Point to point

1. Mrs. Rodger got a weekly raise of $145. If she gets paid
every other week, write an integer describing how the raise
will affect her paycheck.
Solution:
Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x +
145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by
$ 145.
2. The value of x + x(x x ) when x = 2 is:
(a) 10, (b) 16, (c) 18, (d) 36, (e) 64
Solution:
x + x(x x )
Put the value of x = 2 in the above expression we get,
2 + 2(2 2)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
Answer: (a)
3. Mr. Jones sold two pipes at $1.20 each. Based on the
cost, his profit one was 20% and his loss on the other was
20%. On the sale of the pipes, he:
(a) broke even, (b) lost 4 cents, (c) gained 4 cents, (d) lost
10 cents, (e) gained 10 cents
Solution:
20 % profit on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Similarly, 20 % loss on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Therefore, in one pipe his profit is $ 0.24 and in the other
pipe his loss is $ 0.24.
Since both profit and loss amount is same so, it’s broke
even.
Answer: (a)
4. The distance light travels in one year is approximately
5,870,000,000,000 miles. The distance light travels in 100
years is:
(a) 587 × 10 8 miles, (b) 587 × 10 10 miles, (c) 587 × 10 -10
miles, (d) 587 × 10 12 miles, (e) 587 × 10 -12 miles
Solution:
The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 × 10 12 miles.
Answer: (d)
5. A man has $ 10,000 to invest. He invests $ 4000 at 5 %
and $ 3500 at 4 %. In order to have a yearly income of $
500, he must invest the remainder at:
(a) 6 % , (b) 6.1 %, (c) 6.2 %, (d) 6.3 %, (e) 6.4 %
Solution:
Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.
= $ 4000 × 5/100.
= $ 4000 × 0.05.
= $ 200.
Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.
= $ 3500 × 4/100.
= $ 3500 × 0.04.
= $ 140.
Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $
140 = $ 340.
Remaining income amount in order to have a yearly income
of $ 500 = $ 500 - $ 340.
= $ 160.
Total invested amount = $ 4000 + $ 3500 = $7500.
Remaining invest amount = $ 10000 - $ 7500 = $ 2500.
We know that, Interest = Principal × Rate × Time
Interest = $ 160,
Principal = $ 2500,
Rate = r [we need to find the value of r],
Time = 1 year.
160 = 2500 × r × 1.
160 = 2500r
160/2500 = 2500r/2500 [divide both sides by 2500]
0.064 = r
r = 0.064
Change it to a percent by moving the decimal to the right
two places r = 6.4 %
Therefore, he invested the remaining amount $ 2500 at 6.4
% in order to get $ 500 income every year.
Answer: (e)
6. Jones covered a distance of 50 miles on his first trip. On
a later trip he traveled 300 miles while going three times as
fast. His new time compared with the old time was:
(a) three times as much, (b) twice as much, (c) the same,
(d) half as much, (e) a third as much
Solution:
Let speed of the 1st trip x miles / hr. and speed of the 2nd
trip 3x / hr.
We know that
Speed = Distance/Time.
Or, Time = Distance/Speed.
So, times taken to covered a distance of 50 miles on his
first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his
later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the
old time was: twice as much.
Answer: (b)
7. If (0.2) x = 2 and log 2 = 0.3010, then the value of x to
the nearest tenth is:
(a) -10.0, (b) -0.5, (c) -0.4, (d) -0.2, (e) 10.0
Solution:
(0.2) x = 2.
Taking log on both sides
log (0.2) x = log 2.
x log (0.2) = 0.3010, [since log 2 = 0.3010].
x log (2 / 10 ) = 0.3010.
x [log 2 - log 10] = 0.3010.
x [log 2 - 1] = 0.3010,[since log 10=1].
x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].
x[-0.699] = 0.3010.
x = 0.3010 /-0.699 .
x = -0.4306….
x = -0.4 (nearest tenth)
Answer: (c)
8. If 10 2y = 25, then 10 -y equals:
(a) -1 / 5, (b) 1 / 625, (c) 1/ 50 , (d) 1 / 25 , (e) 1 / 5
Solution:
10 2y = 25
(10 y ) 2 = 5 2
10 y = 5
1 /10 y = 1/ 5
10 -y = 1/ 5
Answer: (e)
9. The fraction (5x-11) / (2x 2 + x - 6) was obtained by
adding the two fractions A/ (x + 2) and B / (2x - 3) . The
values of A and B must be, respectively:
(a) 5x, -11, (b) -11, 5x, (c) -1, 3, (d) 3, -1, (e) 5, -11
Solution:
Answer: (d)
10. The sum of three numbers is 98. The ratio of the first to
the second is 2/ 3, and the ratio of the second to the third is
5 / 8 . The second number is:
(a) 15, (b) 20, (c) 30, (d) 32, (e) 33
Solution:
Let the three numbers be x, y and z.
Sum of the numbers is 98.
x + y + z = 98………………(i)
The ratio of the first to the second is 2 /3 .
x/y = 2 /3 .
x = 2 /3 × y.
x = 2y / 3 .
The ratio of the second to the third is 5 /8 .
y /z = 5 /8 .
z /y = 8 /5 .
z = 8 /5 × y.
z = 8y / 5 .
Put the value of x = 2y / 3 and z = 8y / 5 in (i).
2y / 3 + y + 8y / 5 = 98
49y / 15 = 98.
49y = 98 × 15.
49y = 1470.
y = 1470 /49 .
y = 30 .
Therefore, the second number is 30.
Answer: (c)
Unsolved Questions:
1. Fahrenheit temperature F is a linear function of Celsius
temperature C. The ordered pair (0, 32) is an ordered pair of
this function because 0°C is equivalent to 32°F, the freezing
point of water. The ordered pair (100, 212) is also an
ordered pair of this function because 100°C is equivalent to
212° F, the boiling point of water.
2. A sports field is 300 feet long. Write a formula that gives
the length of x sports fields in feet. Then use this formula to
determine the number of sports fields in 720 feet.
3. A recipe calls for 2 1/2 cups and I want to make 1 1/2
recipes. How many cups do I need?
4. Mario answered 30% of the questions correctly. The test
contained a total of 80 questions. How many questions did
Mario answer correctly?