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Detailed Solution for Test: Exponents- 1 - Question 3

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Test: Exponents- 1 - Question 5

If n is a positive integer greater than 2, what is the greatest prime factor of 3^{n} + 3^{n} + 3^{n} – 3^{n-2}?

Test: Exponents- 1 - Question 6

If ‘x’ and ‘y’ are non-negative integers, what is the value of x + y?

(1) x^{4} is even, where x is a prime number.

(2) x^{y }is odd.

Detailed Solution for Test: Exponents- 1 - Question 6

Test: Exponents- 1 - Question 7

Find the value of n that satisfies the equation 2(-3)^{4n} = 18(27)^{n+2}

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Test: Exponents- 1 - Question 8

The intensity of radiation emanating from a nuclear event is measured on an exponential scale where the second and fourth points indicate intensities of 25 and 625, respectively. On that scale, what would the intensity at the third point be?

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Test: Exponents- 1 - Question 9

Positive integer P lies between 1 and 30. What is the value of P?

(1) P has at least two prime factors

(2) The cube of P is less than 300

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Test: Exponents- 1 - Question 11

The half-life of a radioactive element is defined as the amount of time required for the amount of the element to decrease by half. If the half-life of an element is 3 years, how long will it take for the element to be reduced to one-eighth of its original amount?

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Test: Exponents- 1 - Question 13

Is x^{y }≥ 1 if both x and y are non-zero integers?

(1) y = -x

(2) y = 2^{k} where k is a non-zero integer

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Test: Exponents- 1 - Question 14

Find the value of positive integer P that lies between 1 and 30 and is a perfect square.

(1) P has at least one Prime factor

(2) The cube of P is less than 300

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Test: Exponents- 1 - Question 15

If k is an integer then find the value of

(1) 2^{r} – 2^{k} = 2^{6}, where r is an integer

(2) 14 + k = 3k – 2r, where r is an integer

Detailed Solution for Test: Exponents- 1 - Question 15

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