QUANT-2

The thin rectangular sheet of metal shown in the figure is 8 inches wide and x inches long. An open box is to be made by cutting a 2-inch square from each corner of the sheet of metal and then folding up the sides. If the volume of the box is to be 48 cubic inches, what is the value of x?

• A 6

• B 8

• C 10

• D 12

• E 14

Answer explanation

A folded cube has a length of x-4, a width of 8-4, and a height of 2, so the volume = (x- 4)·(8-4)·2=48, the solution is x=10.

T = {2, 3, 4, 5, 6, 7, 8}

Quantity A

The total number of positive 4-digit integers that can be formed where each digit is in set T and the 4 digits in each 4-digit integer are different from each other

Quantity B

(7)(6)(5)(4)

• Quantity A greater

• Quantity B greater

• C

• D

Answer explanation

Choose 4 non-repeating numbers from the 7 numbers in the set T to form a four-digit number, there may be A (7, 4) = 7×6×5×4 construction methods .

m and n are integers.

Quantity A

√(10^2m)(10²ⁿ)

Quantity B

10mn

• A

• B

• C

• D

Answer explanation

n is an integer.

Quantity A

(−1)ⁿ(−1)ⁿ⁺²

Quantity B

1

• A

• B

• C

• D

Answer explanation

If p and n are prime numbers, p-n=4, and 3/2 < p/n < 2, what is the value of p?

• 3

• 5

• 7

• 11

• 13

The table shows the percent distrbution of financial support for a nonprofit organization, by source. The amount of financial support from individuals is approximately what percent less than the amount from corporations?

A 24%

B 35%

C 41%

D 69%

E 88%

• A

• B

• C

• D

• E

Answer explanation

It can be seen from the table that personal sources account for 22%, and corporate sources account for 37%, so the percentage of personal sources is less than corporate sources =

(37%-22%)/37%≈0.4054≈41%.

The legs of a right triangle are in the ratio of 3 to 1. If the length of the hypotenuse of the triangle is √40, then the perimeter of the triangle is between.

A 14 and 15

B 13 and 14

C 12 and 13

D 11 and 12

E 10 and 11

• A

• B

• C

• D

• E

Answer explanation

Let the length of the short side be x, then the length of the long side is 3x, according to the Pythagorean theorem, x^2+(3x)^2=( √40)^2=40, solve x=2, 3x =6, so the perimeter of a right triangle=2+6+ 40=  which is about a little more than 14.40−−

In a distribution of the values of the variable x, the 50th percentile is 48.5 and the 60th percentile is 56.5.

Quantity A

The 40th percentile of the distribution of the values of x

Quantity B

40.5

• A

• B

• C

• D

Answer explanation

The value corresponding to the 50th percentile is 48.5, and the value corresponding to the 60th percentile is 56.5. Find whether the value corresponding to the 40th percentile is equal to 40.5. It is not known whether the data x is symmetrically distributed, so it is impossible to judge.

A coffee shop sells its own brand of ground coffee packaged in two sizes-small and large. The small size is priced at k dollars per package, and the large size is priced at m dollars per package. If the total price of 4 packages of the coffee is $30, which of the following could be the values of k and m? Indicate all such values.

A k=4 and m=6

B k=4 and m=16

C k=5 and m=10

D k=5 and m=15

E k=7 and m=8

• A

• B

• C

• D

• E

Answer explanation

According to the requirements of the topic, the following table can be listed, and the options can be substituted respectively, and the k and m in the options can be observed, and any expression can be satisfied.

If -8 ≤ h ≤ 10 and h+m=-4, what is the least possible value of mh?

A 0

B 32

C 56

D 112

E 140

• A

• B

• C

• D

• E

Answer explanation

According to h+m=-4, replace m with h, and get m=-4-h

At this time, mh=-(4+h)h

When h is -8, mh=-32

When h is 10, mh=-140

Therefore, the minimum value of mh is -140