300难题-DS：第76-83题 练习册详情

1

Exactly 3 deposits have been made in a savings account and the amounts of the deposits are 3 consecutive integer multiples of $7. If the sum of the deposits is between $120 and $170, what is the amount of each of the deposits?

1.The amount of one of the deposits is $49.

2.The amount of one of the deposits is $63.

• 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.

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2

If m and n are positive integers, what is the value of $$\frac{3}{m}+\frac{n}{4}$$ ?

1.mn=12

2.$$\frac{3}{m}$$ is in lowest terms and $$\frac{n}{4}$$ is in lowest terms.

• 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.

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3

Is x an integer?

1.$$x^{2}$$ is an integer.

2.$$\frac{x}{2}$$ is not an integer.

• 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.

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4

If x and z are integers: is x + $$z^{2}$$ odd?

1.x is odd and z is even.

2.x -z is odd.

• 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.

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5

If b is the product of three consecutive positive integers c, c + 1, and c + 2, is b a multiple of 24?

1.b is a multiple of 8.

2.c is odd.

• 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.

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6

Each entry in the multiplication table above is an integer that is either positive,negative, or zero. What is the value of a ?

1.$$ h\neq 0$$

2.c = f

• 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.

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7

If 1 < d < 2, is the tenths digit of the decimal representation of d equal to 9 ?

1.d + 0.01 < 2

2.d + 0.05 > 2

• 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.

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8

If s is an integer, is 24 a divisor of s ?

1.Each of the numbers 3 and 8 is a divisor of s.

2.Each of the numbers 4 and 6 is a divisor of s.

• 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.

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