The value of x is at most 450.
a
x 450
c
x ≤ 450

d
x ≥ 450

Junior PSAT

TrainingPacket

2016-17

Math Department  

AnswerKey

Section 3: Math Test — No Calculator

QUESTION 1.

Choice C is correct. Subtracting 6 from each side of 5x + 6 = 10 yields 5x = 4.

Dividing both sides of 5x = 4 by 5 yields x =

_4

5

. Te value of x can now be

substituted into the expression 10x + 3, giving 10 ( _4

5 ) + 3 = 11.

Alternatively, the expression 10x + 3 can be rewritten as 2(5x + 6) − 9, and

10 can be substituted for 5x + 6, giving 2(10) − 9 = 11.

Choices A, B, and D are incorrect. Each of these choices leads to 5x + 6 ≠ 10,

contradicting the given equation, 5x + 6 = 10. For example, choice A is

incorrect because if the value of 10x + 3 were 4, then it would follow that

x = 0.1, and the value of 5x + 6 would be 6.5, not 10.

QUESTION 2.

Choice B is correct. Multiplying each side of x + y = 0 by 2 gives 2x + 2y = 0.

Ten, adding the corresponding sides of 2x + 2y = 0 and 3x − 2y = 10 gives

5x = 10. Dividing each side of 5x = 10 by 5 gives x = 2. Finally, substituting

2 for x in x + y = 0 gives 2 + y = 0, or y = −2. Terefore, the solution to the

given system of equations is (2, −2).

Alternatively, the equation x + y = 0 can be rewritten as x = −y, and substituting x for −y in 3x − 2y = 10 gives 5x = 10, or x = 2. Te value of y can then

be found in the same way as before.

Choices A, C, and D are incorrect because when the given values of x and

y are substituted into x + y = 0 and 3x − 2y = 10, either one or both of the

equations are not true. Tese answers may result from sign errors or other

computational errors.

QUESTION 3.

Choice A is correct. Te price of the job, in dollars, is calculated using

the expression 60 + 12nh, where 60 is a fxed price and 12nh depends on the

number of landscapers, n, working the job and the number of hours, h, the job

takes those n landscapers. Since nh is the total number of hours of work done

when n landscapers work h hours, the cost of the job increases by $12 for each

hour a landscaper works. Terefore, of the choices given, the best interpretation

of the number 12 is that the company charges $12 per hour for each landscaper.

Choice B is incorrect because the number of landscapers that will work each

job is represented by n in the equation, not by the number 12. Choice C is

incorrect because the price of the job increases by 12n dollars each hour,

which will not be equal to 12 dollars unless n = 1. Choice D is incorrect

because the total number of hours each landscaper works is equal to h. Te

number of hours each landscaper works in a day is not provided.

QUESTION 4.

Choice A is correct. If a polynomial expression is in the form (x)2

+ 2(x)(y) +

(y)2

, then it is equivalent to (x + y)2

. Because 9a4

+ 12a2

b2

+ 4b4

= (3a2

)2

+

2(3a2

)(2b2

) + (2b2

)2

, it can be rewritten as (3a2

+ 2b2

)2

.

Choice B is incorrect. Te expression (3a + 2b)4

is equivalent to the product

(3a + 2b)(3a + 2b)(3a + 2b)(3a + 2b). Tis product will contain the term

4(3a)3

(2b) = 216a3

b. However, the given polynomial, 9a4

+ 12a2

b2

+ 4b4

,

does not contain the term 216a3

b. Terefore, 9a4

+ 12a2

b2

+ 4b4 ≠ (3a + 2b)4

.

Choice C is incorrect. Te expression (9a2

+ 4b2

)2

is equivalent to the

product (9a2

+ 4b2

)(9a2

+ 4b2

). Tis product will contain the term (9a2

)

(9a2

that looks hard

Step-by-step explanation:

b

mxb67

step-by-step explanation:

answer: plz put a pic in so i can answer it

step-by-step explanation: