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If the distances between two consecutive ticks are the same, what is the value of x?

A. \(4^{11}\) B. \(2(4^{11})\) C. \(3(4^{11})\) D. \(4^{12}\) E. \(5(4^{11})\)

==> If you set the distance between two consecutive ticks as d, you get \(d=-2(4^{11})-(-4^{12})=4^{12}-2(4^{11})=(4-2)4^{11}=2(4^{11}).\) Then, you get \(x=-2(4^{11})+2d=-2(4^{11})+2*2(4^{11})=(-2+4)(4^{11})=2(4^{11}).\)

We define the average (harmonic mean) as the reciprocal of the average (arithmetic mean) of reciprocals. What is the average (harmonic mean) of 2, 3, and 6?

A. 1/3 B. 1/2 C. 1 D. 2 E. 3

==> If you find the average of the reciprocals, you get \(\frac{++}{3}=\frac{1}{3}\) .

Since it is the reciprocal of that, the answer is E. Answer: E
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There is a parallelogram that has a side length of 8 and 7. Which of the following can be the area of the parallelogram?

I. 47 II. 55 III. 56

A. I. only B. II. only C. III. only D. I and II only E. I, II and III

Attachment:

6.7.png [ 2.08 KiB | Viewed 212 times ]

==>The area of parallelogram is base*height. However, since a rectangle is a parallelogram and if one side length is 8 and the other is 7, you get the area of 8*7=56. The one side length of the parallelogram, which is 8, remains the same and the height is less than or equal to 7, so the area of the parallelogram becomes ≤56.

Therefore, the answer is I. 47 II. 55 III. 56 all possible.

For an investment, you start off with $1,000, the interest rate of 5%, and you deposited two years as compound interest. What is the total interest earned in 2 years?

Which of the following is the closest value of x such that \(x^{20}+x^2+0.0000019=0.09\)?

A. 0.1 B. 0.01 C. 0.3 D. 0.03 E. 0.003

==> From \(x^{20}+x^2+0.0000019=0.09, x^{20}\) and 0.0000019 are very close to 0, so you can ignore them, and the equation becomes \(x^2=0.09=0.3^2\). Thus, you get x=0.3.

A ball dropped from a certain height. The height that it reached after rebounding from the floor was 60 percent of the initial height. The height was 292cm when it touched the floor for the third time. What was the initial height? A. 80cm B. 90cm C. 100cm D. 120cm E. 130cm

ANS: If we consider the initial height as x, then from x+2(60%)x+2(60%)^2(x)=292, we get x=100. Hence, the correct answer is C.

the question should hv use total height instead of just height...

What is the median of the consecutive multiples of 7 in the first 50 positive integers?

A. 14 B. 21 C. 28 D. 35 E. 42

==> Since it is the first 50 positive integers, you need to find the median of the consecutive multiples of 7, you get 7, 14, 21, 28, 35, 42, 49, and the median is 28.

A ball dropped from a certain height. The height that it reached after rebounding from the floor was 60 percent of the initial height. The height was 292cm when it touched the floor for the third time. What was the initial height? A. 80cm B. 90cm C. 100cm D. 120cm E. 130cm

ANS: If we consider the initial height as x, then from x+2(60%)x+2(60%)^2(x)=292, we get x=100. Hence, the correct answer is C.

the question should hv use total height instead of just height...

Yes. You are right. The question should be changed as follows.

One ball will drop from a certain height. The height it will reach after rebounding from the floor is 60 percent of the previous height. The total travel is 292cm when it touches the floor on third time. What is the value of the original height?
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What is the number of multiples of 6 from -35 to 69?

A. 14 B. 16 C. 17 D. 20 E. 21

==> 0 becomes the multiple of all integers. From 1~69, 11 of them are multiples of 6, from -1~-35, 5 of them are multiples of 6, hence you get 11+5+1=17.

If the sum of the first 50 even numbers is 2,550, what is the sum of the first 50 odd numbers?

A. 1,275 B. 2,550 C. 2,500 D. 2,600 E. 3,000

==> You get 2+4+…..+98+100=2,550, then 1+3+….+97+99=?. If you compare each numbers, 1 is 1 less than 2, 3 is 1 less than 4, 97 is 1 less than 98, and 99 is 1 less than 100. Since there are 50 numbers in total, it is 50 less than 2,550.

Therefore, the answer is C. Answer: C
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If -1＜x＜0, which of the following listsx^-2, x^-1, x, x^2, 1 in an ascending order?

A. x^-1, x, x^2, 1, x^-2 B. x^-2, x, x^2, 1, x^-1 C. x^-1, x^2, x, 1, x^-2 D. x^-1, x, x^2, x^-2, 1 E. x, x^-1, x^2, 1, x^-2

==> If you substitute x=-0.1, from x^-1=(-0.1)^-1=1/(-0.1)=-10, x=-0.1, x^2=(-0.1)^2=0.01, x^-2=(-0.1)^-2=1/(-0.1)^2=1/0.01=100, you get x^-1, x, x^2, 1, x^-2.