QUANT JUNE EXAM 1

Greg's weekly salary is $187,which is 15 percent less than Karla's weekly salary. If Karla's weekly salary increases by 10 percent, by what percent must Greg's weekly salary increase in order to equal Karla's new weekly salary? Give your answer to the nearest tenth of a percent.

• 27.4

• 29.4

• 31

• 29

• 40

Answer explanation

It can be seen from the question that 187=K (1-15%), K=187/0.85. Immediately afterwards, K's weekly salary increases by 10%, to 187/0.85 · (1+10%)=1.1 · 187/0.85. At this time, G’s weekly salary must increase by x percent to make the two wages equal. The formula 187(1+x%)=1.1·187/0.85 can be solved to get x%≈29.4%.

Last Monday a certain store sold 17 wrenches at x dollars each. Last Tuesday the store reduced its prices and sold an additional 8 wrenches at 0.5x dollars each. Which of the following is equal to the average (arithmetic mean) price, in dollars, Of the 25 wrenches that the store sold last Monday and Tuesday?

• A 0.68x

• B 0.73x

• C 0.76x

• D 0..81x

• E 0.84x

Answer explanation

Last Monday, 17 pieces were sold at a unit price of x, and last Tuesday at a unit price of 0.5x 8 pieces, the average price of selling these 25 pieces = (17·x+8·0.5x)/25=0.84x.

The units digit of 7n is r, and the units digit of 9n is t, where n, r, and t are positive integers. Which of the following could be the value of r+t? Indicate all such values.

• A10

• B 12

• C 14

• D 16

Answer explanation

7n The ones digit is cycled according to 7, 9, 3, 1,

9nThe ones digit of the cycle is 9, 1, 9, 1, so the sum of the two ones is 16, 10, 12,

2 cycles.

At a certain dealership, 2/5 of the trucks have four-wheel drive, and 1/3 of the vehicles that have four-wheel drive are trucks. Of the vehicles that are trucks or have four-wheel drive, what fraction are trucks that have four-wheel drive? Give your answer as a fraction.

• 1/9

• 2/9

• 4/9

• 1

Answer explanation

If 20 red cubes and 7 white cubes, all of equal size, are fitted together to form one large cube, as shown above, what is the greatest fraction of the surface area of the large cube that could be red?

• A 8/9

• B 47/54

• C 23/27

• D 5/6

• E 20/27

Answer explanation

Because you want as many red faces as possible, then the white faces should be as few as possible. You can arrange six white cubes to be located in the middle of the six outer faces, so that only one white face is exposed, and the other A white cube is located at the center. In this case, the exposed white faces are at least 6, and on the contrary, the red faces can take up to 9×6-6=48 faces. Therefore, when the red faces are at most The ratio is 48/54=8/9.

If 15 percent of the students in a class are 16 years old or older, what is the least possible number of students in the class?

• 10

• 30

• 20

• 25

• 15

Answer explanation

Among all people, 15%, that is, 3/20 people are 16 years old and above, then the total number must be at least a multiple of 20, so that the number of people 16 years old and above can be an integer, so The total number of people is at least 20 people.

d is the greatest common divisor of 36 and 60, m is the least common multiple of 36 and 60.

Quantity A

36/d

Quantity B

m/60

• Quantity A

• Quantity B

• Both Are Equal

• Can't be determined

Answer explanation

The short division can get the greatest common divisor of 36 and 60 as d=12, and the least common multiple m=180. So QA=36/12=3, QB=180/60=3.

1 < x < 2

Quantity A

1/x+2/x+ 3/x

Quantity B

x +x/2+ x/3

• A is greater

• B is greater

• Both are Equal

• Can't be determined

Answer explanation

Simplify to get QA=6/x, QB=11x/6

The first step: subtraction, it is not easy to resolve, and it cannot be compared with 0

a > 0, x≠0

Quantity A

ax⁴

Quantity B

(ax)⁴

• A is greater

• A is greater

• Both are Equal

• Can't be determined

Answer explanation

(ax)^4=a^4x^4, then QA/QB= ax^4/ a^4x^4=1/a^3

 When a>1, QA/QB=1/a^3<1

 When 0<a<1, QA/QB=1/a^3>1

Quantity A

The remainder when 2³² is divided by 3

Quantity B

1

• Quantity A is greater

• Quantity B is greater

• Both Equal

• Can't be described

Answer explanation

Find the law——21Divide 3 and leave 2,22Divide 3 and leave 1,23  Divide 3 and leave 2,24  When dividing by 3, the remainder is 1...that is, the remainder is 2 for odd times and 1 for even times, so232Dividing 3 leaves 1.