniors is ﬁve fewer than twice the number of juniors, and 30% of the students in the band are neither juniors nor seniors.

Quantity A Quantity B

The number of juniors in the band

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

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LESSON 2 MATH

SCRATCH PAPER SCRATCH PAPER

2

Question 4 of 5

S is a sequence s₁, s₂, s₃…s_n in which every term after the ﬁrst is one less than three times the previous term. If s₅ – s₃ = 28, which of the following is the ﬁrst term in the sequence?

If 20 percent of the trees in a certain park are evergreens, and 40 percent of the non-evergreens are maple trees, and there are 75 percent as many oak trees as maple trees in the park, what fraction of the trees in the park are not maples, oaks, or evergreens?