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Bob's Math Solutions - Step by step with Answers

McGraw-Hill's SAT Chapter 2 Section 2
6th Grade Pre-Algebra: Schneider Assignments - Week of October 18, 2014


McGraw-Hill's SAT Chapter 2 Section 2

1. If 2m+k=12 and k=10, what is the value of m?

A: 2m=12-10
m=2/2
m=1

2. The average (arithmetic mean) of three numbers is 50. If two of the numbers are 35 and 50, what is the third number?

Solution:
(30+50+x)/3=50
x+30+50=50*3
x=150-80
x=70

3.
   A5
   A3
   A5
+ 2A
--------
157

In the correctly worked addition problem
above, each A represents the same digit. What
is the value of A?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 6

A:
We know the sum must end in 7. Since 5(A5)+3(A3)+5(A5)=13, A must be 4 to make it 7.
A5 45
A3 43
A5 45
2A 24
---- -----
157 157

4. What number is the same percent of 225 as 9 is of 25?

Solution:

9/25=x/225
x=9/25*225
x=9*9
x=81

5. If 2x  1 = 32, what is the value of x?
A: Because I could have converted the 32 to 2x2x2x2x2, x-1=5. x=4.

6. VOTING RESULTS FOR REFERENDUM

  Yes No Total

Men

26

35

61

Women

33

43

76

Total

59

78

137

The table above, representing the results of a vote taken by the Zoning Commission on a recent referendum, is only partially completed. Based on the table, how many women on the Commission voted no?

7. Kenny and Mike each begin with the same number of baseball cards. After Mike gives Kenny 12 cards, Kenny has twice as many as Mike. How many cards do they have all together?

If each of them has 36 cards, After Mike gives Kenny 12 cards, Kenny has 48 cards and Mike has 24 cards. So, the total cards are 36+36-72.
8. A bag of Texas Tillie’s Trail Mix contains x ounces of walnuts, 15 ounces of peanuts, and 20 ounces of pecans. Which of the following expressions gives the fraction of the mix that is walnuts?

Since total Mix are x+15+20, the fraction of the mix that is walnuts is x/(x+35)

9. In the diagram above, if  m,  which of the following is equivalent to a + d + f + g?

(A) 2c + 2f

(B) b + c+ e+ h

(C) 2d+ 2e

(D) a +d +e+ h

(E) 2b + 2g

 



math1\


Answer is C.

10. For which of the following ordered pairs (x, y) is 2x + 3y >6 and x- y >6?

A: The only answer A (7,-1) satisfied both inequalities.

11. When n is divided by 12, the remainder is 6. What is the remainder when n is divided by 6?

A: If n has a remainder of 6 when it is divided by 12, it must be 6 more than a multiple of 12. Pick any one you like: 18 (12+6), for example. When 18 is divided by 6, the remainder is 0.




13. At a pet store, if d represents the number of dogs and c represents the number of cats, then
which of the following is equivalent to the statement “The number of dogs is 3 fewer than 4 times the number of cats?”

A: It must be d=4c-3.





15. A $50,000 prize is divided among four winners in a ratio of 4:3:2:1. What is the greatest
amount of money that any winner receives?

A: 50000/(4+3+2+1)*4
50000/10*4
5000*4=20,000





17. A jar contains only red, white, and blue marbles. It contains twice as many red marbles as
white marbles and three times as many white marbles as blue marbles. If a marble is drawn
at random, what is the probability that it is white?

A: If there is 1 blue marble, there are 3 white marble and 6 red marble.
6+3+1=10
So, 3/10 is the answer.

18. A certain class has 6 girls and 5 boys. Four of these students are to line up in the front of the room, with two girls on either end and two boys in between. How many such arrangements are possible?

A: 18. D Think about how many options you have to fill each place, from left to right. Since the first person must be a girl, you have 6 options. Since the next must be a boy, you have 5 options. Since the next must be a boy, you have 4 options (one is already up there). Since
the next must be a girl, you have 5 options left. This means that the total number of possible arrangements is (6)(5)(4)(5) = 600.




19.D If the two lines are parallel, then they have the same slope. The slope of l is , so the slope of m must be Cross-multiply: 3k = 48 Divide by 3: k = 16
Therefore, the rectangle has a width of 16 and a
height of 12, so its area is (16)(12) = 192.
(Chapter 10, Lesson 4: Coordinate Geometry)


20. A rectangular solid is a centimeters long, b centimeters wide, and c centimeters high. Its
volume is v cubic centimeters and its surface area is s square centimeters. If a, b, c, v, and s
are all integers, and v is odd, which of the following must be true?
I. a + b + c is odd.
II. a=v/bc
III. s is even.

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III

A: 20. E If v is the volume of the solid, then abc = v. Solving this equation for a gives , so statement II must be true. Now go to the answer choices, and notice that you can eliminate any choice without II, namely (A) and (C). Also notice from the original equation that v could not be odd if any of the integers a, b, or c were even, therefore they must all be odd. This implies that a + b + c is odd, so statement I must be true. This eliminates choice (D). To check statement
III, you need an expression for the surface area of the solid, which is 2(ab) + 2(bc) + 2(ac) = 2(ab + bc + ac). Since this is a multiple of 2, it is even, so statement III is also true.

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