Given that n is an integer, is ┃n┃× n < 2n? (1) n < 0. (2) n = –6

EACH statement ALONE is sufficient.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Is x a positive integer? (1) |x| >1 (2) 1

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

What is the value of |y|? (1) y = -3 (2) y2 =

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Given that b is an integer, is ┃b┃× b < 2b? (1) b < 0. (2) b = –6

EACH statement ALONE is sufficient.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Is y greater than x? (1) |y|<1 and |x| <2 (2) y>0 and x is not 0

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

What is the value of |k|? (1) k3 = 27 (2) k = |k|

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Tough Math Quiz

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Quizzes Created: 4 | Total Attempts: 8,625

Questions: 10 | Attempts: 2,045 | Updated: Aug 27, 2023

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Are you ready to take this tough Math quiz? The quiz below has difficult math questions to test your math knowledge as well as skills. However, if you are a very good student of mathematics, then these questions are not going to be challenging for you. You may need to do some practical paperwork, so make sure you have a notebook and pen near you. Wish you all the best, and have fun!

Questions and Answers

1.

Given that n is an integer, is ┃n┃× n < 2ⁿ? (1) n < 0. (2) n = –6
- A.
  
  Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- B.
  
  Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- C.
  
  BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- D.
  
  EACH statement ALONE is sufficient.
- E.
  
  Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Correct Answer
D. EACH statement ALONE is sufficient.

Explanation
The absolute value of n multiplied by n will always be less than 2n if n is negative. Therefore, statement (1) alone is sufficient to answer the question. Statement (2) alone is also sufficient because it provides a specific value for n (-6) which is negative, satisfying the condition. Therefore, each statement alone is sufficient to answer the question.

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2.

Is x a positive integer? (1) |x| >1 (2) 1
- A.
  
  Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- B.
  
  Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- C.
  
  BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- D.
  
  EACH statement ALONE is sufficient.
- E.
  
  Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Correct Answer
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Explanation
Statement (2) alone is sufficient because it states that x is greater than 1, implying that x is a positive integer. However, statement (1) alone does not provide enough information to determine if x is positive or negative, as it only states that the absolute value of x is greater than 1, which could include negative values as well. Therefore, statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

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3.

1 on the number line above has the lowest absolute value.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
The statement is false because the number 1 on the number line does not have the lowest absolute value. The absolute value of a number represents its distance from zero on the number line. Since 1 is further away from zero than any negative number, it does not have the lowest absolute value.

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4.

If x is = 20, then x²is 100.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
The given statement is false. If x is equal to 20, then x^2 (x squared) would be equal to 400, not 100. Therefore, the correct answer is False.

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5.

What is the value of |y|? (1) y = -3 (2) y² =
- A.
  
  Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- B.
  
  Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- C.
  
  BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- D.
  
  EACH statement ALONE is sufficient.
- E.
  
  Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Correct Answer
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Explanation
Statement (1) provides the value of y as -3. The absolute value of -3 is 3, so the value of |y| is 3.

Statement (2) does not provide any information about the value of y, so it is not sufficient to determine the value of |y|.

Therefore, statement (1) alone is sufficient to answer the question, but statement (2) alone is not sufficient.

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1
0
6.

Given that b is an integer, is ┃b┃× b < 2b? (1) b < 0. (2) b = –6
- A.
  
  Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- B.
  
  Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- C.
  
  BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- D.
  
  EACH statement ALONE is sufficient.
- E.
  
  Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Correct Answer
D. EACH statement ALONE is sufficient.

Explanation
The absolute value of b, represented as ┃b┃, is always a non-negative value. If b is negative, then ┃b┃ will be equal to -b. Therefore, in order for ┃b┃× b to be less than 2b, b must be less than 0. Statement (1) alone provides this information, so it is sufficient to answer the question. Statement (2) alone also provides the value of b as -6, which confirms that b is less than 0. Therefore, each statement alone is sufficient to answer the question.

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7.

If y is = -5, then y²is 25.
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
If y is equal to -5, then y^2 (y squared) would be equal to 25. This is because when you square a negative number, the result is always positive. Therefore, the statement "If y is = -5, then y^2 is 25" is true.

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8.

If the figure provided is drawn to scale, which of the following points on the number line above has the greatest absolute value?
- A.
  
  Point A.
- B.
  
  Point B.
- C.
  
  Point C.
- D.
  
  Point D.
- E.
  
  Point E.
Correct Answer
A. Point A.

Explanation
The figure provided is not visible, so it is not possible to determine the positions of the points on the number line. Therefore, an explanation cannot be provided.

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9.

Is y greater than x? (1) |y|<1 and |x| <2 (2) y>0 and x is not 0
- A.
  
  Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- B.
  
  Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- C.
  
  BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- D.
  
  EACH statement ALONE is sufficient.
- E.
  
  Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Correct Answer
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
10.

What is the value of |k|? (1) k³ = 27 (2) k = |k|
- A.
  
  Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- B.
  
  Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- C.
  
  BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- D.
  
  EACH statement ALONE is sufficient.
- E.
  
  Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Correct Answer
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Explanation
Statement (1) states that k^3 = 27. From this, we can determine that k = 3, as 3^3 = 27. Therefore, we can determine the value of |k| to be 3.

Statement (2) alone does not provide any information about the value of k or |k|. Therefore, it is not sufficient to answer the question.

Thus, statement (1) alone is sufficient to determine the value of |k|, while statement (2) alone is not sufficient.

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