GED Mathematical Reasoning

Question 1

What is the value of 2/5 multiplied by ¾ divide by 8/5

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Question 2

Simplify 6^2 - 3^2

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

Answer: C

To simplify the expression 6^2 - 3^2, we first calculate the squares of 6 and 3, which are 36 and 9 respectively. Subtracting 9 from 36 gives us the result of 27.

A) 6
This choice is incorrect because the expression involves squaring the numbers 6 and 3, not simply subtracting them directly.

B) 9
This option is incorrect as it represents the square of the number 3, which is one part of the expression. However, the overall expression involves subtracting this square from the square of 6, resulting in a different value.

D) 3
This option is incorrect as it represents one of the numbers in the original expression, but the operation involves squaring this number and subtracting it from the square of another number.

Conclusion
The correct answer is C, 27, as the expression simplifies to 6^2 - 3^2 = 36 - 9 = 27. This calculation follows the order of operations, first squaring the numbers and then subtracting the results to arrive at the final solution.

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Question 3

2^3 * 27^(1/3) * 1^3

Your Answer: Option(s)

Correct Answer: Option(s) B

Rationale

Option B) 24

To simplify this expression, start by evaluating the exponents individually. 2^3 equals 8, 27^(1/3) equals 3 (since the cube root of 27 is 3), and any number raised to the power of 1 is that number itself. Multiplying these results together gives 8 * 3 * 1 = 24.

A) 54
This answer is incorrect because the calculation involves multiplication and not addition. The correct solution requires evaluating each term separately and then multiplying the results together, rather than adding them.

C) 72
This option is incorrect because the calculation involves multiplication, not addition. To arrive at the correct answer, it is essential to correctly evaluate each exponent before multiplying the results together.

D) 18
This choice is incorrect as it does not follow the correct order of operations for evaluating exponents and multiplication. The expression provided involves multiplying the results of each term, not adding them together.

Conclusion
The correct answer to the given expression 2^3 * 27^(1/3) * 1^3 is 24. By correctly evaluating each exponent and then multiplying the results together, the final answer is obtained. It is crucial to follow the proper order of operations, considering exponentiation before multiplication, to arrive at the accurate solution.

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Question 4

((5^3 * 2^4)^2)(5^(-2) * 2^5)

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

Correct thing here.

The correct answer is C) 5^4 * 2^13. To solve this expression, first simplify the terms within the parentheses by applying the rules of exponents, then multiply the terms outside the parentheses accordingly.

A) 5^3 * 2^11
This choice simplifies to a different result. The exponent of 4 for 5 and 13 for 2 in the correct answer indicates a miscalculation in exponentiation.

B) 5^(-12) * 2^40
The exponents in this choice are significantly different from the correct answer. The negative exponent on 5 and the excessively high exponent on 2 do not align with the given expression.

D) (-5)^8 * 2^13
This choice introduces a negative sign to the 5 without parentheses, altering the value of the expression. Additionally, the exponent for 5 is different from the correct answer, leading to an incorrect result.

Conclusion
The correct simplification of the given expression ((5^3 * 2^4)^2)(5^(-2) * 2^5) yields 5^4 * 2^13, denoted by choice C. The application of exponent rules and the subsequent multiplication of terms result in this particular numerical outcome. Choices A, B, and D present alternate calculations or inaccuracies in the exponents, leading to incorrect solutions when applied to the original expression.

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Question 5

The mass of an amoeba is approximately 4.0 X 10^(-6) grams. Approximately how many amoebas are present in a sample that weighs 1 gram?

Your Answer: Option(s)

Correct Answer: Option(s) A

Rationale

A) 2.5 × 10^5

To determine the number of amoebas in the sample, you need to divide the total weight of the sample (1 gram) by the weight of a single amoeba (4.0 × 10^(-6) grams). This division yields 2.5 × 10^5, indicating that approximately 250,000 amoebas can be found in a 1-gram sample.

B) 4.0 × 10^7
This choice incorrectly multiplies the weight of an individual amoeba by the total weight of the sample, leading to an overestimation of the number of amoebas in the sample. This calculation neglects the division needed to find the correct quantity.

C) 4.0 × 10^5
This option also incorrectly multiplies the weight of a single amoeba by the total weight of the sample. By using this method, the calculation does not reflect the correct number of amoebas present in the 1-gram sample.

D) 2.5 × 10^7
Similarly to option B, this choice incorrectly multiplies the weights instead of dividing the total weight of the sample by the weight of one amoeba. This miscalculation leads to an inflated estimation of the number of amoebas in the sample.

Conclusion
By correctly dividing the total weight of the sample by the weight of a single amoeba, you arrive at the accurate estimation of approximately 250,000 amoebas in a 1-gram sample. Understanding this relationship between individual and total weights is crucial in accurately determining quantities based on given measurements.

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Value of 2/5 multiplied by ¾ divided by 8/5 is 3/16.

Answer: C

Option B) 24

Correct thing here.

A) 2.5 × 10^5

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Value of 2/5 multiplied by ¾ divided by 8/5 is 3/16.

Answer: C

Option B) 24

Correct thing here.

A) 2.5 × 10^5

Free Preview Ended

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