Tough Math Quiz

1. Given that b is an integer, is ┃b┃× b < 2b?

(1) b < 0.

(2) b = –6

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.

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.

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.

2. If x is = 20, then x²is 100.

True

False

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.

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.

3. If y is = -5, then y²is 25.

True

False

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.

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.

4.

1 on the number line above has the lowest absolute value.

True

False

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.

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.

5.

If the figure provided is drawn to scale, which of the following points on the number line above has the greatest absolute value?

Point A.

Point B.

Point C.

Point D.

Point E.

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.

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.

6. 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.

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.

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.

7. What is the value of |y|?

(1) y = -3
(2) y² = $%24%5Cleft%20%7C%20-y%20%5Cright%20%7C%5E%7B2%7D%24$

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.

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.

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.

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

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.

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.

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.

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

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.

Explanation

10. Given that n is an integer, is ┃n┃× n < 2ⁿ?

(1) n < 0.

(2) n = –6

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.

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.

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.