Quant-3

When the integer k is divided by 6, the remainder is 4. What is the remainder when 8k is divided by 6?

• 3

• 2

• 4

• 5

• 6

Answer explanation

If k is a positive integer and n is the ones digit of 7k, what is the greatest possible value of |n-7|?

• 0

• 2

• 4

• 6

• -6

Answer explanation

7kThe single digit values ​​of are 7, 9, 3, 1, so the possible values ​​of |n-7| are 0, 2, 4, 6, and the maximum value is |1-7|=6.

Each person in a group of nine people was asked how many movies the person saw last month. The numbers of movies seen last month by five people in the group are 1, 1, 0, 2 and 2, respectively. numbers of movies seen last month by the other four people in the group is 3, what is the greatest possible value of the median of the numbers of movies seen last month by all the people in the group?

A 0

B 1

C 2

D 3

E 4

• A

• B

• C

• D

• E

Answer explanation

To find the greatest possible value of the median of the numbers of movies seen last month by all the people in the group, we need to arrange the numbers in ascending order. We know that five people saw 0, 1, 1, 2, and 2 movies, respectively, so these five numbers will be the smallest five in the group's list of numbers.

The other four people saw three movies, so we need to place these four numbers in such a way that the median is as large as possible. To do this, we can place two of the threes after the 2's and two of the threes before the 1's. This gives us the following arrangement:

0, 1, 1, 2, 2, 3, 3, 3, 3

The median of this list is 2, which is the greatest possible value for the median. Therefore, the correct answer is (C) 2.

A rectangular floor will be completely covered with square tiles, each of which has sides of length 6 inches. If tiles are laid side by side with no space between them and no tiles are cut, then the number of tiles needed to cover the floor is 1,080. Which of the following could be the dimensions of the floor? (Note12 inches=1 foot.)

A 15 feet by 9 feet

B 15 feet by 18 feet

C 30 feet by 18 feet

D 30 feet by 36 feet

E 45 feet by 36 feet

• A

• B

• C

• D

• E

Answer explanation

The area of ​​each square brick is 6×6=36 square inches, and 1080 pieces are shared, indicating that the total area of ​​the room is 36*1080 square inches, and 1feet=12 inches, then 1 square feet=144 square inches , so the total area of ​​the room is 36*1080/144= 270 square feet; option B is 15*18=270, choose B.

x²+y²=25. Both x and y are integers and x > y.

Quantity A

x

Quantity B

4

• A

• B

• C

• D

Answer explanation

(±3)^2+(±4)^2=25, guarantee x>y, then x, y can be 4, 3, or 4, -3, or 3, -4, or -3 , -4. Then x can take 4 or 3 or -3, it may be equal to 4 or less than 4, choose D.

For all positive integer n, the function f is defined by the equation f(n)= n(n+1)/2

m is a positive integer

Quantity A

(−1)^f(4m+1)

Quantity B

(−1)^f(4m+2)

• A

• B

• C

• D

Answer explanation

x and y are integers, and x < y-4

Quantity A

The number of even integers between x and y

Quantity B

The number of odd integers between x and y

• A

• B

• C

• D

Answer explanation

Special value method——

When x=1, y=6, there are 2 even numbers between 1 and 6 (2&4), and 2 odd numbers (3&5);

When x=1, y=7, there are 3 even numbers between 1 and 7 (2&4&6), and 2 odd numbers (3&5);

k is a positive integer greater than 1

Quantity A

The remainder when -k is divided by 2k²

Quantity B

0

• A

• B

• C

• D

Answer explanation

k^{2}-k=k(k-1), since k is a positive integer greater than 1, k(k-1) is two consecutive integers, one of which must be even, so k( k-1) The whole must be divisible by 2 with a remainder of 0.

Quantity A

The perimeter of ABCD

Quantity B

The sum of the lengths of diagonals AC and BD

• A

• B

• C

• D

Answer explanation

AB+BC>ACAD+DC>ACAB+AD>BDCB+CD>BDAdd the left and right sides of the four inequalities respectively, and get 2(AB+BC+CD+DA)>2(AC+BD), That is (AB+BC+CD+DA)>(AC+BD)

For which of the following values of x does the expression √ 24/(x+1) represent an irrational number? Indicate all such numbers.

A 12.5

B 36.5

C 53

D 71

E 95

• A

• B

• C

• D

• E

Answer explanation